Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.6% → 55.6%

Time: 32.9s

Alternatives: 34

Speedup: 5.6×

• 89.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.6% 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: 55.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.8%

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

   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 y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 42.8%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.9%

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

Alternative 2: 38.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, t\_1, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ t_3 := b \cdot y0 - i \cdot y1\\ t_4 := i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+204}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-32}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y5 \cdot y0, z \cdot t\_3\right)\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-42}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, t\_3, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_1, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2
         (*
          a
          (fma
           y1
           (- (* z y3) (* x y2))
           (fma b t_1 (* y5 (- (* t y2) (* y y3)))))))
        (t_3 (- (* b y0) (* i y1)))
        (t_4 (* i (* z (fma c t (* k (- y1)))))))
   (if (<= z -1.8e+265)
     t_2
     (if (<= z -9e+204)
       t_4
       (if (<= z -4.5e-32)
         (*
          k
          (fma
           (- (* b y4) (* i y5))
           (- y)
           (fma y2 (- (* y1 y4) (* y5 y0)) (* z t_3))))
         (if (<= z -4.4e-212)
           t_2
           (if (<= z 4.6e-42)
             (* (- j) (fma x t_3 (* y4 (fma b (- t) (* y1 y3)))))
             (if (<= z 3.8e+60)
               (*
                b
                (+
                 (fma a t_1 (* y4 (- (* t j) (* y k))))
                 (* (- (* z k) (* x j)) y0)))
               t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = a * fma(y1, ((z * y3) - (x * y2)), fma(b, t_1, (y5 * ((t * y2) - (y * y3)))));
	double t_3 = (b * y0) - (i * y1);
	double t_4 = i * (z * fma(c, t, (k * -y1)));
	double tmp;
	if (z <= -1.8e+265) {
		tmp = t_2;
	} else if (z <= -9e+204) {
		tmp = t_4;
	} else if (z <= -4.5e-32) {
		tmp = k * fma(((b * y4) - (i * y5)), -y, fma(y2, ((y1 * y4) - (y5 * y0)), (z * t_3)));
	} else if (z <= -4.4e-212) {
		tmp = t_2;
	} else if (z <= 4.6e-42) {
		tmp = -j * fma(x, t_3, (y4 * fma(b, -t, (y1 * y3))));
	} else if (z <= 3.8e+60) {
		tmp = b * (fma(a, t_1, (y4 * ((t * j) - (y * k)))) + (((z * k) - (x * j)) * y0));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, t_1, Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))))
	t_3 = Float64(Float64(b * y0) - Float64(i * y1))
	t_4 = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))))
	tmp = 0.0
	if (z <= -1.8e+265)
		tmp = t_2;
	elseif (z <= -9e+204)
		tmp = t_4;
	elseif (z <= -4.5e-32)
		tmp = Float64(k * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-y), fma(y2, Float64(Float64(y1 * y4) - Float64(y5 * y0)), Float64(z * t_3))));
	elseif (z <= -4.4e-212)
		tmp = t_2;
	elseif (z <= 4.6e-42)
		tmp = Float64(Float64(-j) * fma(x, t_3, Float64(y4 * fma(b, Float64(-t), Float64(y1 * y3)))));
	elseif (z <= 3.8e+60)
		tmp = Float64(b * Float64(fma(a, t_1, Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(z * k) - Float64(x * j)) * y0)));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1 + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+265], t$95$2, If[LessEqual[z, -9e+204], t$95$4, If[LessEqual[z, -4.5e-32], N[(k * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-y) + N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-212], t$95$2, If[LessEqual[z, 4.6e-42], N[((-j) * N[(x * t$95$3 + N[(y4 * N[(b * (-t) + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+60], N[(b * N[(N[(a * t$95$1 + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.80000000000000001e265 or -4.50000000000000005e-32 < z < -4.40000000000000006e-212

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 59.7%

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

   if -1.80000000000000001e265 < z < -9.00000000000000004e204 or 3.80000000000000009e60 < z

   1. Initial program 29.7%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 47.0%

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

   6. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 63.0

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

   8. Simplified 63.0%

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

   if -9.00000000000000004e204 < z < -4.50000000000000005e-32

   1. Initial program 17.7%

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

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

      2. mul-1-neg N/A

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

      3. associate--l+ N/A

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

      4. mul-1-neg N/A

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

      5. *-commutative N/A

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

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

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

      7. neg-mul-1 N/A

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

   5. Simplified 53.7%

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

   if -4.40000000000000006e-212 < z < 4.60000000000000008e-42

   1. Initial program 32.5%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 52.1%

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

   6. Taylor expanded in y5 around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   8. Simplified 50.6%

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

   if 4.60000000000000008e-42 < z < 3.80000000000000009e60

   1. Initial program 45.0%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 70.4

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

   5. Simplified 70.4%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+204}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-32}:\\ \;\;\;\;k \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -y, \mathsf{fma}\left(y2, y1 \cdot y4 - y5 \cdot y0, z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-42}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 44.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \mathsf{fma}\left(c, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ t_3 := a \cdot b - c \cdot i\\ t_4 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(t\_1, -k, \mathsf{fma}\left(t\_3, x, y3 \cdot t\_4\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;y3 \cdot \left(y \cdot t\_4 - \mathsf{fma}\left(j, y1 \cdot y4 - y5 \cdot y0, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.78 \cdot 10^{+109}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(t\_1, -j, \mathsf{fma}\left(z, t\_3, t\_4 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2
         (*
          i
          (-
           (* y1 (- (* x j) (* z k)))
           (fma c (- (* x y) (* z t)) (* y5 (- (* t j) (* y k)))))))
        (t_3 (- (* a b) (* c i)))
        (t_4 (- (* c y4) (* a y5))))
   (if (<= i -4.5e+67)
     t_2
     (if (<= i -1.25e-239)
       (* y (fma t_1 (- k) (fma t_3 x (* y3 t_4))))
       (if (<= i 7.8e-56)
         (*
          y3
          (-
           (* y t_4)
           (fma j (- (* y1 y4) (* y5 y0)) (* z (- (* c y0) (* a y1))))))
         (if (<= i 1.78e+109)
           (* (- t) (fma t_1 (- j) (fma z t_3 (* t_4 y2))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y4) - (i * y5);
	double t_2 = i * ((y1 * ((x * j) - (z * k))) - fma(c, ((x * y) - (z * t)), (y5 * ((t * j) - (y * k)))));
	double t_3 = (a * b) - (c * i);
	double t_4 = (c * y4) - (a * y5);
	double tmp;
	if (i <= -4.5e+67) {
		tmp = t_2;
	} else if (i <= -1.25e-239) {
		tmp = y * fma(t_1, -k, fma(t_3, x, (y3 * t_4)));
	} else if (i <= 7.8e-56) {
		tmp = y3 * ((y * t_4) - fma(j, ((y1 * y4) - (y5 * y0)), (z * ((c * y0) - (a * y1)))));
	} else if (i <= 1.78e+109) {
		tmp = -t * fma(t_1, -j, fma(z, t_3, (t_4 * y2)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y4) - Float64(i * y5))
	t_2 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - fma(c, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * j) - Float64(y * k))))))
	t_3 = Float64(Float64(a * b) - Float64(c * i))
	t_4 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (i <= -4.5e+67)
		tmp = t_2;
	elseif (i <= -1.25e-239)
		tmp = Float64(y * fma(t_1, Float64(-k), fma(t_3, x, Float64(y3 * t_4))));
	elseif (i <= 7.8e-56)
		tmp = Float64(y3 * Float64(Float64(y * t_4) - fma(j, Float64(Float64(y1 * y4) - Float64(y5 * y0)), Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (i <= 1.78e+109)
		tmp = Float64(Float64(-t) * fma(t_1, Float64(-j), fma(z, t_3, Float64(t_4 * y2))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.5e+67], t$95$2, If[LessEqual[i, -1.25e-239], N[(y * N[(t$95$1 * (-k) + N[(t$95$3 * x + N[(y3 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.8e-56], N[(y3 * N[(N[(y * t$95$4), $MachinePrecision] - N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.78e+109], N[((-t) * N[(t$95$1 * (-j) + N[(z * t$95$3 + N[(t$95$4 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.4999999999999998e67 or 1.7800000000000001e109 < i

   1. Initial program 21.4%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 62.7%

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

   if -4.4999999999999998e67 < i < -1.25e-239

   1. Initial program 35.3%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 55.7%

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

   if -1.25e-239 < i < 7.8e-56

   1. Initial program 28.8%

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

   3. Taylor expanded in y3 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 54.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-y3\right)} \]

   if 7.8e-56 < i < 1.7800000000000001e109

   1. Initial program 33.3%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 53.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \mathsf{fma}\left(c, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-56}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \mathsf{fma}\left(j, y1 \cdot y4 - y5 \cdot y0, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.78 \cdot 10^{+109}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \mathsf{fma}\left(c, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 40.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(k, y1 \cdot y4 - y5 \cdot y0, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right) \cdot y2\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+247}:\\ \;\;\;\;-y0 \cdot \mathsf{fma}\left(c, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y5, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -2.9e+57)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j -1.6e-91)
     (*
      (fma
       k
       (- (* y1 y4) (* y5 y0))
       (fma (- (* c y0) (* a y1)) x (* t (- (* a y5) (* c y4)))))
      y2)
     (if (<= j 1.25e+44)
       (*
        y
        (fma
         (- (* b y4) (* i y5))
         (- k)
         (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
       (if (<= j 2.45e+247)
         (-
          (*
           y0
           (fma
            c
            (- (* z y3) (* x y2))
            (fma y5 (fma k y2 (* j (- y3))) (* b (- (* x j) (* z k)))))))
         (* j (* y1 (fma x i (* y4 (- y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -2.9e+57) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -1.6e-91) {
		tmp = fma(k, ((y1 * y4) - (y5 * y0)), fma(((c * y0) - (a * y1)), x, (t * ((a * y5) - (c * y4))))) * y2;
	} else if (j <= 1.25e+44) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else if (j <= 2.45e+247) {
		tmp = -(y0 * fma(c, ((z * y3) - (x * y2)), fma(y5, fma(k, y2, (j * -y3)), (b * ((x * j) - (z * k))))));
	} else {
		tmp = j * (y1 * fma(x, i, (y4 * -y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -2.9e+57)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -1.6e-91)
		tmp = Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y5 * y0)), fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))) * y2);
	elseif (j <= 1.25e+44)
		tmp = Float64(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (j <= 2.45e+247)
		tmp = Float64(-Float64(y0 * fma(c, Float64(Float64(z * y3) - Float64(x * y2)), fma(y5, fma(k, y2, Float64(j * Float64(-y3))), Float64(b * Float64(Float64(x * j) - Float64(z * k)))))));
	else
		tmp = Float64(j * Float64(y1 * fma(x, i, Float64(y4 * Float64(-y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -2.9e+57], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.6e-91], N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $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] * y2), $MachinePrecision], If[LessEqual[j, 1.25e+44], 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[j, 2.45e+247], (-N[(y0 * N[(c * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), N[(j * N[(y1 * N[(x * i + N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.9000000000000002e57

   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 t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 55.0%

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

   6. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 61.3

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

   8. Simplified 61.3%

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

   if -2.9000000000000002e57 < j < -1.59999999999999998e-91

   1. Initial program 45.0%

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

   3. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Simplified 57.2%

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

   if -1.59999999999999998e-91 < j < 1.2499999999999999e44

   1. Initial program 27.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 50.6%

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

   if 1.2499999999999999e44 < j < 2.4499999999999999e247

   1. Initial program 25.7%

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

   3. Taylor expanded in y0 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 65.2%

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

   if 2.4499999999999999e247 < j

   1. Initial program 37.5%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 62.5%

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

   6. Taylor expanded in y1 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 87.9

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

   8. Simplified 87.9%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(k, y1 \cdot y4 - y5 \cdot y0, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right) \cdot y2\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+247}:\\ \;\;\;\;-y0 \cdot \mathsf{fma}\left(c, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(y5, \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right), b \cdot \left(x \cdot j - z \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 44.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := t \cdot j - y \cdot k\\ t_3 := i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \mathsf{fma}\left(c, t\_1, y5 \cdot t\_2\right)\right)\\ t_4 := c \cdot y4 - a \cdot y5\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot t\_4\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-229}:\\ \;\;\;\;y3 \cdot \left(y \cdot t\_4 - \mathsf{fma}\left(j, y1 \cdot y4 - y5 \cdot y0, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_1, y4 \cdot t\_2\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (* i (- (* y1 (- (* x j) (* z k))) (fma c t_1 (* y5 t_2)))))
        (t_4 (- (* c y4) (* a y5))))
   (if (<= i -4.5e+67)
     t_3
     (if (<= i -1.25e-239)
       (*
        y
        (fma
         (- (* b y4) (* i y5))
         (- k)
         (fma (- (* a b) (* c i)) x (* y3 t_4))))
       (if (<= i 1.2e-229)
         (*
          y3
          (-
           (* y t_4)
           (fma j (- (* y1 y4) (* y5 y0)) (* z (- (* c y0) (* a y1))))))
         (if (<= i 1.25e+51)
           (* b (+ (fma a t_1 (* y4 t_2)) (* (- (* z k) (* x j)) y0)))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double t_2 = (t * j) - (y * k);
	double t_3 = i * ((y1 * ((x * j) - (z * k))) - fma(c, t_1, (y5 * t_2)));
	double t_4 = (c * y4) - (a * y5);
	double tmp;
	if (i <= -4.5e+67) {
		tmp = t_3;
	} else if (i <= -1.25e-239) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * t_4)));
	} else if (i <= 1.2e-229) {
		tmp = y3 * ((y * t_4) - fma(j, ((y1 * y4) - (y5 * y0)), (z * ((c * y0) - (a * y1)))));
	} else if (i <= 1.25e+51) {
		tmp = b * (fma(a, t_1, (y4 * t_2)) + (((z * k) - (x * j)) * y0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) - fma(c, t_1, Float64(y5 * t_2))))
	t_4 = Float64(Float64(c * y4) - Float64(a * y5))
	tmp = 0.0
	if (i <= -4.5e+67)
		tmp = t_3;
	elseif (i <= -1.25e-239)
		tmp = Float64(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * t_4))));
	elseif (i <= 1.2e-229)
		tmp = Float64(y3 * Float64(Float64(y * t_4) - fma(j, Float64(Float64(y1 * y4) - Float64(y5 * y0)), Float64(z * Float64(Float64(c * y0) - Float64(a * y1))))));
	elseif (i <= 1.25e+51)
		tmp = Float64(b * Float64(fma(a, t_1, Float64(y4 * t_2)) + Float64(Float64(Float64(z * k) - Float64(x * j)) * y0)));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1 + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.5e+67], t$95$3, If[LessEqual[i, -1.25e-239], 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 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e-229], N[(y3 * N[(N[(y * t$95$4), $MachinePrecision] - N[(j * N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e+51], N[(b * N[(N[(a * t$95$1 + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.4999999999999998e67 or 1.25e51 < i

   1. Initial program 24.0%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 61.2%

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

   if -4.4999999999999998e67 < i < -1.25e-239

   1. Initial program 35.3%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 55.7%

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

   if -1.25e-239 < i < 1.2e-229

   1. Initial program 20.5%

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

   3. Taylor expanded in y3 around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 59.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot \left(-y3\right)} \]

   if 1.2e-229 < i < 1.25e51

   1. Initial program 33.0%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 50.9

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

   5. Simplified 50.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, y \cdot x - t \cdot z, y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - z \cdot k\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{+67}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \mathsf{fma}\left(c, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-229}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) - \mathsf{fma}\left(j, y1 \cdot y4 - y5 \cdot y0, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) - \mathsf{fma}\left(c, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot j - y \cdot k\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(k, y1 \cdot y4 - y5 \cdot y0, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right) \cdot y2\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -2.9e+57)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j -1.6e-91)
     (*
      (fma
       k
       (- (* y1 y4) (* y5 y0))
       (fma (- (* c y0) (* a y1)) x (* t (- (* a y5) (* c y4)))))
      y2)
     (if (<= j 3.2e+72)
       (*
        y
        (fma
         (- (* b y4) (* i y5))
         (- k)
         (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
       (*
        (- j)
        (fma x (- (* b y0) (* i y1)) (* y4 (fma b (- t) (* y1 y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -2.9e+57) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -1.6e-91) {
		tmp = fma(k, ((y1 * y4) - (y5 * y0)), fma(((c * y0) - (a * y1)), x, (t * ((a * y5) - (c * y4))))) * y2;
	} else if (j <= 3.2e+72) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else {
		tmp = -j * fma(x, ((b * y0) - (i * y1)), (y4 * fma(b, -t, (y1 * y3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -2.9e+57)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -1.6e-91)
		tmp = Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y5 * y0)), fma(Float64(Float64(c * y0) - Float64(a * y1)), x, Float64(t * Float64(Float64(a * y5) - Float64(c * y4))))) * y2);
	elseif (j <= 3.2e+72)
		tmp = Float64(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	else
		tmp = Float64(Float64(-j) * fma(x, Float64(Float64(b * y0) - Float64(i * y1)), Float64(y4 * fma(b, Float64(-t), Float64(y1 * y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -2.9e+57], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.6e-91], N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $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] * y2), $MachinePrecision], If[LessEqual[j, 3.2e+72], N[(y * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-j) * N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(b * (-t) + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.9000000000000002e57

   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 t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 55.0%

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

   6. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 61.3

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

   8. Simplified 61.3%

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

   if -2.9000000000000002e57 < j < -1.59999999999999998e-91

   1. Initial program 45.0%

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

   3. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. sub-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

   5. Simplified 57.2%

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

   if -1.59999999999999998e-91 < j < 3.2000000000000001e72

   1. Initial program 28.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 51.4%

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

   if 3.2000000000000001e72 < j

   1. Initial program 25.7%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y5 around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   8. Simplified 59.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(k, y1 \cdot y4 - y5 \cdot y0, \mathsf{fma}\left(c \cdot y0 - a \cdot y1, x, t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right) \cdot y2\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -3.6e+98)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j -1.4e-91)
     (*
      b
      (+
       (fma a (- (* x y) (* z t)) (* y4 (- (* t j) (* y k))))
       (* (- (* z k) (* x j)) y0)))
     (if (<= j 3.2e+72)
       (*
        y
        (fma
         (- (* b y4) (* i y5))
         (- k)
         (fma (- (* a b) (* c i)) x (* y3 (- (* c y4) (* a y5))))))
       (*
        (- j)
        (fma x (- (* b y0) (* i y1)) (* y4 (fma b (- t) (* y1 y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -3.6e+98) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -1.4e-91) {
		tmp = b * (fma(a, ((x * y) - (z * t)), (y4 * ((t * j) - (y * k)))) + (((z * k) - (x * j)) * y0));
	} else if (j <= 3.2e+72) {
		tmp = y * fma(((b * y4) - (i * y5)), -k, fma(((a * b) - (c * i)), x, (y3 * ((c * y4) - (a * y5)))));
	} else {
		tmp = -j * fma(x, ((b * y0) - (i * y1)), (y4 * fma(b, -t, (y1 * y3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -3.6e+98)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -1.4e-91)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(z * t)), Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(z * k) - Float64(x * j)) * y0)));
	elseif (j <= 3.2e+72)
		tmp = Float64(y * fma(Float64(Float64(b * y4) - Float64(i * y5)), Float64(-k), fma(Float64(Float64(a * b) - Float64(c * i)), x, Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	else
		tmp = Float64(Float64(-j) * fma(x, Float64(Float64(b * y0) - Float64(i * y1)), Float64(y4 * fma(b, Float64(-t), Float64(y1 * y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -3.6e+98], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.4e-91], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+72], N[(y * N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * (-k) + N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * x + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-j) * N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(b * (-t) + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.59999999999999981e98

   1. Initial program 19.3%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 56.5%

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

   6. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 63.7

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

   8. Simplified 63.7%

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

   if -3.59999999999999981e98 < j < -1.4e-91

   1. Initial program 42.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 50.5

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

   5. Simplified 50.5%

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

   if -1.4e-91 < j < 3.2000000000000001e72

   1. Initial program 28.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 51.4%

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

   if 3.2000000000000001e72 < j

   1. Initial program 25.7%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 58.9%

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

   6. Taylor expanded in y5 around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   8. Simplified 59.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;j \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, t\_1, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, t\_1, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 13:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= j -3.6e+98)
     (* t (* y5 (fma a y2 (* i (- j)))))
     (if (<= j -3.3e-80)
       (*
        b
        (+ (fma a t_1 (* y4 (- (* t j) (* y k)))) (* (- (* z k) (* x j)) y0)))
       (if (<= j 1.12e-148)
         (*
          a
          (fma
           y1
           (- (* z y3) (* x y2))
           (fma b t_1 (* y5 (- (* t y2) (* y y3))))))
         (if (<= j 13.0)
           (* i (* z (fma c t (* k (- y1)))))
           (*
            (- j)
            (fma x (- (* b y0) (* i y1)) (* y4 (fma b (- t) (* y1 y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (j <= -3.6e+98) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -3.3e-80) {
		tmp = b * (fma(a, t_1, (y4 * ((t * j) - (y * k)))) + (((z * k) - (x * j)) * y0));
	} else if (j <= 1.12e-148) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, t_1, (y5 * ((t * y2) - (y * y3)))));
	} else if (j <= 13.0) {
		tmp = i * (z * fma(c, t, (k * -y1)));
	} else {
		tmp = -j * fma(x, ((b * y0) - (i * y1)), (y4 * fma(b, -t, (y1 * y3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (j <= -3.6e+98)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -3.3e-80)
		tmp = Float64(b * Float64(fma(a, t_1, Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(z * k) - Float64(x * j)) * y0)));
	elseif (j <= 1.12e-148)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, t_1, Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (j <= 13.0)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))));
	else
		tmp = Float64(Float64(-j) * fma(x, Float64(Float64(b * y0) - Float64(i * y1)), Float64(y4 * fma(b, Float64(-t), Float64(y1 * y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.6e+98], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.3e-80], N[(b * N[(N[(a * t$95$1 + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e-148], N[(a * N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$1 + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 13.0], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-j) * N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(b * (-t) + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.59999999999999981e98

   1. Initial program 19.3%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 56.5%

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

   6. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 63.7

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

   8. Simplified 63.7%

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

   if -3.59999999999999981e98 < j < -3.3e-80

   1. Initial program 41.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 53.4

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

   5. Simplified 53.4%

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

   if -3.3e-80 < j < 1.1199999999999999e-148

   1. Initial program 31.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 45.8%

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

   if 1.1199999999999999e-148 < j < 13

   1. Initial program 15.6%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 40.9%

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

   6. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 48.2

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

   8. Simplified 48.2%

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

   if 13 < j

   1. Initial program 30.8%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 55.6%

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

   6. Taylor expanded in y5 around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   8. Simplified 55.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - z \cdot t, y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(z \cdot k - x \cdot j\right) \cdot y0\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 13:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -0.00145:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 13:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -0.00145)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j 1.12e-148)
     (*
      a
      (fma
       y1
       (- (* z y3) (* x y2))
       (fma b (- (* x y) (* z t)) (* y5 (- (* t y2) (* y y3))))))
     (if (<= j 13.0)
       (* i (* z (fma c t (* k (- y1)))))
       (*
        (- j)
        (fma x (- (* b y0) (* i y1)) (* y4 (fma b (- t) (* y1 y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -0.00145) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= 1.12e-148) {
		tmp = a * fma(y1, ((z * y3) - (x * y2)), fma(b, ((x * y) - (z * t)), (y5 * ((t * y2) - (y * y3)))));
	} else if (j <= 13.0) {
		tmp = i * (z * fma(c, t, (k * -y1)));
	} else {
		tmp = -j * fma(x, ((b * y0) - (i * y1)), (y4 * fma(b, -t, (y1 * y3))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -0.00145)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= 1.12e-148)
		tmp = Float64(a * fma(y1, Float64(Float64(z * y3) - Float64(x * y2)), fma(b, Float64(Float64(x * y) - Float64(z * t)), Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (j <= 13.0)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))));
	else
		tmp = Float64(Float64(-j) * fma(x, Float64(Float64(b * y0) - Float64(i * y1)), Float64(y4 * fma(b, Float64(-t), Float64(y1 * y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -0.00145], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e-148], 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[j, 13.0], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-j) * N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(b * (-t) + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -0.00145

   1. Initial program 25.0%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 54.8

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

   8. Simplified 54.8%

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

   if -0.00145 < j < 1.1199999999999999e-148

   1. Initial program 32.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 46.3%

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

   if 1.1199999999999999e-148 < j < 13

   1. Initial program 15.6%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 40.9%

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

   6. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 48.2

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

   8. Simplified 48.2%

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

   if 13 < j

   1. Initial program 30.8%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 55.6%

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

   6. Taylor expanded in y5 around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   8. Simplified 55.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.00145:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(y1, z \cdot y3 - x \cdot y2, \mathsf{fma}\left(b, x \cdot y - z \cdot t, y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;j \leq 13:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+78}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* z (fma c t (* k (- y1)))))))
   (if (<= z -1.8e+265)
     (* a (* z (* t (- b))))
     (if (<= z -1.18e+126)
       t_1
       (if (<= z -4.8e-209)
         (* a (* y3 (fma y1 z (* y (- y5)))))
         (if (<= z 9e+78)
           (*
            (- j)
            (fma x (- (* b y0) (* i y1)) (* y4 (fma b (- t) (* y1 y3)))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (z * fma(c, t, (k * -y1)));
	double tmp;
	if (z <= -1.8e+265) {
		tmp = a * (z * (t * -b));
	} else if (z <= -1.18e+126) {
		tmp = t_1;
	} else if (z <= -4.8e-209) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (z <= 9e+78) {
		tmp = -j * fma(x, ((b * y0) - (i * y1)), (y4 * fma(b, -t, (y1 * y3))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))))
	tmp = 0.0
	if (z <= -1.8e+265)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (z <= -1.18e+126)
		tmp = t_1;
	elseif (z <= -4.8e-209)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (z <= 9e+78)
		tmp = Float64(Float64(-j) * fma(x, Float64(Float64(b * y0) - Float64(i * y1)), Float64(y4 * fma(b, Float64(-t), Float64(y1 * y3)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+265], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.18e+126], t$95$1, If[LessEqual[z, -4.8e-209], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+78], N[((-j) * N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(b * (-t) + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.80000000000000001e265

   1. Initial program 15.4%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 31.3%

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

   6. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-*.f64 39.4

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

   8. Simplified 39.4%

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

   9. Taylor expanded in j around 0

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

       1. mul-1-neg N/A

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

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

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

       3. mul-1-neg N/A

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

       4. lower-*.f64 N/A

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

       5. mul-1-neg N/A

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

       6. associate-*r* N/A

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

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

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

       8. mul-1-neg N/A

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

       9. lower-*.f64 N/A

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

       10. mul-1-neg N/A

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

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

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

       12. mul-1-neg N/A

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

       13. lower-*.f64 N/A

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

       14. mul-1-neg N/A

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

       15. lower-neg.f64 54.4

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

   11. Simplified 54.4%

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

   if -1.80000000000000001e265 < z < -1.18e126 or 8.9999999999999999e78 < z

   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 i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 46.2%

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

   6. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-neg.f64 61.3

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

   8. Simplified 61.3%

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

   if -1.18e126 < z < -4.8000000000000002e-209

   1. Initial program 20.3%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 45.8%

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

   6. Taylor expanded in y3 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 38.9

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

   8. Simplified 38.9%

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

   if -4.8000000000000002e-209 < z < 8.9999999999999999e78

   1. Initial program 34.3%

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

   3. Taylor expanded in j around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 47.4%

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

   6. Taylor expanded in y5 around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   8. Simplified 46.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+78}:\\ \;\;\;\;\left(-j\right) \cdot \mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-74}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-279}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \mathsf{fma}\left(b, y, y1 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.95e+94)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j -3.5e-74)
     (* (* t b) (fma j y4 (* z (- a))))
     (if (<= j -1.05e-175)
       (* y (* c (fma y3 y4 (* x (- i)))))
       (if (<= j -3.5e-279)
         (* (* x a) (fma b y (* y1 (- y2))))
         (if (<= j 5.1e-149)
           (* a (* y3 (fma y1 z (* y (- y5)))))
           (if (<= j 7e+73)
             (* i (* z (fma c t (* k (- y1)))))
             (* j (* y1 (fma x i (* y4 (- y3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.95e+94) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -3.5e-74) {
		tmp = (t * b) * fma(j, y4, (z * -a));
	} else if (j <= -1.05e-175) {
		tmp = y * (c * fma(y3, y4, (x * -i)));
	} else if (j <= -3.5e-279) {
		tmp = (x * a) * fma(b, y, (y1 * -y2));
	} else if (j <= 5.1e-149) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (j <= 7e+73) {
		tmp = i * (z * fma(c, t, (k * -y1)));
	} else {
		tmp = j * (y1 * fma(x, i, (y4 * -y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.95e+94)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -3.5e-74)
		tmp = Float64(Float64(t * b) * fma(j, y4, Float64(z * Float64(-a))));
	elseif (j <= -1.05e-175)
		tmp = Float64(y * Float64(c * fma(y3, y4, Float64(x * Float64(-i)))));
	elseif (j <= -3.5e-279)
		tmp = Float64(Float64(x * a) * fma(b, y, Float64(y1 * Float64(-y2))));
	elseif (j <= 5.1e-149)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (j <= 7e+73)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))));
	else
		tmp = Float64(j * Float64(y1 * fma(x, i, Float64(y4 * Float64(-y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.95e+94], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.5e-74], N[(N[(t * b), $MachinePrecision] * N[(j * y4 + N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.05e-175], N[(y * N[(c * N[(y3 * y4 + N[(x * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.5e-279], N[(N[(x * a), $MachinePrecision] * N[(b * y + N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.1e-149], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+73], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y1 * N[(x * i + N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.94999999999999993e94

   1. Initial program 20.3%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 54.7%

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

   6. Taylor expanded in y5 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 61.7

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

   8. Simplified 61.7%

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

   if -1.94999999999999993e94 < j < -3.50000000000000015e-74

   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 t around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

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

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

      4. neg-mul-1 N/A

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

      5. lower-*.f64 N/A

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

   5. Simplified 39.7%

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

   6. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-*.f64 42.6

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

   8. Simplified 42.6%

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

   if -3.50000000000000015e-74 < j < -1.05e-175

   1. Initial program 37.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

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

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

      6. neg-mul-1 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. lower-neg.f64 N/A

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

      13. sub-neg N/A

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

   5. Simplified 45.7%

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

   6. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 38.5

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

   8. Simplified 38.5%

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

   if -1.05e-175 < j < -3.5000000000000001e-279

   1. Initial program 16.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 53.3%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-*.f64 58.6

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

   8. Simplified 58.6%

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

   if -3.5000000000000001e-279 < j < 5.09999999999999983e-149

   1. Initial program 37.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. mul-1-neg N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y3 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 49.1

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

   8. Simplified 49.1%

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

   if 5.09999999999999983e-149 < j < 7.00000000000000004e73

   1. Initial program 25.5%

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

   3. Taylor expanded in i around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 40.7

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 40.7%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if 7.00000000000000004e73 < j

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} + -1 \cdot \left(y3 \cdot y4\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(x, i, -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{\mathsf{neg}\left(y3 \cdot y4\right)}\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(-1 \cdot y4\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      11. lower-neg.f64 56.7

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-y4\right)}\right)\right) \]

   8. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \left(-y4\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.95 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-74}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \mathsf{fma}\left(j, y4, z \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-279}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \mathsf{fma}\left(b, y, y1 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;-\left(y5 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) \cdot y0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* z (fma c t (* k (- y1)))))))
   (if (<= z -1.8e+265)
     (* a (* z (* t (- b))))
     (if (<= z -1.18e+126)
       t_1
       (if (<= z -2e-175)
         (* a (* y3 (fma y1 z (* y (- y5)))))
         (if (<= z -4.8e-280)
           (* y (* c (fma y3 y4 (* x (- i)))))
           (if (<= z 2.7e-8)
             (- (* (* y5 (fma k y2 (* j (- y3)))) 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 = i * (z * fma(c, t, (k * -y1)));
	double tmp;
	if (z <= -1.8e+265) {
		tmp = a * (z * (t * -b));
	} else if (z <= -1.18e+126) {
		tmp = t_1;
	} else if (z <= -2e-175) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (z <= -4.8e-280) {
		tmp = y * (c * fma(y3, y4, (x * -i)));
	} else if (z <= 2.7e-8) {
		tmp = -((y5 * fma(k, y2, (j * -y3))) * 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(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))))
	tmp = 0.0
	if (z <= -1.8e+265)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (z <= -1.18e+126)
		tmp = t_1;
	elseif (z <= -2e-175)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (z <= -4.8e-280)
		tmp = Float64(y * Float64(c * fma(y3, y4, Float64(x * Float64(-i)))));
	elseif (z <= 2.7e-8)
		tmp = Float64(-Float64(Float64(y5 * fma(k, y2, Float64(j * Float64(-y3)))) * 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[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+265], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.18e+126], t$95$1, If[LessEqual[z, -2e-175], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-280], N[(y * N[(c * N[(y3 * y4 + N[(x * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-8], (-N[(N[(y5 * N[(k * y2 + N[(j * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision]), t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.80000000000000001e265

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 31.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 39.4

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       6. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(b \cdot t\right) \cdot z}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(b \cdot t\right)\right) \cdot z\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)} \cdot z\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot t\right)\right) \cdot z\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot t\right)\right)} \cdot z\right) \]

       11. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot z\right) \]

       12. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-1 \cdot t\right)}\right) \cdot z\right) \]

       13. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(-1 \cdot t\right)\right)} \cdot z\right) \]

       14. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \cdot z\right) \]

       15. lower-neg.f64 54.4

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-t\right)}\right) \cdot z\right) \]

   11. Simplified 54.4%

       \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(-t\right)\right) \cdot z\right)} \]

   if -1.80000000000000001e265 < z < -1.18e126 or 2.70000000000000002e-8 < z

   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 i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 45.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 56.1

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 56.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if -1.18e126 < z < -2e-175

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 44.4%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 40.0

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   if -2e-175 < z < -4.7999999999999996e-280

   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 y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 51.3%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(c \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(y3, y4, -1 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(-1 \cdot i\right) \cdot x}\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(-1 \cdot i\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot x\right)\right) \]

      7. lower-neg.f64 55.7

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(-i\right)} \cdot x\right)\right) \]

   8. Simplified 55.7%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \mathsf{fma}\left(y3, y4, \left(-i\right) \cdot x\right)\right)} \]

   if -4.7999999999999996e-280 < z < 2.70000000000000002e-8

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \left(\mathsf{neg}\left(y0\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot y0\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \left(-1 \cdot y0\right)} \]

   5. Simplified 48.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y5, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), b \cdot \left(j \cdot x - z \cdot k\right)\right)\right) \cdot \left(-y0\right)} \]

   6. Taylor expanded in y5 around inf

      \[\leadsto \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \cdot \left(\mathsf{neg}\left(y0\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(j \cdot y3\right) + k \cdot y2\right)\right)} \cdot \left(\mathsf{neg}\left(y0\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(y5 \cdot \color{blue}{\left(k \cdot y2 + -1 \cdot \left(j \cdot y3\right)\right)}\right) \cdot \left(\mathsf{neg}\left(y0\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(y5 \cdot \color{blue}{\mathsf{fma}\left(k, y2, -1 \cdot \left(j \cdot y3\right)\right)}\right) \cdot \left(\mathsf{neg}\left(y0\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \left(y5 \cdot \mathsf{fma}\left(k, y2, \color{blue}{\mathsf{neg}\left(j \cdot y3\right)}\right)\right) \cdot \left(\mathsf{neg}\left(y0\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto \left(y5 \cdot \mathsf{fma}\left(k, y2, \color{blue}{\mathsf{neg}\left(j \cdot y3\right)}\right)\right) \cdot \left(\mathsf{neg}\left(y0\right)\right) \]

      6. lower-*.f64 44.1

         \[\leadsto \left(y5 \cdot \mathsf{fma}\left(k, y2, -\color{blue}{j \cdot y3}\right)\right) \cdot \left(-y0\right) \]

   8. Simplified 44.1%

      \[\leadsto \color{blue}{\left(y5 \cdot \mathsf{fma}\left(k, y2, -j \cdot y3\right)\right)} \cdot \left(-y0\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;-\left(y5 \cdot \mathsf{fma}\left(k, y2, j \cdot \left(-y3\right)\right)\right) \cdot y0\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.1% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.86:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-279}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \mathsf{fma}\left(b, y, y1 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.86)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j -3.5e-279)
     (* (* x a) (fma b y (* y1 (- y2))))
     (if (<= j 5.1e-149)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (if (<= j 7e+73)
         (* i (* z (fma c t (* k (- y1)))))
         (* j (* y1 (fma x i (* y4 (- y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.86) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -3.5e-279) {
		tmp = (x * a) * fma(b, y, (y1 * -y2));
	} else if (j <= 5.1e-149) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (j <= 7e+73) {
		tmp = i * (z * fma(c, t, (k * -y1)));
	} else {
		tmp = j * (y1 * fma(x, i, (y4 * -y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.86)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -3.5e-279)
		tmp = Float64(Float64(x * a) * fma(b, y, Float64(y1 * Float64(-y2))));
	elseif (j <= 5.1e-149)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (j <= 7e+73)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))));
	else
		tmp = Float64(j * Float64(y1 * fma(x, i, Float64(y4 * Float64(-y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.86], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.5e-279], N[(N[(x * a), $MachinePrecision] * N[(b * y + N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.1e-149], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+73], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y1 * N[(x * i + N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.8600000000000001

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 51.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(a \cdot y2 + -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\mathsf{fma}\left(a, y2, -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot j\right)\right) \]

      8. lower-neg.f64 55.5

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-i\right)} \cdot j\right)\right) \]

   8. Simplified 55.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \left(-i\right) \cdot j\right)\right)} \]

   if -1.8600000000000001 < j < -3.5000000000000001e-279

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 40.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot x\right)} \cdot \left(-1 \cdot \left(y1 \cdot y2\right) + b \cdot y\right) \]

      4. +-commutative N/A

         \[\leadsto \left(a \cdot x\right) \cdot \color{blue}{\left(b \cdot y + -1 \cdot \left(y1 \cdot y2\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(a \cdot x\right) \cdot \color{blue}{\mathsf{fma}\left(b, y, -1 \cdot \left(y1 \cdot y2\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(a \cdot x\right) \cdot \mathsf{fma}\left(b, y, \color{blue}{\mathsf{neg}\left(y1 \cdot y2\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(a \cdot x\right) \cdot \mathsf{fma}\left(b, y, \color{blue}{\mathsf{neg}\left(y1 \cdot y2\right)}\right) \]

      8. lower-*.f64 34.3

         \[\leadsto \left(a \cdot x\right) \cdot \mathsf{fma}\left(b, y, -\color{blue}{y1 \cdot y2}\right) \]

   8. Simplified 34.3%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \mathsf{fma}\left(b, y, -y1 \cdot y2\right)} \]

   if -3.5000000000000001e-279 < j < 5.09999999999999983e-149

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 49.1

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 49.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   if 5.09999999999999983e-149 < j < 7.00000000000000004e73

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 40.7

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 40.7%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if 7.00000000000000004e73 < j

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} + -1 \cdot \left(y3 \cdot y4\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(x, i, -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{\mathsf{neg}\left(y3 \cdot y4\right)}\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(-1 \cdot y4\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      11. lower-neg.f64 56.7

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-y4\right)}\right)\right) \]

   8. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \left(-y4\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.86:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-279}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \mathsf{fma}\left(b, y, y1 \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.9% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.48 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.48e+29)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j -6e-303)
     (* y (* y4 (fma (- b) k (* c y3))))
     (if (<= j 5.1e-149)
       (* a (* y3 (fma y1 z (* y (- y5)))))
       (if (<= j 7e+73)
         (* i (* z (fma c t (* k (- y1)))))
         (* j (* y1 (fma x i (* y4 (- y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.48e+29) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -6e-303) {
		tmp = y * (y4 * fma(-b, k, (c * y3)));
	} else if (j <= 5.1e-149) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (j <= 7e+73) {
		tmp = i * (z * fma(c, t, (k * -y1)));
	} else {
		tmp = j * (y1 * fma(x, i, (y4 * -y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.48e+29)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -6e-303)
		tmp = Float64(y * Float64(y4 * fma(Float64(-b), k, Float64(c * y3))));
	elseif (j <= 5.1e-149)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (j <= 7e+73)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))));
	else
		tmp = Float64(j * Float64(y1 * fma(x, i, Float64(y4 * Float64(-y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.48e+29], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-303], N[(y * N[(y4 * N[((-b) * k + N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.1e-149], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+73], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y1 * N[(x * i + N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.48e29

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(a \cdot y2 + -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\mathsf{fma}\left(a, y2, -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot j\right)\right) \]

      8. lower-neg.f64 58.5

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-i\right)} \cdot j\right)\right) \]

   8. Simplified 58.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \left(-i\right) \cdot j\right)\right)} \]

   if -1.48e29 < j < -6.00000000000000055e-303

   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. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 31.0

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 31.0%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   if -6.00000000000000055e-303 < j < 5.09999999999999983e-149

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 57.7%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 50.9

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   if 5.09999999999999983e-149 < j < 7.00000000000000004e73

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 40.7

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 40.7%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if 7.00000000000000004e73 < j

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} + -1 \cdot \left(y3 \cdot y4\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(x, i, -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{\mathsf{neg}\left(y3 \cdot y4\right)}\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(-1 \cdot y4\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      11. lower-neg.f64 56.7

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-y4\right)}\right)\right) \]

   8. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \left(-y4\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.48 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-303}:\\ \;\;\;\;y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* z (fma c t (* k (- y1)))))))
   (if (<= z -1.8e+265)
     (* a (* z (* t (- b))))
     (if (<= z -1.18e+126)
       t_1
       (if (<= z -4.2e-212)
         (* a (* y3 (fma y1 z (* y (- y5)))))
         (if (<= z 1.2e-7) (* j (* y1 (fma x i (* y4 (- y3))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (z * fma(c, t, (k * -y1)));
	double tmp;
	if (z <= -1.8e+265) {
		tmp = a * (z * (t * -b));
	} else if (z <= -1.18e+126) {
		tmp = t_1;
	} else if (z <= -4.2e-212) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (z <= 1.2e-7) {
		tmp = j * (y1 * fma(x, i, (y4 * -y3)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))))
	tmp = 0.0
	if (z <= -1.8e+265)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (z <= -1.18e+126)
		tmp = t_1;
	elseif (z <= -4.2e-212)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (z <= 1.2e-7)
		tmp = Float64(j * Float64(y1 * fma(x, i, Float64(y4 * Float64(-y3)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+265], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.18e+126], t$95$1, If[LessEqual[z, -4.2e-212], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-7], N[(j * N[(y1 * N[(x * i + N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.80000000000000001e265

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 31.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 39.4

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       6. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(b \cdot t\right) \cdot z}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(b \cdot t\right)\right) \cdot z\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)} \cdot z\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot t\right)\right) \cdot z\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot t\right)\right)} \cdot z\right) \]

       11. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot z\right) \]

       12. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-1 \cdot t\right)}\right) \cdot z\right) \]

       13. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(-1 \cdot t\right)\right)} \cdot z\right) \]

       14. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \cdot z\right) \]

       15. lower-neg.f64 54.4

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-t\right)}\right) \cdot z\right) \]

   11. Simplified 54.4%

       \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(-t\right)\right) \cdot z\right)} \]

   if -1.80000000000000001e265 < z < -1.18e126 or 1.19999999999999989e-7 < z

   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 i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 45.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 56.1

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 56.1%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if -1.18e126 < z < -4.1999999999999999e-212

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 45.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 38.9

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   if -4.1999999999999999e-212 < z < 1.19999999999999989e-7

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} + -1 \cdot \left(y3 \cdot y4\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(x, i, -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{\mathsf{neg}\left(y3 \cdot y4\right)}\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(-1 \cdot y4\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      11. lower-neg.f64 38.4

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-y4\right)}\right)\right) \]

   8. Simplified 38.4%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \left(-y4\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.8% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(\mathsf{fma}\left(-b, x, y3 \cdot y5\right) \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* z (fma c t (* k (- y1)))))))
   (if (<= z -1.8e+265)
     (* a (* z (* t (- b))))
     (if (<= z -1.18e+126)
       t_1
       (if (<= z -9.5e-218)
         (* a (* y3 (fma y1 z (* y (- y5)))))
         (if (<= z 1.35e+62) (* j (* (fma (- b) x (* y3 y5)) y0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (z * fma(c, t, (k * -y1)));
	double tmp;
	if (z <= -1.8e+265) {
		tmp = a * (z * (t * -b));
	} else if (z <= -1.18e+126) {
		tmp = t_1;
	} else if (z <= -9.5e-218) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else if (z <= 1.35e+62) {
		tmp = j * (fma(-b, x, (y3 * y5)) * y0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))))
	tmp = 0.0
	if (z <= -1.8e+265)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	elseif (z <= -1.18e+126)
		tmp = t_1;
	elseif (z <= -9.5e-218)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	elseif (z <= 1.35e+62)
		tmp = Float64(j * Float64(fma(Float64(-b), x, Float64(y3 * y5)) * 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[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+265], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.18e+126], t$95$1, If[LessEqual[z, -9.5e-218], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+62], N[(j * N[(N[((-b) * x + N[(y3 * y5), $MachinePrecision]), $MachinePrecision] * y0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.80000000000000001e265

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 31.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 39.4

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       6. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(b \cdot t\right) \cdot z}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(b \cdot t\right)\right) \cdot z\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)} \cdot z\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot t\right)\right) \cdot z\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot t\right)\right)} \cdot z\right) \]

       11. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot z\right) \]

       12. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-1 \cdot t\right)}\right) \cdot z\right) \]

       13. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(-1 \cdot t\right)\right)} \cdot z\right) \]

       14. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \cdot z\right) \]

       15. lower-neg.f64 54.4

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-t\right)}\right) \cdot z\right) \]

   11. Simplified 54.4%

       \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(-t\right)\right) \cdot z\right)} \]

   if -1.80000000000000001e265 < z < -1.18e126 or 1.35e62 < z

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 60.7

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 60.7%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if -1.18e126 < z < -9.49999999999999967e-218

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 38.3

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   if -9.49999999999999967e-218 < z < 1.35e62

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot y0}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \left(\mathsf{neg}\left(y0\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot y0\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - -1 \cdot \left(b \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \cdot \left(-1 \cdot y0\right)} \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(y5, \mathsf{fma}\left(k, y2, y3 \cdot \left(-j\right)\right), b \cdot \left(j \cdot x - z \cdot k\right)\right)\right) \cdot \left(-y0\right)} \]

   6. Taylor expanded in j 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. lower-*.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. lower-*.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. associate-*r* N/A

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot x} + y3 \cdot y5\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, x, y3 \cdot y5\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, x, y3 \cdot y5\right)\right) \]

      6. lower-neg.f64 N/A

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, x, y3 \cdot y5\right)\right) \]

      7. lower-*.f64 31.6

         \[\leadsto j \cdot \left(y0 \cdot \mathsf{fma}\left(-b, x, \color{blue}{y3 \cdot y5}\right)\right) \]

   8. Simplified 31.6%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \mathsf{fma}\left(-b, x, y3 \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+265}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(\mathsf{fma}\left(-b, x, y3 \cdot y5\right) \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.6% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.18 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.18e+29)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j -4.1e-220)
     (* y (* c (fma y3 y4 (* x (- i)))))
     (if (<= j 7e+73)
       (* i (* z (fma c t (* k (- y1)))))
       (* j (* y1 (fma x i (* y4 (- y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.18e+29) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= -4.1e-220) {
		tmp = y * (c * fma(y3, y4, (x * -i)));
	} else if (j <= 7e+73) {
		tmp = i * (z * fma(c, t, (k * -y1)));
	} else {
		tmp = j * (y1 * fma(x, i, (y4 * -y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.18e+29)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= -4.1e-220)
		tmp = Float64(y * Float64(c * fma(y3, y4, Float64(x * Float64(-i)))));
	elseif (j <= 7e+73)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))));
	else
		tmp = Float64(j * Float64(y1 * fma(x, i, Float64(y4 * Float64(-y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.18e+29], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.1e-220], N[(y * N[(c * N[(y3 * y4 + N[(x * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+73], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y1 * N[(x * i + N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.18e29

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(a \cdot y2 + -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\mathsf{fma}\left(a, y2, -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot j\right)\right) \]

      8. lower-neg.f64 58.5

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-i\right)} \cdot j\right)\right) \]

   8. Simplified 58.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \left(-i\right) \cdot j\right)\right)} \]

   if -1.18e29 < j < -4.09999999999999991e-220

   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 y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in c around inf

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot x\right) + y3 \cdot y4\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y \cdot \left(c \cdot \color{blue}{\left(y3 \cdot y4 + -1 \cdot \left(i \cdot x\right)\right)}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(c \cdot \color{blue}{\mathsf{fma}\left(y3, y4, -1 \cdot \left(i \cdot x\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(-1 \cdot i\right) \cdot x}\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(-1 \cdot i\right) \cdot x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot x\right)\right) \]

      7. lower-neg.f64 29.2

         \[\leadsto y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, \color{blue}{\left(-i\right)} \cdot x\right)\right) \]

   8. Simplified 29.2%

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \mathsf{fma}\left(y3, y4, \left(-i\right) \cdot x\right)\right)} \]

   if -4.09999999999999991e-220 < j < 7.00000000000000004e73

   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 i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 36.5%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 38.3

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if 7.00000000000000004e73 < j

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} + -1 \cdot \left(y3 \cdot y4\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(x, i, -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{\mathsf{neg}\left(y3 \cdot y4\right)}\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(-1 \cdot y4\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      11. lower-neg.f64 56.7

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-y4\right)}\right)\right) \]

   8. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \left(-y4\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.18 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(c \cdot \mathsf{fma}\left(y3, y4, x \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 22.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 22000000000:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y4 (* c y3)))))
   (if (<= c -5.2e+83)
     t_1
     (if (<= c 8.5e-238)
       (* a (* y3 (* z y1)))
       (if (<= c 22000000000.0)
         (* b (* (* t j) y4))
         (if (<= c 1.4e+89) (* z (* a (* y1 y3))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double tmp;
	if (c <= -5.2e+83) {
		tmp = t_1;
	} else if (c <= 8.5e-238) {
		tmp = a * (y3 * (z * y1));
	} else if (c <= 22000000000.0) {
		tmp = b * ((t * j) * y4);
	} else if (c <= 1.4e+89) {
		tmp = z * (a * (y1 * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (y4 * (c * y3))
    if (c <= (-5.2d+83)) then
        tmp = t_1
    else if (c <= 8.5d-238) then
        tmp = a * (y3 * (z * y1))
    else if (c <= 22000000000.0d0) then
        tmp = b * ((t * j) * y4)
    else if (c <= 1.4d+89) then
        tmp = z * (a * (y1 * y3))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double tmp;
	if (c <= -5.2e+83) {
		tmp = t_1;
	} else if (c <= 8.5e-238) {
		tmp = a * (y3 * (z * y1));
	} else if (c <= 22000000000.0) {
		tmp = b * ((t * j) * y4);
	} else if (c <= 1.4e+89) {
		tmp = z * (a * (y1 * y3));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y4 * (c * y3))
	tmp = 0
	if c <= -5.2e+83:
		tmp = t_1
	elif c <= 8.5e-238:
		tmp = a * (y3 * (z * y1))
	elif c <= 22000000000.0:
		tmp = b * ((t * j) * y4)
	elif c <= 1.4e+89:
		tmp = z * (a * (y1 * y3))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(y4 * Float64(c * y3)))
	tmp = 0.0
	if (c <= -5.2e+83)
		tmp = t_1;
	elseif (c <= 8.5e-238)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (c <= 22000000000.0)
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	elseif (c <= 1.4e+89)
		tmp = Float64(z * Float64(a * Float64(y1 * y3)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y4 * (c * y3));
	tmp = 0.0;
	if (c <= -5.2e+83)
		tmp = t_1;
	elseif (c <= 8.5e-238)
		tmp = a * (y3 * (z * y1));
	elseif (c <= 22000000000.0)
		tmp = b * ((t * j) * y4);
	elseif (c <= 1.4e+89)
		tmp = z * (a * (y1 * y3));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e+83], t$95$1, If[LessEqual[c, 8.5e-238], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 22000000000.0], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e+89], N[(z * N[(a * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.2000000000000002e83 or 1.3999999999999999e89 < c

   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 y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 44.9%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 34.0

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 34.0%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(c \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

       2. lower-*.f64 31.2

          \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   11. Simplified 31.2%

       \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   if -5.2000000000000002e83 < c < 8.5000000000000006e-238

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 38.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 32.5

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 19.2

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   11. Simplified 19.2%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   if 8.5000000000000006e-238 < c < 2.2e10

   1. Initial program 20.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 40.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 24.3

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 24.3%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 29.3

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 29.3%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]

   if 2.2e10 < c < 1.3999999999999999e89

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 46.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 54.4

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 54.4%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. lower-*.f64 40.0

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   11. Simplified 40.0%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       2. lift-*.f64 N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(y1 \cdot y3\right)} \cdot z\right) \]

       3. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(y1 \cdot y3\right)\right) \cdot z} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(y1 \cdot y3\right)\right) \cdot z} \]

       5. lower-*.f64 54.7

          \[\leadsto \color{blue}{\left(a \cdot \left(y1 \cdot y3\right)\right)} \cdot z \]

   13. Applied egg-rr 54.7%

       \[\leadsto \color{blue}{\left(a \cdot \left(y1 \cdot y3\right)\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 22000000000:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(a \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \left(i \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-246}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.7e-25)
   (* t (* i (* j (- y5))))
   (if (<= j 7.4e-246)
     (* (- t) (* a (* z b)))
     (if (<= j 2.5e+68) (* (- a) (* y3 (* y y5))) (* y1 (* i (* x j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.7e-25) {
		tmp = t * (i * (j * -y5));
	} else if (j <= 7.4e-246) {
		tmp = -t * (a * (z * b));
	} else if (j <= 2.5e+68) {
		tmp = -a * (y3 * (y * y5));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.7d-25)) then
        tmp = t * (i * (j * -y5))
    else if (j <= 7.4d-246) then
        tmp = -t * (a * (z * b))
    else if (j <= 2.5d+68) then
        tmp = -a * (y3 * (y * y5))
    else
        tmp = y1 * (i * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.7e-25) {
		tmp = t * (i * (j * -y5));
	} else if (j <= 7.4e-246) {
		tmp = -t * (a * (z * b));
	} else if (j <= 2.5e+68) {
		tmp = -a * (y3 * (y * y5));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.7e-25:
		tmp = t * (i * (j * -y5))
	elif j <= 7.4e-246:
		tmp = -t * (a * (z * b))
	elif j <= 2.5e+68:
		tmp = -a * (y3 * (y * y5))
	else:
		tmp = y1 * (i * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.7e-25)
		tmp = Float64(t * Float64(i * Float64(j * Float64(-y5))));
	elseif (j <= 7.4e-246)
		tmp = Float64(Float64(-t) * Float64(a * Float64(z * b)));
	elseif (j <= 2.5e+68)
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	else
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.7e-25)
		tmp = t * (i * (j * -y5));
	elseif (j <= 7.4e-246)
		tmp = -t * (a * (z * b));
	elseif (j <= 2.5e+68)
		tmp = -a * (y3 * (y * y5));
	else
		tmp = y1 * (i * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.7e-25], N[(t * N[(i * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.4e-246], N[((-t) * N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+68], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.70000000000000001e-25

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. lower-*.f64 47.9

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   8. Simplified 47.9%

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot y5\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot y5\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]

       2. lower-*.f64 42.1

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot y5\right)}\right) \cdot \left(-t\right) \]

   11. Simplified 42.1%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot y5\right)\right)} \cdot \left(-t\right) \]

   if -1.70000000000000001e-25 < j < 7.4e-246

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 27.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. lower-*.f64 22.5

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   8. Simplified 22.5%

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot z\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot z\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]

       2. lower-*.f64 24.1

          \[\leadsto \left(a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   11. Simplified 24.1%

       \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot z\right)\right)} \cdot \left(-t\right) \]

   if 7.4e-246 < j < 2.5000000000000002e68

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 39.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 37.1

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 37.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       7. lower-neg.f64 29.2

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-y\right)}\right)\right) \]

   11. Simplified 29.2%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-y\right)\right)}\right) \]

   if 2.5000000000000002e68 < j

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

       3. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(x \cdot j\right)}\right) \cdot y1 \]

       4. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right)} \cdot y1 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right) \cdot y1} \]

       6. associate-*l* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot j\right)\right)} \cdot y1 \]

       7. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right)} \cdot y1 \]

       9. lower-*.f64 42.4

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

   11. Simplified 42.4%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \left(i \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-246}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.06 \cdot 10^{-26}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-246}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.06e-26)
   (* (- i) (* j (* t y5)))
   (if (<= j 7.4e-246)
     (* (- t) (* a (* z b)))
     (if (<= j 2.5e+68) (* (- a) (* y3 (* y y5))) (* y1 (* i (* x j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.06e-26) {
		tmp = -i * (j * (t * y5));
	} else if (j <= 7.4e-246) {
		tmp = -t * (a * (z * b));
	} else if (j <= 2.5e+68) {
		tmp = -a * (y3 * (y * y5));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.06d-26)) then
        tmp = -i * (j * (t * y5))
    else if (j <= 7.4d-246) then
        tmp = -t * (a * (z * b))
    else if (j <= 2.5d+68) then
        tmp = -a * (y3 * (y * y5))
    else
        tmp = y1 * (i * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.06e-26) {
		tmp = -i * (j * (t * y5));
	} else if (j <= 7.4e-246) {
		tmp = -t * (a * (z * b));
	} else if (j <= 2.5e+68) {
		tmp = -a * (y3 * (y * y5));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.06e-26:
		tmp = -i * (j * (t * y5))
	elif j <= 7.4e-246:
		tmp = -t * (a * (z * b))
	elif j <= 2.5e+68:
		tmp = -a * (y3 * (y * y5))
	else:
		tmp = y1 * (i * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.06e-26)
		tmp = Float64(Float64(-i) * Float64(j * Float64(t * y5)));
	elseif (j <= 7.4e-246)
		tmp = Float64(Float64(-t) * Float64(a * Float64(z * b)));
	elseif (j <= 2.5e+68)
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	else
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.06e-26)
		tmp = -i * (j * (t * y5));
	elseif (j <= 7.4e-246)
		tmp = -t * (a * (z * b));
	elseif (j <= 2.5e+68)
		tmp = -a * (y3 * (y * y5));
	else
		tmp = y1 * (i * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.06e-26], N[((-i) * N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.4e-246], N[((-t) * N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+68], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.06000000000000001e-26

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. lower-*.f64 47.9

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   8. Simplified 47.9%

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot \left(j \cdot \left(t \cdot y5\right)\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot \left(j \cdot \left(t \cdot y5\right)\right) \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(i\right)\right) \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(i\right)\right) \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 39.7

          \[\leadsto \left(-i\right) \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 39.7%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]

   if -1.06000000000000001e-26 < j < 7.4e-246

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 27.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. lower-*.f64 22.5

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   8. Simplified 22.5%

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot z\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot z\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]

       2. lower-*.f64 24.1

          \[\leadsto \left(a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   11. Simplified 24.1%

       \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot z\right)\right)} \cdot \left(-t\right) \]

   if 7.4e-246 < j < 2.5000000000000002e68

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 39.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 37.1

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 37.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       7. lower-neg.f64 29.2

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-y\right)}\right)\right) \]

   11. Simplified 29.2%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-y\right)\right)}\right) \]

   if 2.5000000000000002e68 < j

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

       3. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(x \cdot j\right)}\right) \cdot y1 \]

       4. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right)} \cdot y1 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right) \cdot y1} \]

       6. associate-*l* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot j\right)\right)} \cdot y1 \]

       7. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right)} \cdot y1 \]

       9. lower-*.f64 42.4

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

   11. Simplified 42.4%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.06 \cdot 10^{-26}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 7.4 \cdot 10^{-246}:\\ \;\;\;\;\left(-t\right) \cdot \left(a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.1% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.42 \cdot 10^{+22}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-204}:\\ \;\;\;\;-b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.42e+22)
   (* (- i) (* j (* t y5)))
   (if (<= j 3.1e-204)
     (- (* b (* k (* y y4))))
     (if (<= j 2.5e+68) (* (- a) (* y3 (* y y5))) (* y1 (* i (* x j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.42e+22) {
		tmp = -i * (j * (t * y5));
	} else if (j <= 3.1e-204) {
		tmp = -(b * (k * (y * y4)));
	} else if (j <= 2.5e+68) {
		tmp = -a * (y3 * (y * y5));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-1.42d+22)) then
        tmp = -i * (j * (t * y5))
    else if (j <= 3.1d-204) then
        tmp = -(b * (k * (y * y4)))
    else if (j <= 2.5d+68) then
        tmp = -a * (y3 * (y * y5))
    else
        tmp = y1 * (i * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.42e+22) {
		tmp = -i * (j * (t * y5));
	} else if (j <= 3.1e-204) {
		tmp = -(b * (k * (y * y4)));
	} else if (j <= 2.5e+68) {
		tmp = -a * (y3 * (y * y5));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -1.42e+22:
		tmp = -i * (j * (t * y5))
	elif j <= 3.1e-204:
		tmp = -(b * (k * (y * y4)))
	elif j <= 2.5e+68:
		tmp = -a * (y3 * (y * y5))
	else:
		tmp = y1 * (i * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.42e+22)
		tmp = Float64(Float64(-i) * Float64(j * Float64(t * y5)));
	elseif (j <= 3.1e-204)
		tmp = Float64(-Float64(b * Float64(k * Float64(y * y4))));
	elseif (j <= 2.5e+68)
		tmp = Float64(Float64(-a) * Float64(y3 * Float64(y * y5)));
	else
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -1.42e+22)
		tmp = -i * (j * (t * y5));
	elseif (j <= 3.1e-204)
		tmp = -(b * (k * (y * y4)));
	elseif (j <= 2.5e+68)
		tmp = -a * (y3 * (y * y5));
	else
		tmp = y1 * (i * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.42e+22], N[((-i) * N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.1e-204], (-N[(b * N[(k * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[j, 2.5e+68], N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.42e22

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. lower-*.f64 52.2

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   8. Simplified 52.2%

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot \left(t \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot \left(j \cdot \left(t \cdot y5\right)\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot \left(j \cdot \left(t \cdot y5\right)\right) \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(i\right)\right) \cdot \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(i\right)\right) \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

       7. lower-*.f64 44.5

          \[\leadsto \left(-i\right) \cdot \left(j \cdot \color{blue}{\left(y5 \cdot t\right)}\right) \]

   11. Simplified 44.5%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot \left(y5 \cdot t\right)\right)} \]

   if -1.42e22 < j < 3.0999999999999999e-204

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 47.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 30.4

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 30.4%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(k \cdot \left(y \cdot y4\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

       4. lower-neg.f64 N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot \left(k \cdot \left(y \cdot y4\right)\right) \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\left(k \cdot \left(y \cdot y4\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \left(k \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

       7. lower-*.f64 21.9

          \[\leadsto \left(-b\right) \cdot \left(k \cdot \color{blue}{\left(y4 \cdot y\right)}\right) \]

   11. Simplified 21.9%

       \[\leadsto \color{blue}{\left(-b\right) \cdot \left(k \cdot \left(y4 \cdot y\right)\right)} \]

   if 3.0999999999999999e-204 < j < 2.5000000000000002e68

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 35.3

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 35.3%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       7. lower-neg.f64 28.0

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-y\right)}\right)\right) \]

   11. Simplified 28.0%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-y\right)\right)}\right) \]

   if 2.5000000000000002e68 < j

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

       3. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(x \cdot j\right)}\right) \cdot y1 \]

       4. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right)} \cdot y1 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right) \cdot y1} \]

       6. associate-*l* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot j\right)\right)} \cdot y1 \]

       7. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right)} \cdot y1 \]

       9. lower-*.f64 42.4

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

   11. Simplified 42.4%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.42 \cdot 10^{+22}:\\ \;\;\;\;\left(-i\right) \cdot \left(j \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-204}:\\ \;\;\;\;-b \cdot \left(k \cdot \left(y \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(a \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.32 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.15e+58)
   (* y (* b (* k (- y4))))
   (if (<= y4 -8.2e-224)
     (* x (* y1 (* a (- y2))))
     (if (<= y4 1.32e+169) (* a (* z (* t (- b)))) (* b (* j (* t y4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.15e+58) {
		tmp = y * (b * (k * -y4));
	} else if (y4 <= -8.2e-224) {
		tmp = x * (y1 * (a * -y2));
	} else if (y4 <= 1.32e+169) {
		tmp = a * (z * (t * -b));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.15d+58)) then
        tmp = y * (b * (k * -y4))
    else if (y4 <= (-8.2d-224)) then
        tmp = x * (y1 * (a * -y2))
    else if (y4 <= 1.32d+169) then
        tmp = a * (z * (t * -b))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.15e+58) {
		tmp = y * (b * (k * -y4));
	} else if (y4 <= -8.2e-224) {
		tmp = x * (y1 * (a * -y2));
	} else if (y4 <= 1.32e+169) {
		tmp = a * (z * (t * -b));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.15e+58:
		tmp = y * (b * (k * -y4))
	elif y4 <= -8.2e-224:
		tmp = x * (y1 * (a * -y2))
	elif y4 <= 1.32e+169:
		tmp = a * (z * (t * -b))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.15e+58)
		tmp = Float64(y * Float64(b * Float64(k * Float64(-y4))));
	elseif (y4 <= -8.2e-224)
		tmp = Float64(x * Float64(y1 * Float64(a * Float64(-y2))));
	elseif (y4 <= 1.32e+169)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.15e+58)
		tmp = y * (b * (k * -y4));
	elseif (y4 <= -8.2e-224)
		tmp = x * (y1 * (a * -y2));
	elseif (y4 <= 1.32e+169)
		tmp = a * (z * (t * -b));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.15e+58], N[(y * N[(b * N[(k * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -8.2e-224], N[(x * N[(y1 * N[(a * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.32e+169], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -1.15000000000000001e58

   1. Initial program 23.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 53.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 46.9

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 46.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(k \cdot y4\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto y \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(k \cdot y4\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(\mathsf{neg}\left(k \cdot y4\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(k \cdot y4\right)\right)}\right) \]

       4. lower-*.f64 N/A

          \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \left(k \cdot y4\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(k \cdot y4\right)\right)}\right) \]

       6. *-commutative N/A

          \[\leadsto y \cdot \left(b \cdot \left(\mathsf{neg}\left(\color{blue}{y4 \cdot k}\right)\right)\right) \]

       7. distribute-rgt-neg-in N/A

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(y4 \cdot \left(\mathsf{neg}\left(k\right)\right)\right)}\right) \]

       8. mul-1-neg N/A

          \[\leadsto y \cdot \left(b \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot k\right)}\right)\right) \]

       9. lower-*.f64 N/A

          \[\leadsto y \cdot \left(b \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot k\right)\right)}\right) \]

       10. mul-1-neg N/A

           \[\leadsto y \cdot \left(b \cdot \left(y4 \cdot \color{blue}{\left(\mathsf{neg}\left(k\right)\right)}\right)\right) \]

       11. lower-neg.f64 34.7

           \[\leadsto y \cdot \left(b \cdot \left(y4 \cdot \color{blue}{\left(-k\right)}\right)\right) \]

   11. Simplified 34.7%

       \[\leadsto y \cdot \color{blue}{\left(b \cdot \left(y4 \cdot \left(-k\right)\right)\right)} \]

   if -1.15000000000000001e58 < y4 < -8.19999999999999972e-224

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 34.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot y1\right)} \cdot \left(y3 \cdot z - x \cdot y2\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(a \cdot y1\right) \cdot \color{blue}{\left(y3 \cdot z - x \cdot y2\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(a \cdot y1\right) \cdot \left(\color{blue}{y3 \cdot z} - x \cdot y2\right) \]

      6. lower-*.f64 24.5

         \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot z - \color{blue}{x \cdot y2}\right) \]

   8. Simplified 24.5%

      \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

   9. Taylor expanded in y3 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(x \cdot \left(y1 \cdot y2\right)\right) \cdot a}\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{x \cdot \left(\left(y1 \cdot y2\right) \cdot a\right)}\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \color{blue}{\left(a \cdot \left(y1 \cdot y2\right)\right)}\right) \]

       5. distribute-rgt-neg-out N/A

          \[\leadsto \color{blue}{x \cdot \left(\mathsf{neg}\left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       6. mul-1-neg N/A

          \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       7. lower-*.f64 N/A

          \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot \left(y1 \cdot y2\right)\right)\right)} \]

       8. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot \left(y1 \cdot y2\right)\right)} \]

       9. *-commutative N/A

          \[\leadsto x \cdot \left(\left(-1 \cdot a\right) \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

       10. associate-*r* N/A

           \[\leadsto x \cdot \color{blue}{\left(\left(\left(-1 \cdot a\right) \cdot y2\right) \cdot y1\right)} \]

       11. lower-*.f64 N/A

           \[\leadsto x \cdot \color{blue}{\left(\left(\left(-1 \cdot a\right) \cdot y2\right) \cdot y1\right)} \]

       12. lower-*.f64 N/A

           \[\leadsto x \cdot \left(\color{blue}{\left(\left(-1 \cdot a\right) \cdot y2\right)} \cdot y1\right) \]

       13. mul-1-neg N/A

           \[\leadsto x \cdot \left(\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \cdot y2\right) \cdot y1\right) \]

       14. lower-neg.f64 19.4

           \[\leadsto x \cdot \left(\left(\color{blue}{\left(-a\right)} \cdot y2\right) \cdot y1\right) \]

   11. Simplified 19.4%

       \[\leadsto \color{blue}{x \cdot \left(\left(\left(-a\right) \cdot y2\right) \cdot y1\right)} \]

   if -8.19999999999999972e-224 < y4 < 1.3199999999999999e169

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 24.5

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 24.5%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       6. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(b \cdot t\right) \cdot z}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(b \cdot t\right)\right) \cdot z\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)} \cdot z\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot t\right)\right) \cdot z\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot t\right)\right)} \cdot z\right) \]

       11. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot z\right) \]

       12. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-1 \cdot t\right)}\right) \cdot z\right) \]

       13. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(-1 \cdot t\right)\right)} \cdot z\right) \]

       14. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \cdot z\right) \]

       15. lower-neg.f64 29.8

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-t\right)}\right) \cdot z\right) \]

   11. Simplified 29.8%

       \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(-t\right)\right) \cdot z\right)} \]

   if 1.3199999999999999e169 < y4

   1. Initial program 15.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 29.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{\left(\mathsf{neg}\left(x \cdot y0\right)\right)} + t \cdot y4\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{x \cdot \left(\mathsf{neg}\left(y0\right)\right)} + t \cdot y4\right)\right) \]

      5. neg-mul-1 N/A

         \[\leadsto b \cdot \left(j \cdot \left(x \cdot \color{blue}{\left(-1 \cdot y0\right)} + t \cdot y4\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot y0, t \cdot y4\right)}\right) \]

      7. neg-mul-1 N/A

         \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(y0\right)}, t \cdot y4\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(y0\right)}, t \cdot y4\right)\right) \]

      9. *-commutative N/A

         \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, \mathsf{neg}\left(y0\right), \color{blue}{y4 \cdot t}\right)\right) \]

      10. lower-*.f64 60.4

          \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, -y0, \color{blue}{y4 \cdot t}\right)\right) \]

   8. Simplified 60.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \mathsf{fma}\left(x, -y0, y4 \cdot t\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       3. lower-*.f64 52.2

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 52.2%

       \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(b \cdot \left(k \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -8.2 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(a \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 1.32 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 19.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -2.05 \cdot 10^{+129}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.8 \cdot 10^{+58}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -2.05e+129)
   (* (- a) (* y (* y3 y5)))
   (if (<= y3 -2.8e+58)
     (* y1 (* a (* z y3)))
     (if (<= y3 1.3e+156) (* a (* z (* t (- b)))) (* b (* (* t j) y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -2.05e+129) {
		tmp = -a * (y * (y3 * y5));
	} else if (y3 <= -2.8e+58) {
		tmp = y1 * (a * (z * y3));
	} else if (y3 <= 1.3e+156) {
		tmp = a * (z * (t * -b));
	} else {
		tmp = b * ((t * j) * y4);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-2.05d+129)) then
        tmp = -a * (y * (y3 * y5))
    else if (y3 <= (-2.8d+58)) then
        tmp = y1 * (a * (z * y3))
    else if (y3 <= 1.3d+156) then
        tmp = a * (z * (t * -b))
    else
        tmp = b * ((t * j) * y4)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -2.05e+129) {
		tmp = -a * (y * (y3 * y5));
	} else if (y3 <= -2.8e+58) {
		tmp = y1 * (a * (z * y3));
	} else if (y3 <= 1.3e+156) {
		tmp = a * (z * (t * -b));
	} else {
		tmp = b * ((t * j) * y4);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -2.05e+129:
		tmp = -a * (y * (y3 * y5))
	elif y3 <= -2.8e+58:
		tmp = y1 * (a * (z * y3))
	elif y3 <= 1.3e+156:
		tmp = a * (z * (t * -b))
	else:
		tmp = b * ((t * j) * y4)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -2.05e+129)
		tmp = Float64(Float64(-a) * Float64(y * Float64(y3 * y5)));
	elseif (y3 <= -2.8e+58)
		tmp = Float64(y1 * Float64(a * Float64(z * y3)));
	elseif (y3 <= 1.3e+156)
		tmp = Float64(a * Float64(z * Float64(t * Float64(-b))));
	else
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -2.05e+129)
		tmp = -a * (y * (y3 * y5));
	elseif (y3 <= -2.8e+58)
		tmp = y1 * (a * (z * y3));
	elseif (y3 <= 1.3e+156)
		tmp = a * (z * (t * -b));
	else
		tmp = b * ((t * j) * y4);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -2.05e+129], N[((-a) * N[(y * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.8e+58], N[(y1 * N[(a * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.3e+156], N[(a * N[(z * N[(t * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -2.0500000000000001e129

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 54.6

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 54.6%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       2. lower-neg.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]

       3. *-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y3 \cdot y5\right) \cdot y}\right)\right) \]

       5. lower-*.f64 46.7

          \[\leadsto a \cdot \left(-\color{blue}{\left(y3 \cdot y5\right)} \cdot y\right) \]

   11. Simplified 46.7%

       \[\leadsto a \cdot \color{blue}{\left(-\left(y3 \cdot y5\right) \cdot y\right)} \]

   if -2.0500000000000001e129 < y3 < -2.7999999999999998e58

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 47.9

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 47.9%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. lower-*.f64 44.0

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   11. Simplified 44.0%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(y3 \cdot z\right) \cdot y1\right)} \]

       3. associate-*r* N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right) \cdot y1} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right) \cdot y1} \]

       5. lower-*.f64 44.0

          \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right)} \cdot y1 \]

   13. Applied egg-rr 44.0%

       \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right) \cdot y1} \]

   if -2.7999999999999998e58 < y3 < 1.30000000000000009e156

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 41.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 24.4

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 24.4%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(a \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       5. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(b \cdot \left(t \cdot z\right)\right)\right)} \]

       6. associate-*r* N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(b \cdot t\right) \cdot z}\right)\right) \]

       7. distribute-lft-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(b \cdot t\right)\right) \cdot z\right)} \]

       8. mul-1-neg N/A

          \[\leadsto a \cdot \left(\color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)} \cdot z\right) \]

       9. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(b \cdot t\right)\right) \cdot z\right)} \]

       10. mul-1-neg N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(b \cdot t\right)\right)} \cdot z\right) \]

       11. distribute-rgt-neg-in N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot z\right) \]

       12. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-1 \cdot t\right)}\right) \cdot z\right) \]

       13. lower-*.f64 N/A

           \[\leadsto a \cdot \left(\color{blue}{\left(b \cdot \left(-1 \cdot t\right)\right)} \cdot z\right) \]

       14. mul-1-neg N/A

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right) \cdot z\right) \]

       15. lower-neg.f64 22.9

           \[\leadsto a \cdot \left(\left(b \cdot \color{blue}{\left(-t\right)}\right) \cdot z\right) \]

   11. Simplified 22.9%

       \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot \left(-t\right)\right) \cdot z\right)} \]

   if 1.30000000000000009e156 < y3

   1. Initial program 15.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 34.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 24.1

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 24.1%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 39.4

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 39.4%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.05 \cdot 10^{+129}:\\ \;\;\;\;\left(-a\right) \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.8 \cdot 10^{+58}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 1.3 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(z \cdot \left(t \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- a) (* y3 (* y y5)))))
   (if (<= y -5e+89)
     t_1
     (if (<= y -5e+51)
       (* y (* c (* y3 y4)))
       (if (<= y 1.85e+181) (* b (* (* t j) y4)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -a * (y3 * (y * y5));
	double tmp;
	if (y <= -5e+89) {
		tmp = t_1;
	} else if (y <= -5e+51) {
		tmp = y * (c * (y3 * y4));
	} else if (y <= 1.85e+181) {
		tmp = b * ((t * j) * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (y3 * (y * y5))
    if (y <= (-5d+89)) then
        tmp = t_1
    else if (y <= (-5d+51)) then
        tmp = y * (c * (y3 * y4))
    else if (y <= 1.85d+181) then
        tmp = b * ((t * j) * y4)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -a * (y3 * (y * y5));
	double tmp;
	if (y <= -5e+89) {
		tmp = t_1;
	} else if (y <= -5e+51) {
		tmp = y * (c * (y3 * y4));
	} else if (y <= 1.85e+181) {
		tmp = b * ((t * j) * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = -a * (y3 * (y * y5))
	tmp = 0
	if y <= -5e+89:
		tmp = t_1
	elif y <= -5e+51:
		tmp = y * (c * (y3 * y4))
	elif y <= 1.85e+181:
		tmp = b * ((t * j) * 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(Float64(-a) * Float64(y3 * Float64(y * y5)))
	tmp = 0.0
	if (y <= -5e+89)
		tmp = t_1;
	elseif (y <= -5e+51)
		tmp = Float64(y * Float64(c * Float64(y3 * y4)));
	elseif (y <= 1.85e+181)
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = -a * (y3 * (y * y5));
	tmp = 0.0;
	if (y <= -5e+89)
		tmp = t_1;
	elseif (y <= -5e+51)
		tmp = y * (c * (y3 * y4));
	elseif (y <= 1.85e+181)
		tmp = b * ((t * j) * y4);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[((-a) * N[(y3 * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+89], t$95$1, If[LessEqual[y, -5e+51], N[(y * N[(c * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+181], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999983e89 or 1.8500000000000002e181 < y

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 49.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 50.9

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around 0

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y \cdot y5\right)\right)}\right) \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y \cdot y5\right)\right)}\right) \]

       2. *-commutative N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(\mathsf{neg}\left(\color{blue}{y5 \cdot y}\right)\right)\right) \]

       3. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]

       4. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

       5. lower-*.f64 N/A

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot y\right)\right)}\right) \]

       6. mul-1-neg N/A

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       7. lower-neg.f64 44.5

          \[\leadsto a \cdot \left(y3 \cdot \left(y5 \cdot \color{blue}{\left(-y\right)}\right)\right) \]

   11. Simplified 44.5%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y5 \cdot \left(-y\right)\right)}\right) \]

   if -4.99999999999999983e89 < y < -5e51

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 63.5%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 75.8

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 75.8%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot c\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto y \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot c\right)} \]

       3. lower-*.f64 63.1

          \[\leadsto y \cdot \left(\color{blue}{\left(y3 \cdot y4\right)} \cdot c\right) \]

   11. Simplified 63.1%

       \[\leadsto y \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot c\right)} \]

   if -5e51 < y < 1.8500000000000002e181

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 40.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 26.3

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 26.3%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 19.2

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 19.2%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(y3 \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 31.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.55e+44)
   (* t (* y5 (fma a y2 (* i (- j)))))
   (if (<= j 7e+73)
     (* i (* z (fma c t (* k (- y1)))))
     (* j (* y1 (fma x i (* y4 (- y3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -1.55e+44) {
		tmp = t * (y5 * fma(a, y2, (i * -j)));
	} else if (j <= 7e+73) {
		tmp = i * (z * fma(c, t, (k * -y1)));
	} else {
		tmp = j * (y1 * fma(x, i, (y4 * -y3)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -1.55e+44)
		tmp = Float64(t * Float64(y5 * fma(a, y2, Float64(i * Float64(-j)))));
	elseif (j <= 7e+73)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-y1)))));
	else
		tmp = Float64(j * Float64(y1 * fma(x, i, Float64(y4 * Float64(-y3)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -1.55e+44], N[(t * N[(y5 * N[(a * y2 + N[(i * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+73], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y1 * N[(x * i + N[(y4 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.54999999999999998e44

   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 t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot j\right) + a \cdot y2\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\left(a \cdot y2 + -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \color{blue}{\mathsf{fma}\left(a, y2, -1 \cdot \left(i \cdot j\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-1 \cdot i\right) \cdot j}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(\mathsf{neg}\left(i\right)\right)} \cdot j\right)\right) \]

      8. lower-neg.f64 61.3

         \[\leadsto t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \color{blue}{\left(-i\right)} \cdot j\right)\right) \]

   8. Simplified 61.3%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, \left(-i\right) \cdot j\right)\right)} \]

   if -1.54999999999999998e44 < j < 7.00000000000000004e73

   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 i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 33.9%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 31.3

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 31.3%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]

   if 7.00000000000000004e73 < j

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y1 around -inf

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(y1 \cdot \left(-1 \cdot \left(y3 \cdot y4\right) + i \cdot x\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\left(i \cdot x + -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto j \cdot \left(y1 \cdot \left(\color{blue}{x \cdot i} + -1 \cdot \left(y3 \cdot y4\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(x, i, -1 \cdot \left(y3 \cdot y4\right)\right)}\right) \]

      6. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{\mathsf{neg}\left(y3 \cdot y4\right)}\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-1 \cdot y4\right)}\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, \color{blue}{y3 \cdot \left(-1 \cdot y4\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(\mathsf{neg}\left(y4\right)\right)}\right)\right) \]

      11. lower-neg.f64 56.7

          \[\leadsto j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \color{blue}{\left(-y4\right)}\right)\right) \]

   8. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y3 \cdot \left(-y4\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(y5 \cdot \mathsf{fma}\left(a, y2, i \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+73}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y1 \cdot \mathsf{fma}\left(x, i, y4 \cdot \left(-y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (fma y1 z (* y (- y5)))))))
   (if (<= y -4.7e+169)
     t_1
     (if (<= y 6e+112) (* i (* z (fma c t (* k (- 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 * (y3 * fma(y1, z, (y * -y5)));
	double tmp;
	if (y <= -4.7e+169) {
		tmp = t_1;
	} else if (y <= 6e+112) {
		tmp = i * (z * fma(c, t, (k * -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 * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))))
	tmp = 0.0
	if (y <= -4.7e+169)
		tmp = t_1;
	elseif (y <= 6e+112)
		tmp = Float64(i * Float64(z * fma(c, t, Float64(k * Float64(-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[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e+169], t$95$1, If[LessEqual[y, 6e+112], N[(i * N[(z * N[(c * t + N[(k * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6999999999999998e169 or 5.99999999999999958e112 < y

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 46.9%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 50.1

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 50.1%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   if -4.6999999999999998e169 < y < 5.99999999999999958e112

   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 i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot i}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(\mathsf{neg}\left(i\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \color{blue}{\left(-1 \cdot i\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \cdot \left(-1 \cdot i\right)} \]

   5. Simplified 46.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(c, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot j - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - z \cdot k\right)\right) \cdot \left(-i\right)} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

      3. cancel-sign-sub-inv N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t + \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\mathsf{fma}\left(c, t, \left(\mathsf{neg}\left(k\right)\right) \cdot y1\right)}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(\mathsf{neg}\left(k\right)\right) \cdot y1}\right)\right) \]

      6. lower-neg.f64 35.5

         \[\leadsto i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \color{blue}{\left(-k\right)} \cdot y1\right)\right) \]

   8. Simplified 35.5%

      \[\leadsto \color{blue}{i \cdot \left(z \cdot \mathsf{fma}\left(c, t, \left(-k\right) \cdot y1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(z \cdot \mathsf{fma}\left(c, t, k \cdot \left(-y1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 27.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -0.0015:\\ \;\;\;\;t \cdot \left(i \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -0.0015)
   (* t (* i (* j (- y5))))
   (if (<= j 5.6e+68)
     (* a (* y3 (fma y1 z (* y (- y5)))))
     (* y1 (* i (* x j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -0.0015) {
		tmp = t * (i * (j * -y5));
	} else if (j <= 5.6e+68) {
		tmp = a * (y3 * fma(y1, z, (y * -y5)));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -0.0015)
		tmp = Float64(t * Float64(i * Float64(j * Float64(-y5))));
	elseif (j <= 5.6e+68)
		tmp = Float64(a * Float64(y3 * fma(y1, z, Float64(y * Float64(-y5)))));
	else
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -0.0015], N[(t * N[(i * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.6e+68], N[(a * N[(y3 * N[(y1 * z + N[(y * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -0.0015

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 51.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(j\right), \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(\mathsf{neg}\left(t\right)\right) \]

      2. lower-*.f64 49.6

         \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, a \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   8. Simplified 49.6%

      \[\leadsto \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \color{blue}{a \cdot \left(b \cdot z\right)}\right) \cdot \left(-t\right) \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot y5\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot y5\right)\right)} \cdot \left(\mathsf{neg}\left(t\right)\right) \]

       2. lower-*.f64 44.8

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot y5\right)}\right) \cdot \left(-t\right) \]

   11. Simplified 44.8%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot y5\right)\right)} \cdot \left(-t\right) \]

   if -0.0015 < j < 5.6e68

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 40.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 30.3

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 30.3%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   if 5.6e68 < j

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

       3. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(x \cdot j\right)}\right) \cdot y1 \]

       4. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right)} \cdot y1 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right) \cdot y1} \]

       6. associate-*l* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot j\right)\right)} \cdot y1 \]

       7. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right)} \cdot y1 \]

       9. lower-*.f64 42.4

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

   11. Simplified 42.4%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -0.0015:\\ \;\;\;\;t \cdot \left(i \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, y \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y4 (* c y3)))))
   (if (<= c -5.2e+83)
     t_1
     (if (<= c 8.5e-238)
       (* a (* y3 (* z y1)))
       (if (<= c 4.8e+140) (* b (* (* t j) 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 * (y4 * (c * y3));
	double tmp;
	if (c <= -5.2e+83) {
		tmp = t_1;
	} else if (c <= 8.5e-238) {
		tmp = a * (y3 * (z * y1));
	} else if (c <= 4.8e+140) {
		tmp = b * ((t * j) * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (y4 * (c * y3))
    if (c <= (-5.2d+83)) then
        tmp = t_1
    else if (c <= 8.5d-238) then
        tmp = a * (y3 * (z * y1))
    else if (c <= 4.8d+140) then
        tmp = b * ((t * j) * y4)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * (c * y3));
	double tmp;
	if (c <= -5.2e+83) {
		tmp = t_1;
	} else if (c <= 8.5e-238) {
		tmp = a * (y3 * (z * y1));
	} else if (c <= 4.8e+140) {
		tmp = b * ((t * j) * y4);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y4 * (c * y3))
	tmp = 0
	if c <= -5.2e+83:
		tmp = t_1
	elif c <= 8.5e-238:
		tmp = a * (y3 * (z * y1))
	elif c <= 4.8e+140:
		tmp = b * ((t * j) * 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 * Float64(y4 * Float64(c * y3)))
	tmp = 0.0
	if (c <= -5.2e+83)
		tmp = t_1;
	elseif (c <= 8.5e-238)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (c <= 4.8e+140)
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y4 * (c * y3));
	tmp = 0.0;
	if (c <= -5.2e+83)
		tmp = t_1;
	elseif (c <= 8.5e-238)
		tmp = a * (y3 * (z * y1));
	elseif (c <= 4.8e+140)
		tmp = b * ((t * j) * y4);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y4 * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e+83], t$95$1, If[LessEqual[c, 8.5e-238], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+140], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.2000000000000002e83 or 4.7999999999999999e140 < c

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 34.8

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 34.8%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(c \cdot y3\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

       2. lower-*.f64 32.7

          \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   11. Simplified 32.7%

       \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\left(y3 \cdot c\right)}\right) \]

   if -5.2000000000000002e83 < c < 8.5000000000000006e-238

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 38.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 32.5

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 32.5%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 19.2

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   11. Simplified 19.2%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   if 8.5000000000000006e-238 < c < 4.7999999999999999e140

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 35.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 24.0

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 24.0%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 26.1

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 26.1%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 25.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 21.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -5.2e-73)
   (* b (* (* t j) y4))
   (if (<= j 1.25e+94) (* c (* y (* y3 y4))) (* y1 (* i (* x j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -5.2e-73) {
		tmp = b * ((t * j) * y4);
	} else if (j <= 1.25e+94) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-5.2d-73)) then
        tmp = b * ((t * j) * y4)
    else if (j <= 1.25d+94) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = y1 * (i * (x * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -5.2e-73) {
		tmp = b * ((t * j) * y4);
	} else if (j <= 1.25e+94) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = y1 * (i * (x * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -5.2e-73:
		tmp = b * ((t * j) * y4)
	elif j <= 1.25e+94:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = y1 * (i * (x * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -5.2e-73)
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	elseif (j <= 1.25e+94)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -5.2e-73)
		tmp = b * ((t * j) * y4);
	elseif (j <= 1.25e+94)
		tmp = c * (y * (y3 * y4));
	else
		tmp = y1 * (i * (x * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -5.2e-73], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.25e+94], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.2000000000000002e-73

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 49.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 31.3

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 31.3%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 23.5

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 23.5%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]

   if -5.2000000000000002e-73 < j < 1.25000000000000003e94

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 49.4%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 29.9

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 29.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto c \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot y\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot y\right)} \]

       4. lower-*.f64 21.3

          \[\leadsto c \cdot \left(\color{blue}{\left(y3 \cdot y4\right)} \cdot y\right) \]

   11. Simplified 21.3%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]

   if 1.25000000000000003e94 < j

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 61.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   8. Simplified 59.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]

   9. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto i \cdot \color{blue}{\left(\left(j \cdot x\right) \cdot y1\right)} \]

       2. associate-*r* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]

       3. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(x \cdot j\right)}\right) \cdot y1 \]

       4. associate-*l* N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right)} \cdot y1 \]

       5. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(i \cdot x\right) \cdot j\right) \cdot y1} \]

       6. associate-*l* N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(x \cdot j\right)\right)} \cdot y1 \]

       7. *-commutative N/A

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

       8. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right)} \cdot y1 \]

       9. lower-*.f64 43.9

          \[\leadsto \left(i \cdot \color{blue}{\left(j \cdot x\right)}\right) \cdot y1 \]

   11. Simplified 43.9%

       \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x\right)\right) \cdot y1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 25.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.3% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -2.8e+68)
   (* b (* (* t j) y4))
   (if (<= t 8.2e+25) (* c (* y (* y3 y4))) (* j (* b (* t y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2.8e+68) {
		tmp = b * ((t * j) * y4);
	} else if (t <= 8.2e+25) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (t <= (-2.8d+68)) then
        tmp = b * ((t * j) * y4)
    else if (t <= 8.2d+25) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = j * (b * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -2.8e+68) {
		tmp = b * ((t * j) * y4);
	} else if (t <= 8.2e+25) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = j * (b * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -2.8e+68:
		tmp = b * ((t * j) * y4)
	elif t <= 8.2e+25:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = j * (b * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (t <= -2.8e+68)
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	elseif (t <= 8.2e+25)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(j * Float64(b * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (t <= -2.8e+68)
		tmp = b * ((t * j) * y4);
	elseif (t <= 8.2e+25)
		tmp = c * (y * (y3 * y4));
	else
		tmp = j * (b * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[t, -2.8e+68], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+25], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(b * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e68

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 29.6

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 29.6%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 31.4

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 31.4%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]

   if -2.8e68 < t < 8.19999999999999933e25

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(\mathsf{neg}\left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot k}\right)\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto y \cdot \left(\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot \left(\mathsf{neg}\left(k\right)\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto y \cdot \left(\left(b \cdot y4 - i \cdot y5\right) \cdot \color{blue}{\left(-1 \cdot k\right)} + \left(x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto y \cdot \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4 - i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto y \cdot \mathsf{fma}\left(\color{blue}{b \cdot y4} - i \cdot y5, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - \color{blue}{i \cdot y5}, -1 \cdot k, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      12. lower-neg.f64 N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \color{blue}{\mathsf{neg}\left(k\right)}, x \cdot \left(a \cdot b - c \cdot i\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, \mathsf{neg}\left(k\right), \color{blue}{x \cdot \left(a \cdot b - c \cdot i\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)}\right) \]

   5. Simplified 41.6%

      \[\leadsto \color{blue}{y \cdot \mathsf{fma}\left(b \cdot y4 - i \cdot y5, -k, \mathsf{fma}\left(a \cdot b - c \cdot i, x, y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(-1 \cdot \left(b \cdot k\right) + c \cdot y3\right)\right)} \]

      2. associate-*r* N/A

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{\left(-1 \cdot b\right) \cdot k} + c \cdot y3\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot b, k, c \cdot y3\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      5. lower-neg.f64 N/A

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(b\right)}, k, c \cdot y3\right)\right) \]

      6. lower-*.f64 28.5

         \[\leadsto y \cdot \left(y4 \cdot \mathsf{fma}\left(-b, k, \color{blue}{c \cdot y3}\right)\right) \]

   8. Simplified 28.5%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-b, k, c \cdot y3\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto c \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot y\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto c \cdot \color{blue}{\left(\left(y3 \cdot y4\right) \cdot y\right)} \]

       4. lower-*.f64 20.5

          \[\leadsto c \cdot \left(\color{blue}{\left(y3 \cdot y4\right)} \cdot y\right) \]

   11. Simplified 20.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y3 \cdot y4\right) \cdot y\right)} \]

   if 8.19999999999999933e25 < t

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in y5 around 0

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot y4\right)\right) + \left(x \cdot \left(b \cdot y0 - i \cdot y1\right) + y1 \cdot \left(y3 \cdot y4\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   8. Simplified 40.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, b \cdot y0 - i \cdot y1, y4 \cdot \mathsf{fma}\left(b, -t, y1 \cdot y3\right)\right) \cdot \left(-j\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right) \cdot b} \]

       2. associate-*l* N/A

          \[\leadsto \color{blue}{j \cdot \left(\left(t \cdot y4\right) \cdot b\right)} \]

       3. *-commutative N/A

          \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4\right)\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(t \cdot y4\right)\right)} \]

       5. lower-*.f64 N/A

          \[\leadsto j \cdot \color{blue}{\left(b \cdot \left(t \cdot y4\right)\right)} \]

       6. *-commutative N/A

          \[\leadsto j \cdot \left(b \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       7. lower-*.f64 25.0

          \[\leadsto j \cdot \left(b \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 25.0%

       \[\leadsto \color{blue}{j \cdot \left(b \cdot \left(y4 \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 24.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 21.1% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -5.2e+183)
   (* a (* y3 (* z y1)))
   (if (<= z 2.4e+61) (* b (* (* t j) y4)) (* a (* y1 (* z y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -5.2e+183) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= 2.4e+61) {
		tmp = b * ((t * j) * y4);
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-5.2d+183)) then
        tmp = a * (y3 * (z * y1))
    else if (z <= 2.4d+61) then
        tmp = b * ((t * j) * y4)
    else
        tmp = a * (y1 * (z * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -5.2e+183) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= 2.4e+61) {
		tmp = b * ((t * j) * y4);
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -5.2e+183:
		tmp = a * (y3 * (z * y1))
	elif z <= 2.4e+61:
		tmp = b * ((t * j) * y4)
	else:
		tmp = a * (y1 * (z * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -5.2e+183)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (z <= 2.4e+61)
		tmp = Float64(b * Float64(Float64(t * j) * y4));
	else
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -5.2e+183)
		tmp = a * (y3 * (z * y1));
	elseif (z <= 2.4e+61)
		tmp = b * ((t * j) * y4);
	else
		tmp = a * (y1 * (z * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -5.2e+183], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+61], N[(b * N[(N[(t * j), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999999e183

   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 a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 44.6

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 44.6%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 34.8

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   11. Simplified 34.8%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   if -5.1999999999999999e183 < z < 2.3999999999999999e61

   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 t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t \cdot \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot t}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(\mathsf{neg}\left(t\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot t\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + z \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-1 \cdot t\right)} \]

   5. Simplified 39.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y4 - i \cdot y5, -j, \mathsf{fma}\left(z, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot t\right)} \cdot \left(-1 \cdot \left(a \cdot z\right) + j \cdot y4\right) \]

      4. +-commutative N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\left(j \cdot y4 + -1 \cdot \left(a \cdot z\right)\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \color{blue}{\mathsf{fma}\left(j, y4, -1 \cdot \left(a \cdot z\right)\right)} \]

      6. mul-1-neg N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, \color{blue}{\mathsf{neg}\left(a \cdot z\right)}\right) \]

      8. lower-*.f64 20.8

         \[\leadsto \left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -\color{blue}{a \cdot z}\right) \]

   8. Simplified 20.8%

      \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot \mathsf{fma}\left(j, y4, -a \cdot z\right)} \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. associate-*r* N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(\left(j \cdot t\right) \cdot y4\right)} \]

       4. lower-*.f64 21.9

          \[\leadsto b \cdot \left(\color{blue}{\left(j \cdot t\right)} \cdot y4\right) \]

   11. Simplified 21.9%

       \[\leadsto \color{blue}{b \cdot \left(\left(j \cdot t\right) \cdot y4\right)} \]

   if 2.3999999999999999e61 < z

   1. Initial program 30.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 36.5%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 26.9

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 26.9%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. lower-*.f64 25.1

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   11. Simplified 25.1%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 24.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;b \cdot \left(\left(t \cdot j\right) \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.1% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -2.3e+57)
   (* a (* y3 (* z y1)))
   (if (<= z 5.5e+56) (* b (* j (* t y4))) (* a (* y1 (* z y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.3e+57) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= 5.5e+56) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-2.3d+57)) then
        tmp = a * (y3 * (z * y1))
    else if (z <= 5.5d+56) then
        tmp = b * (j * (t * y4))
    else
        tmp = a * (y1 * (z * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.3e+57) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= 5.5e+56) {
		tmp = b * (j * (t * y4));
	} else {
		tmp = a * (y1 * (z * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -2.3e+57:
		tmp = a * (y3 * (z * y1))
	elif z <= 5.5e+56:
		tmp = b * (j * (t * y4))
	else:
		tmp = a * (y1 * (z * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -2.3e+57)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (z <= 5.5e+56)
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	else
		tmp = Float64(a * Float64(y1 * Float64(z * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -2.3e+57)
		tmp = a * (y3 * (z * y1));
	elseif (z <= 5.5e+56)
		tmp = b * (j * (t * y4));
	else
		tmp = a * (y1 * (z * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -2.3e+57], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+56], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999999e57

   1. Initial program 17.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 37.2%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 41.7

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 41.7%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 29.5

          \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   11. Simplified 29.5%

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

   if -2.2999999999999999e57 < z < 5.5000000000000002e56

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(j \cdot \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot j}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(\mathsf{neg}\left(j\right)\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \color{blue}{\left(-1 \cdot j\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) \cdot \left(-1 \cdot j\right)} \]

   5. Simplified 44.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, -\left(b \cdot y4 - i \cdot y5\right), \mathsf{fma}\left(y3, y1 \cdot y4 - y0 \cdot y5, \left(b \cdot y0 - i \cdot y1\right) \cdot x\right)\right) \cdot \left(-j\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(-1 \cdot \left(x \cdot y0\right) + t \cdot y4\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{\left(\mathsf{neg}\left(x \cdot y0\right)\right)} + t \cdot y4\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto b \cdot \left(j \cdot \left(\color{blue}{x \cdot \left(\mathsf{neg}\left(y0\right)\right)} + t \cdot y4\right)\right) \]

      5. neg-mul-1 N/A

         \[\leadsto b \cdot \left(j \cdot \left(x \cdot \color{blue}{\left(-1 \cdot y0\right)} + t \cdot y4\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \color{blue}{\mathsf{fma}\left(x, -1 \cdot y0, t \cdot y4\right)}\right) \]

      7. neg-mul-1 N/A

         \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(y0\right)}, t \cdot y4\right)\right) \]

      8. lower-neg.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, \color{blue}{\mathsf{neg}\left(y0\right)}, t \cdot y4\right)\right) \]

      9. *-commutative N/A

         \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, \mathsf{neg}\left(y0\right), \color{blue}{y4 \cdot t}\right)\right) \]

      10. lower-*.f64 27.6

          \[\leadsto b \cdot \left(j \cdot \mathsf{fma}\left(x, -y0, \color{blue}{y4 \cdot t}\right)\right) \]

   8. Simplified 27.6%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \mathsf{fma}\left(x, -y0, y4 \cdot t\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4\right)\right)} \]

       2. *-commutative N/A

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

       3. lower-*.f64 20.4

          \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   11. Simplified 20.4%

       \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(y4 \cdot t\right)\right)} \]

   if 5.5000000000000002e56 < z

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. associate--l+ N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      6. lower-neg.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

   5. Simplified 35.8%

      \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

   6. Taylor expanded in y3 around inf

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

      5. associate-*r* N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

      8. lower-neg.f64 26.4

         \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

   8. Simplified 26.4%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

   9. Taylor expanded in y1 around inf

      \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

       2. lower-*.f64 24.6

          \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   11. Simplified 24.6%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 23.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 17.2% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y3 (* 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) {
	return a * (y3 * (z * y1));
}

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 * (y3 * (z * y1))
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 * (y3 * (z * y1));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y3 * (z * y1))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y3 * Float64(z * y1)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y3 * (z * y1));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 27.9%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   2. associate--l+ N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

   3. mul-1-neg N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. lower-neg.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   7. lower--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. *-commutative N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   11. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   12. sub-neg N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

5. Simplified 36.0%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y3 around inf

   \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

   3. +-commutative N/A

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

   4. lower-fma.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

   5. associate-*r* N/A

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

   6. lower-*.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

   7. mul-1-neg N/A

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

   8. lower-neg.f64 27.1

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

8. Simplified 27.1%

   \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

9. Taylor expanded in y1 around inf

   \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]
10. Step-by-step derivation

    1. lower-*.f64 14.8

       \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

11. Simplified 14.8%

    \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z\right)}\right) \]

12. Final simplification 14.8%

    \[\leadsto a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right) \]
13. Add Preprocessing

Alternative 34: 17.1% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y1 (* z y3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y1 * (z * y3))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y1 * (z * y3));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y1 * (z * y3))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y1 * Float64(z * y3)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y1 * (z * y3));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y1 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 27.9%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(x \cdot y - t \cdot z\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   2. associate--l+ N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)} \]

   3. mul-1-neg N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto a \cdot \left(\color{blue}{y1 \cdot \left(\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)\right)} + \left(b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right) \]

   5. lower-fma.f64 N/A

      \[\leadsto a \cdot \color{blue}{\mathsf{fma}\left(y1, \mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. lower-neg.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \color{blue}{\mathsf{neg}\left(\left(x \cdot y2 - y3 \cdot z\right)\right)}, b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   7. lower--.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. *-commutative N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   11. lower-*.f64 N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right), b \cdot \left(x \cdot y - t \cdot z\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   12. sub-neg N/A

       \[\leadsto a \cdot \mathsf{fma}\left(y1, \mathsf{neg}\left(\left(y2 \cdot x - z \cdot y3\right)\right), \color{blue}{b \cdot \left(x \cdot y - t \cdot z\right) + \left(\mathsf{neg}\left(-1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\right)}\right) \]

5. Simplified 36.0%

   \[\leadsto \color{blue}{a \cdot \mathsf{fma}\left(y1, -\left(y2 \cdot x - z \cdot y3\right), \mathsf{fma}\left(b, y \cdot x - t \cdot z, y5 \cdot \left(t \cdot y2 - y3 \cdot y\right)\right)\right)} \]

6. Taylor expanded in y3 around inf

   \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(-1 \cdot \left(y \cdot y5\right) + y1 \cdot z\right)\right)} \]

   3. +-commutative N/A

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\left(y1 \cdot z + -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

   4. lower-fma.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \color{blue}{\mathsf{fma}\left(y1, z, -1 \cdot \left(y \cdot y5\right)\right)}\right) \]

   5. associate-*r* N/A

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

   6. lower-*.f64 N/A

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-1 \cdot y\right) \cdot y5}\right)\right) \]

   7. mul-1-neg N/A

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y5\right)\right) \]

   8. lower-neg.f64 27.1

      \[\leadsto a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \color{blue}{\left(-y\right)} \cdot y5\right)\right) \]

8. Simplified 27.1%

   \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \mathsf{fma}\left(y1, z, \left(-y\right) \cdot y5\right)\right)} \]

9. Taylor expanded in y1 around inf

   \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
10. Step-by-step derivation

    1. lower-*.f64 N/A

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

    2. lower-*.f64 14.8

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

11. Simplified 14.8%

    \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]

12. Final simplification 14.8%

    \[\leadsto a \cdot \left(y1 \cdot \left(z \cdot y3\right)\right) \]
13. Add Preprocessing

Developer Target 1: 28.2% 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 2024212 
(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)))))