Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.3% → 37.9%

Time: 1.7min

Alternatives: 45

Speedup: 4.5×

• 88.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.3% 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: 37.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot y3 - k \cdot y2\\ t_2 := i \cdot \left(y \cdot k - t \cdot j\right)\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-18}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-217}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot t_1 + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-298}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot t_3\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-232}:\\ \;\;\;\;y5 \cdot \left(t_2 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot t_1\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+67}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j y3) (* k y2)))
        (t_2 (* i (- (* y k) (* t j))))
        (t_3 (- (* k y2) (* j y3)))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 t_3))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y -2.15e+129)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -4.5e-18)
       t_4
       (if (<= y -4.6e-217)
         (*
          y0
          (+
           (* c (- (* x y2) (* z y3)))
           (+ (* y5 t_1) (* b (- (* z k) (* x j))))))
         (if (<= y -2.7e-298)
           (*
            y1
            (+
             (* a (- (* z y3) (* x y2)))
             (+ (* i (- (* x j) (* z k))) (* y4 t_3))))
           (if (<= y 4.5e-232)
             (* y5 (+ t_2 (+ (* a (- (* t y2) (* y y3))) (* y0 t_1))))
             (if (<= y 7e-72)
               (*
                y2
                (+
                 (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
                 (* t (- (* a y5) (* c y4)))))
               (if (<= y 2.1e+67) t_4 (* y5 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 = (j * y3) - (k * y2);
	double t_2 = i * ((y * k) - (t * j));
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -2.15e+129) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -4.5e-18) {
		tmp = t_4;
	} else if (y <= -4.6e-217) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * t_1) + (b * ((z * k) - (x * j)))));
	} else if (y <= -2.7e-298) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_3)));
	} else if (y <= 4.5e-232) {
		tmp = y5 * (t_2 + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	} else if (y <= 7e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 2.1e+67) {
		tmp = t_4;
	} else {
		tmp = y5 * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (j * y3) - (k * y2)
    t_2 = i * ((y * k) - (t * j))
    t_3 = (k * y2) - (j * y3)
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
    if (y <= (-2.15d+129)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-4.5d-18)) then
        tmp = t_4
    else if (y <= (-4.6d-217)) then
        tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * t_1) + (b * ((z * k) - (x * j)))))
    else if (y <= (-2.7d-298)) then
        tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_3)))
    else if (y <= 4.5d-232) then
        tmp = y5 * (t_2 + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)))
    else if (y <= 7d-72) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y <= 2.1d+67) then
        tmp = t_4
    else
        tmp = y5 * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y3) - (k * y2);
	double t_2 = i * ((y * k) - (t * j));
	double t_3 = (k * y2) - (j * y3);
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -2.15e+129) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -4.5e-18) {
		tmp = t_4;
	} else if (y <= -4.6e-217) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * t_1) + (b * ((z * k) - (x * j)))));
	} else if (y <= -2.7e-298) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_3)));
	} else if (y <= 4.5e-232) {
		tmp = y5 * (t_2 + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	} else if (y <= 7e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 2.1e+67) {
		tmp = t_4;
	} else {
		tmp = y5 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y3) - (k * y2)
	t_2 = i * ((y * k) - (t * j))
	t_3 = (k * y2) - (j * y3)
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y <= -2.15e+129:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -4.5e-18:
		tmp = t_4
	elif y <= -4.6e-217:
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * t_1) + (b * ((z * k) - (x * j)))))
	elif y <= -2.7e-298:
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_3)))
	elif y <= 4.5e-232:
		tmp = y5 * (t_2 + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)))
	elif y <= 7e-72:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y <= 2.1e+67:
		tmp = t_4
	else:
		tmp = y5 * 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(j * y3) - Float64(k * y2))
	t_2 = Float64(i * Float64(Float64(y * k) - Float64(t * j)))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y <= -2.15e+129)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -4.5e-18)
		tmp = t_4;
	elseif (y <= -4.6e-217)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(Float64(y5 * t_1) + Float64(b * Float64(Float64(z * k) - Float64(x * j))))));
	elseif (y <= -2.7e-298)
		tmp = Float64(y1 * Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * t_3))));
	elseif (y <= 4.5e-232)
		tmp = Float64(y5 * Float64(t_2 + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * t_1))));
	elseif (y <= 7e-72)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 2.1e+67)
		tmp = t_4;
	else
		tmp = Float64(y5 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * y3) - (k * y2);
	t_2 = i * ((y * k) - (t * j));
	t_3 = (k * y2) - (j * y3);
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y <= -2.15e+129)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -4.5e-18)
		tmp = t_4;
	elseif (y <= -4.6e-217)
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * t_1) + (b * ((z * k) - (x * j)))));
	elseif (y <= -2.7e-298)
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_3)));
	elseif (y <= 4.5e-232)
		tmp = y5 * (t_2 + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	elseif (y <= 7e-72)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y <= 2.1e+67)
		tmp = t_4;
	else
		tmp = y5 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+129], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-18], t$95$4, If[LessEqual[y, -4.6e-217], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * t$95$1), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-298], N[(y1 * N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-232], N[(y5 * N[(t$95$2 + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-72], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+67], t$95$4, N[(y5 * t$95$2), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.1500000000000001e129

   1. Initial program 24.2%

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

   3. Simplified 30.3%

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

   4. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in y4 around inf 57.9%

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

      1. *-commutative 57.9%

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

   9. Simplified 57.9%

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

   if -2.1500000000000001e129 < y < -4.49999999999999994e-18 or 7.00000000000000001e-72 < y < 2.1000000000000001e67

   1. Initial program 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in y4 around inf 61.5%

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

   if -4.49999999999999994e-18 < y < -4.6000000000000001e-217

   1. Initial program 28.2%

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

   3. Simplified 37.5%

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

   4. Taylor expanded in y0 around inf 57.7%

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

      1. mul-1-neg 57.7%

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

   6. Simplified 57.7%

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

   if -4.6000000000000001e-217 < y < -2.7000000000000001e-298

   1. Initial program 37.9%

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

   3. Simplified 37.9%

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

   4. Taylor expanded in y1 around inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. mul-1-neg 75.1%

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

      3. sub-neg 75.1%

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

   6. Simplified 75.1%

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

   if -2.7000000000000001e-298 < y < 4.49999999999999967e-232

   1. Initial program 45.5%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y5 around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. mul-1-neg 68.5%

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

      3. mul-1-neg 68.5%

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

      4. sub-neg 68.5%

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

      5. sub-neg 68.5%

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

   6. Simplified 68.5%

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

   if 4.49999999999999967e-232 < y < 7.00000000000000001e-72

   1. Initial program 33.4%

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

   3. Simplified 33.4%

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

   4. Taylor expanded in y2 around inf 60.8%

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

   if 2.1000000000000001e67 < y

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y5 around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. mul-1-neg 44.7%

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

      3. mul-1-neg 44.7%

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

      4. sub-neg 44.7%

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

      5. sub-neg 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 7 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-217}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-298}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-232}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 2: 52.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - z \cdot y3\right)\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := x \cdot y - z \cdot t\\ t_4 := a \cdot b - c \cdot i\\ t_5 := t \cdot j - y \cdot k\\ t_6 := k \cdot y2 - j \cdot y3\\ t_7 := b \cdot y4 - i \cdot y5\\ t_8 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;\left(\left(\left(\left(t_3 \cdot t_4 + \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right) + t_1\right) + t_5 \cdot t_7\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + t_6 \cdot t_8 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t_6, t_8, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, t_2, \mathsf{fma}\left(t_3, t_4, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t_5, t_7, t_1\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_5 + y1 \cdot t_6\right) + c \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* c y0) (* a y1)) (- (* x y2) (* z y3))))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (- (* x y) (* z t)))
        (t_4 (- (* a b) (* c i)))
        (t_5 (- (* t j) (* y k)))
        (t_6 (- (* k y2) (* j y3)))
        (t_7 (- (* b y4) (* i y5)))
        (t_8 (- (* y1 y4) (* y0 y5))))
   (if (<=
        (+
         (+
          (+
           (+
            (+ (* t_3 t_4) (* (- (* x j) (* z k)) (- (* i y1) (* b y0))))
            t_1)
           (* t_5 t_7))
          (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
         (* t_6 t_8))
        INFINITY)
     (fma
      t_6
      t_8
      (fma
       (- (* c y4) (* a y5))
       t_2
       (fma
        t_3
        t_4
        (fma (- (* b y0) (* i y1)) (- (* z k) (* x j)) (fma t_5 t_7 t_1)))))
     (* y4 (+ (+ (* b t_5) (* y1 t_6)) (* c 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 = ((c * y0) - (a * y1)) * ((x * y2) - (z * y3));
	double t_2 = (y * y3) - (t * y2);
	double t_3 = (x * y) - (z * t);
	double t_4 = (a * b) - (c * i);
	double t_5 = (t * j) - (y * k);
	double t_6 = (k * y2) - (j * y3);
	double t_7 = (b * y4) - (i * y5);
	double t_8 = (y1 * y4) - (y0 * y5);
	double tmp;
	if (((((((t_3 * t_4) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + t_1) + (t_5 * t_7)) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_6 * t_8)) <= ((double) INFINITY)) {
		tmp = fma(t_6, t_8, fma(((c * y4) - (a * y5)), t_2, fma(t_3, t_4, fma(((b * y0) - (i * y1)), ((z * k) - (x * j)), fma(t_5, t_7, t_1)))));
	} else {
		tmp = y4 * (((b * t_5) + (y1 * t_6)) + (c * 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(Float64(c * y0) - Float64(a * y1)) * Float64(Float64(x * y2) - Float64(z * y3)))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(Float64(a * b) - Float64(c * i))
	t_5 = Float64(Float64(t * j) - Float64(y * k))
	t_6 = Float64(Float64(k * y2) - Float64(j * y3))
	t_7 = Float64(Float64(b * y4) - Float64(i * y5))
	t_8 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(t_3 * t_4) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + t_1) + Float64(t_5 * t_7)) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(t_6 * t_8)) <= Inf)
		tmp = fma(t_6, t_8, fma(Float64(Float64(c * y4) - Float64(a * y5)), t_2, fma(t_3, t_4, fma(Float64(Float64(b * y0) - Float64(i * y1)), Float64(Float64(z * k) - Float64(x * j)), fma(t_5, t_7, t_1)))));
	else
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_5) + Float64(y1 * t_6)) + Float64(c * 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[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(t$95$3 * t$95$4), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(t$95$5 * t$95$7), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$6 * t$95$8), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$6 * t$95$8 + N[(N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision] * t$95$2 + N[(t$95$3 * t$95$4 + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 * t$95$7 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(N[(N[(b * t$95$5), $MachinePrecision] + N[(y1 * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $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 90.7%

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

   3. Simplified 90.8%

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

   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%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y4 around inf 36.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

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

Alternative 3: 52.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

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

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (k * y2) - (j * y3)
	t_3 = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (t_1 * ((b * y4) - (i * y5)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_2 * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = y4 * (((b * t_1) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (k * y2) - (j * y3);
	t_3 = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (t_1 * ((b * y4) - (i * y5)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_2 * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = y4 * (((b * t_1) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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[(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$1 * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $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 90.7%

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

   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%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y4 around inf 36.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

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

Alternative 4: 36.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-85}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + t_3\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-175}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot t_2\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-73}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_1 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_2\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (* c (- (* y y3) (* t y2)))))
   (if (<= y -3.8e+158)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -4.1e-85)
       (* y4 (+ (- (* k (* y1 y2)) (* k (* y b))) t_3))
       (if (<= y -4.2e-175)
         (*
          t
          (+
           (* z (- (* c i) (* a b)))
           (+ (* j (- (* b y4) (* i y5))) (* y2 t_2))))
         (if (<= y -3.5e-215)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= y -5e-219)
             (* c (* t (- (* z i) (* y2 y4))))
             (if (<= y -1.85e-290)
               (*
                x
                (+
                 (+ (* y (- (* a b) (* c i))) (* y2 t_1))
                 (* j (- (* i y1) (* b y0)))))
               (if (<= y 6.9e-264)
                 (* (* t y5) (- (* a y2) (* i j)))
                 (if (<= y 9.2e-73)
                   (*
                    y2
                    (+ (+ (* x t_1) (* k (- (* y1 y4) (* y0 y5)))) (* t t_2)))
                   (if (<= y 2.7e+67)
                     (*
                      y4
                      (+
                       (+
                        (* b (- (* t j) (* y k)))
                        (* y1 (- (* k y2) (* j y3))))
                       t_3))
                     (* y5 (* i (- (* y k) (* t j)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y <= -3.8e+158) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -4.1e-85) {
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_3);
	} else if (y <= -4.2e-175) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)));
	} else if (y <= -3.5e-215) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y <= -5e-219) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y <= -1.85e-290) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	} else if (y <= 6.9e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 9.2e-73) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	} else if (y <= 2.7e+67) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_3);
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (a * y5) - (c * y4)
    t_3 = c * ((y * y3) - (t * y2))
    if (y <= (-3.8d+158)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-4.1d-85)) then
        tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_3)
    else if (y <= (-4.2d-175)) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)))
    else if (y <= (-3.5d-215)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y <= (-5d-219)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y <= (-1.85d-290)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    else if (y <= 6.9d-264) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 9.2d-73) then
        tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
    else if (y <= 2.7d+67) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_3)
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = (c * y0) - (a * y1);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y <= -3.8e+158) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -4.1e-85) {
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_3);
	} else if (y <= -4.2e-175) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)));
	} else if (y <= -3.5e-215) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y <= -5e-219) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y <= -1.85e-290) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	} else if (y <= 6.9e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 9.2e-73) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	} else if (y <= 2.7e+67) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_3);
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = (a * y5) - (c * y4)
	t_3 = c * ((y * y3) - (t * y2))
	tmp = 0
	if y <= -3.8e+158:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -4.1e-85:
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_3)
	elif y <= -4.2e-175:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)))
	elif y <= -3.5e-215:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y <= -5e-219:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y <= -1.85e-290:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	elif y <= 6.9e-264:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 9.2e-73:
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
	elif y <= 2.7e+67:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_3)
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (y <= -3.8e+158)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -4.1e-85)
		tmp = Float64(y4 * Float64(Float64(Float64(k * Float64(y1 * y2)) - Float64(k * Float64(y * b))) + t_3));
	elseif (y <= -4.2e-175)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * t_2))));
	elseif (y <= -3.5e-215)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y <= -5e-219)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y <= -1.85e-290)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y <= 6.9e-264)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 9.2e-73)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_1) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_2)));
	elseif (y <= 2.7e+67)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_3));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = (c * y0) - (a * y1);
	t_2 = (a * y5) - (c * y4);
	t_3 = c * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (y <= -3.8e+158)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -4.1e-85)
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_3);
	elseif (y <= -4.2e-175)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)));
	elseif (y <= -3.5e-215)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y <= -5e-219)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y <= -1.85e-290)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	elseif (y <= 6.9e-264)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 9.2e-73)
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	elseif (y <= 2.7e+67)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_3);
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+158], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e-85], N[(y4 * N[(N[(N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] - N[(k * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-175], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-215], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-219], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-290], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.9e-264], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-73], N[(y2 * N[(N[(N[(x * t$95$1), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+67], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y < -3.7999999999999998e158

   1. Initial program 22.6%

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

   3. Simplified 25.8%

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

   4. Taylor expanded in y around inf 48.6%

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

      1. mul-1-neg 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in y4 around inf 58.4%

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

      1. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -3.7999999999999998e158 < y < -4.09999999999999994e-85

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y4 around inf 48.4%

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

   5. Taylor expanded in j around 0 51.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

      3. *-commutative 51.1%

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

      4. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   if -4.09999999999999994e-85 < y < -4.2e-175

   1. Initial program 30.5%

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

   3. Simplified 30.5%

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

   4. Taylor expanded in t around inf 70.2%

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

      1. associate--l+ 70.2%

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

      2. mul-1-neg 70.2%

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

   6. Simplified 70.2%

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

   if -4.2e-175 < y < -3.5000000000000002e-215

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   4. Taylor expanded in c around inf 25.0%

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

   5. Taylor expanded in y0 around inf 63.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 63.7%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 63.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if -3.5000000000000002e-215 < y < -5.0000000000000002e-219

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in c around inf 66.8%

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

   5. Taylor expanded in t around inf 100.0%

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

   if -5.0000000000000002e-219 < y < -1.84999999999999989e-290

   1. Initial program 37.0%

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

   3. Simplified 37.0%

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

   4. Taylor expanded in x around inf 54.8%

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

   if -1.84999999999999989e-290 < y < 6.89999999999999991e-264

   1. Initial program 31.3%

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

   3. Simplified 37.5%

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

   4. Taylor expanded in y5 around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. mul-1-neg 62.9%

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

      3. mul-1-neg 62.9%

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

      4. sub-neg 62.9%

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

      5. sub-neg 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in t around inf 69.1%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

   9. Simplified 69.1%

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

   if 6.89999999999999991e-264 < y < 9.19999999999999953e-73

   1. Initial program 41.1%

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

   3. Simplified 41.1%

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

   4. Taylor expanded in y2 around inf 57.3%

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

   if 9.19999999999999953e-73 < y < 2.6999999999999999e67

   1. Initial program 23.7%

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

   3. Simplified 23.7%

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

   4. Taylor expanded in y4 around inf 65.1%

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

   if 2.6999999999999999e67 < y

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y5 around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. mul-1-neg 44.7%

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

      3. mul-1-neg 44.7%

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

      4. sub-neg 44.7%

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

      5. sub-neg 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 10 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-85}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-175}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-73}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 5: 37.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-217}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot t_1\right)\right)\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 t_1))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y -3.7e+136)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -7.2e-17)
       t_2
       (if (<= y -3.9e-217)
         (*
          y0
          (+
           (* c (- (* x y2) (* z y3)))
           (+ (* y5 (- (* j y3) (* k y2))) (* b (- (* z k) (* x j))))))
         (if (<= y 2.8e-306)
           (*
            y1
            (+
             (* a (- (* z y3) (* x y2)))
             (+ (* i (- (* x j) (* z k))) (* y4 t_1))))
           (if (<= y 6.9e-264)
             (* (* t y5) (- (* a y2) (* i j)))
             (if (<= y 2.15e-72)
               (*
                y2
                (+
                 (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
                 (* t (- (* a y5) (* c y4)))))
               (if (<= y 1.3e+67) t_2 (* y5 (* i (- (* y k) (* t j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -3.7e+136) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -7.2e-17) {
		tmp = t_2;
	} else if (y <= -3.9e-217) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else if (y <= 2.8e-306) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_1)));
	} else if (y <= 6.9e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 2.15e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 1.3e+67) {
		tmp = t_2;
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
    if (y <= (-3.7d+136)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-7.2d-17)) then
        tmp = t_2
    else if (y <= (-3.9d-217)) then
        tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
    else if (y <= 2.8d-306) then
        tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_1)))
    else if (y <= 6.9d-264) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 2.15d-72) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y <= 1.3d+67) then
        tmp = t_2
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = (k * y2) - (j * y3);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -3.7e+136) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -7.2e-17) {
		tmp = t_2;
	} else if (y <= -3.9e-217) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else if (y <= 2.8e-306) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_1)));
	} else if (y <= 6.9e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 2.15e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 1.3e+67) {
		tmp = t_2;
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y <= -3.7e+136:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -7.2e-17:
		tmp = t_2
	elif y <= -3.9e-217:
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
	elif y <= 2.8e-306:
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_1)))
	elif y <= 6.9e-264:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 2.15e-72:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y <= 1.3e+67:
		tmp = t_2
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_1)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y <= -3.7e+136)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -7.2e-17)
		tmp = t_2;
	elseif (y <= -3.9e-217)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(b * Float64(Float64(z * k) - Float64(x * j))))));
	elseif (y <= 2.8e-306)
		tmp = Float64(y1 * Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) + Float64(y4 * t_1))));
	elseif (y <= 6.9e-264)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 2.15e-72)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 1.3e+67)
		tmp = t_2;
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = (k * y2) - (j * y3);
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y <= -3.7e+136)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -7.2e-17)
		tmp = t_2;
	elseif (y <= -3.9e-217)
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	elseif (y <= 2.8e-306)
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * t_1)));
	elseif (y <= 6.9e-264)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 2.15e-72)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y <= 1.3e+67)
		tmp = t_2;
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+136], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-17], t$95$2, If[LessEqual[y, -3.9e-217], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-306], N[(y1 * N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.9e-264], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-72], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+67], t$95$2, N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -3.7000000000000001e136

   1. Initial program 24.2%

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

   3. Simplified 30.3%

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

   4. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in y4 around inf 57.9%

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

      1. *-commutative 57.9%

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

   9. Simplified 57.9%

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

   if -3.7000000000000001e136 < y < -7.1999999999999999e-17 or 2.1499999999999999e-72 < y < 1.3e67

   1. Initial program 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in y4 around inf 61.5%

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

   if -7.1999999999999999e-17 < y < -3.9000000000000001e-217

   1. Initial program 28.2%

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

   3. Simplified 37.5%

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

   4. Taylor expanded in y0 around inf 57.7%

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

      1. mul-1-neg 57.7%

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

   6. Simplified 57.7%

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

   if -3.9000000000000001e-217 < y < 2.8000000000000001e-306

   1. Initial program 37.9%

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

   3. Simplified 37.9%

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

   4. Taylor expanded in y1 around inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. mul-1-neg 75.1%

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

      3. sub-neg 75.1%

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

   6. Simplified 75.1%

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

   if 2.8000000000000001e-306 < y < 6.89999999999999991e-264

   1. Initial program 30.8%

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

   3. Simplified 38.5%

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

   4. Taylor expanded in y5 around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. mul-1-neg 62.0%

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

      3. mul-1-neg 62.0%

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

      4. sub-neg 62.0%

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

      5. sub-neg 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in t around inf 69.6%

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

      1. associate-*r* 69.6%

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

      2. *-commutative 69.6%

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

   9. Simplified 69.6%

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

   if 6.89999999999999991e-264 < y < 2.1499999999999999e-72

   1. Initial program 41.1%

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

   3. Simplified 41.1%

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

   4. Taylor expanded in y2 around inf 57.3%

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

   if 1.3e67 < y

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y5 around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. mul-1-neg 44.7%

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

      3. mul-1-neg 44.7%

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

      4. sub-neg 44.7%

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

      5. sub-neg 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 7 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-17}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-217}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 6: 36.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-178}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y -8e+127)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -1.95e-16)
       t_1
       (if (<= y -4.7e-178)
         (*
          y0
          (+
           (* c (- (* x y2) (* z y3)))
           (+ (* y5 (- (* j y3) (* k y2))) (* b (- (* z k) (* x j))))))
         (if (<= y 7.7e-264)
           (* (* t y5) (- (* a y2) (* i j)))
           (if (<= y 6e-72)
             (*
              y2
              (+
               (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
               (* t (- (* a y5) (* c y4)))))
             (if (<= y 3.2e+67) t_1 (* y5 (* i (- (* y k) (* t j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -8e+127) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -1.95e-16) {
		tmp = t_1;
	} else if (y <= -4.7e-178) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else if (y <= 7.7e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 6e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 3.2e+67) {
		tmp = t_1;
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: tmp
    t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (y <= (-8d+127)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-1.95d-16)) then
        tmp = t_1
    else if (y <= (-4.7d-178)) then
        tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
    else if (y <= 7.7d-264) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 6d-72) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y <= 3.2d+67) then
        tmp = t_1
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -8e+127) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -1.95e-16) {
		tmp = t_1;
	} else if (y <= -4.7e-178) {
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	} else if (y <= 7.7e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 6e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 3.2e+67) {
		tmp = t_1;
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y <= -8e+127:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -1.95e-16:
		tmp = t_1
	elif y <= -4.7e-178:
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))))
	elif y <= 7.7e-264:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 6e-72:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y <= 3.2e+67:
		tmp = t_1
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y <= -8e+127)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -1.95e-16)
		tmp = t_1;
	elseif (y <= -4.7e-178)
		tmp = Float64(y0 * Float64(Float64(c * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(b * Float64(Float64(z * k) - Float64(x * j))))));
	elseif (y <= 7.7e-264)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 6e-72)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 3.2e+67)
		tmp = t_1;
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y <= -8e+127)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -1.95e-16)
		tmp = t_1;
	elseif (y <= -4.7e-178)
		tmp = y0 * ((c * ((x * y2) - (z * y3))) + ((y5 * ((j * y3) - (k * y2))) + (b * ((z * k) - (x * j)))));
	elseif (y <= 7.7e-264)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 6e-72)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y <= 3.2e+67)
		tmp = t_1;
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	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[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+127], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-16], t$95$1, If[LessEqual[y, -4.7e-178], N[(y0 * N[(N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.7e-264], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-72], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+67], t$95$1, N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -7.99999999999999964e127

   1. Initial program 24.2%

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

   3. Simplified 30.3%

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

   4. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in y4 around inf 57.9%

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

      1. *-commutative 57.9%

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

   9. Simplified 57.9%

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

   if -7.99999999999999964e127 < y < -1.94999999999999989e-16 or 6e-72 < y < 3.19999999999999983e67

   1. Initial program 24.0%

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

   3. Simplified 24.0%

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

   4. Taylor expanded in y4 around inf 61.5%

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

   if -1.94999999999999989e-16 < y < -4.69999999999999999e-178

   1. Initial program 32.6%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in y0 around inf 60.5%

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

      1. mul-1-neg 60.5%

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

   6. Simplified 60.5%

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

   if -4.69999999999999999e-178 < y < 7.69999999999999957e-264

   1. Initial program 29.4%

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

   3. Simplified 34.3%

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

   4. Taylor expanded in y5 around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. mul-1-neg 46.9%

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

      3. mul-1-neg 46.9%

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

      4. sub-neg 46.9%

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

      5. sub-neg 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in t around inf 57.0%

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

      1. associate-*r* 54.6%

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

      2. *-commutative 54.6%

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

   9. Simplified 54.6%

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

   if 7.69999999999999957e-264 < y < 6e-72

   1. Initial program 41.1%

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

   3. Simplified 41.1%

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

   4. Taylor expanded in y2 around inf 57.3%

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

   if 3.19999999999999983e67 < y

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y5 around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. mul-1-neg 44.7%

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

      3. mul-1-neg 44.7%

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

      4. sub-neg 44.7%

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

      5. sub-neg 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-178}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right) + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 7: 33.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-88}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + t_1\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (- (* y y3) (* t y2)))))
   (if (<= y -2.5e+156)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -4e-88)
       (* y4 (+ (- (* k (* y1 y2)) (* k (* y b))) t_1))
       (if (<= y 4.2e-264)
         (* (* t y5) (- (* a y2) (* i j)))
         (if (<= y 2.6e-166)
           (* y5 (* y0 (- (* j y3) (* k y2))))
           (if (<= y 7.2e+67)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               t_1))
             (* y5 (* i (- (* y k) (* t j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y <= -2.5e+156) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -4e-88) {
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1);
	} else if (y <= 4.2e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 2.6e-166) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 7.2e+67) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: tmp
    t_1 = c * ((y * y3) - (t * y2))
    if (y <= (-2.5d+156)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-4d-88)) then
        tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1)
    else if (y <= 4.2d-264) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 2.6d-166) then
        tmp = y5 * (y0 * ((j * y3) - (k * y2)))
    else if (y <= 7.2d+67) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y <= -2.5e+156) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -4e-88) {
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1);
	} else if (y <= 4.2e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 2.6e-166) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 7.2e+67) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * ((y * y3) - (t * y2))
	tmp = 0
	if y <= -2.5e+156:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -4e-88:
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1)
	elif y <= 4.2e-264:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 2.6e-166:
		tmp = y5 * (y0 * ((j * y3) - (k * y2)))
	elif y <= 7.2e+67:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (y <= -2.5e+156)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -4e-88)
		tmp = Float64(y4 * Float64(Float64(Float64(k * Float64(y1 * y2)) - Float64(k * Float64(y * b))) + t_1));
	elseif (y <= 4.2e-264)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 2.6e-166)
		tmp = Float64(y5 * Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y <= 7.2e+67)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_1));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = c * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (y <= -2.5e+156)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -4e-88)
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1);
	elseif (y <= 4.2e-264)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 2.6e-166)
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	elseif (y <= 7.2e+67)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+156], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-88], N[(y4 * N[(N[(N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] - N[(k * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-264], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-166], N[(y5 * N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+67], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.49999999999999996e156

   1. Initial program 22.6%

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

   3. Simplified 25.8%

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

   4. Taylor expanded in y around inf 48.6%

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

      1. mul-1-neg 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in y4 around inf 58.4%

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

      1. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -2.49999999999999996e156 < y < -3.99999999999999974e-88

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y4 around inf 48.4%

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

   5. Taylor expanded in j around 0 51.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

      3. *-commutative 51.1%

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

      4. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   if -3.99999999999999974e-88 < y < 4.2000000000000004e-264

   1. Initial program 29.9%

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

   3. Simplified 39.2%

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

   4. Taylor expanded in y5 around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. mul-1-neg 48.7%

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

      3. mul-1-neg 48.7%

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

      4. sub-neg 48.7%

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

      5. sub-neg 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in t around inf 54.9%

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

      1. associate-*r* 51.3%

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

      2. *-commutative 51.3%

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

   9. Simplified 51.3%

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

   if 4.2000000000000004e-264 < y < 2.59999999999999989e-166

   1. Initial program 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in y5 around inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. mul-1-neg 54.8%

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

      3. mul-1-neg 54.8%

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

      4. sub-neg 54.8%

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

      5. sub-neg 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in y0 around inf 59.6%

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

   if 2.59999999999999989e-166 < y < 7.1999999999999998e67

   1. Initial program 25.2%

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

   3. Simplified 25.2%

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

   4. Taylor expanded in y4 around inf 56.3%

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

   if 7.1999999999999998e67 < y

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y5 around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. mul-1-neg 44.7%

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

      3. mul-1-neg 44.7%

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

      4. sub-neg 44.7%

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

      5. sub-neg 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-88}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 8: 34.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-88}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + t_1\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (- (* y y3) (* t y2)))))
   (if (<= y -4.4e+158)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -3.5e-88)
       (* y4 (+ (- (* k (* y1 y2)) (* k (* y b))) t_1))
       (if (<= y 8.6e-264)
         (* (* t y5) (- (* a y2) (* i j)))
         (if (<= y 1.25e-72)
           (*
            y2
            (+
             (+ (* x (- (* c y0) (* a y1))) (* k (- (* y1 y4) (* y0 y5))))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y 4.8e+67)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               t_1))
             (* y5 (* i (- (* y k) (* t j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y <= -4.4e+158) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -3.5e-88) {
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1);
	} else if (y <= 8.6e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 1.25e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 4.8e+67) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: tmp
    t_1 = c * ((y * y3) - (t * y2))
    if (y <= (-4.4d+158)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-3.5d-88)) then
        tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1)
    else if (y <= 8.6d-264) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 1.25d-72) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y <= 4.8d+67) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = c * ((y * y3) - (t * y2));
	double tmp;
	if (y <= -4.4e+158) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -3.5e-88) {
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1);
	} else if (y <= 8.6e-264) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 1.25e-72) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y <= 4.8e+67) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * ((y * y3) - (t * y2))
	tmp = 0
	if y <= -4.4e+158:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -3.5e-88:
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1)
	elif y <= 8.6e-264:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 1.25e-72:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y <= 4.8e+67:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (y <= -4.4e+158)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -3.5e-88)
		tmp = Float64(y4 * Float64(Float64(Float64(k * Float64(y1 * y2)) - Float64(k * Float64(y * b))) + t_1));
	elseif (y <= 8.6e-264)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 1.25e-72)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y <= 4.8e+67)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_1));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = c * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (y <= -4.4e+158)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -3.5e-88)
		tmp = y4 * (((k * (y1 * y2)) - (k * (y * b))) + t_1);
	elseif (y <= 8.6e-264)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 1.25e-72)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y <= 4.8e+67)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+158], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-88], N[(y4 * N[(N[(N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] - N[(k * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-264], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-72], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+67], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.4000000000000002e158

   1. Initial program 22.6%

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

   3. Simplified 25.8%

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

   4. Taylor expanded in y around inf 48.6%

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

      1. mul-1-neg 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in y4 around inf 58.4%

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

      1. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -4.4000000000000002e158 < y < -3.5000000000000001e-88

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y4 around inf 48.4%

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

   5. Taylor expanded in j around 0 51.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

      3. *-commutative 51.1%

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

      4. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   if -3.5000000000000001e-88 < y < 8.5999999999999994e-264

   1. Initial program 29.3%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in y5 around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. mul-1-neg 47.8%

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

      3. mul-1-neg 47.8%

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

      4. sub-neg 47.8%

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

      5. sub-neg 47.8%

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

   6. Simplified 47.8%

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

   7. Taylor expanded in t around inf 53.9%

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

      1. associate-*r* 50.4%

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

      2. *-commutative 50.4%

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

   9. Simplified 50.4%

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

   if 8.5999999999999994e-264 < y < 1.2499999999999999e-72

   1. Initial program 41.1%

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

   3. Simplified 41.1%

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

   4. Taylor expanded in y2 around inf 57.3%

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

   if 1.2499999999999999e-72 < y < 4.80000000000000004e67

   1. Initial program 23.7%

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

   3. Simplified 23.7%

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

   4. Taylor expanded in y4 around inf 65.1%

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

   if 4.80000000000000004e67 < y

   1. Initial program 29.0%

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

   3. Simplified 29.0%

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

   4. Taylor expanded in y5 around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. mul-1-neg 44.7%

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

      3. mul-1-neg 44.7%

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

      4. sub-neg 44.7%

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

      5. sub-neg 44.7%

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

   6. Simplified 44.7%

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

   7. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 56.1%

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

   9. Simplified 56.1%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-88}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-264}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-72}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 9: 31.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-269}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-189}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(t \cdot b - y1 \cdot y3\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+ (- (* k (* y1 y2)) (* k (* y b))) (* c (- (* y y3) (* t y2)))))))
   (if (<= y -4.4e+157)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -3.8e-89)
       t_1
       (if (<= y 9.5e-269)
         (* (* t y5) (- (* a y2) (* i j)))
         (if (<= y 3.8e-189)
           (* y5 (* y0 (- (* j y3) (* k y2))))
           (if (<= y 4.6e-69)
             (* (* j y4) (- (* t b) (* y1 y3)))
             (if (<= y 5.2e+47) t_1 (* y5 (* i (- (* y k) (* t j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (((k * (y1 * y2)) - (k * (y * b))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -4.4e+157) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -3.8e-89) {
		tmp = t_1;
	} else if (y <= 9.5e-269) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 3.8e-189) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 4.6e-69) {
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	} else if (y <= 5.2e+47) {
		tmp = t_1;
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: tmp
    t_1 = y4 * (((k * (y1 * y2)) - (k * (y * b))) + (c * ((y * y3) - (t * y2))))
    if (y <= (-4.4d+157)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-3.8d-89)) then
        tmp = t_1
    else if (y <= 9.5d-269) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 3.8d-189) then
        tmp = y5 * (y0 * ((j * y3) - (k * y2)))
    else if (y <= 4.6d-69) then
        tmp = (j * y4) * ((t * b) - (y1 * y3))
    else if (y <= 5.2d+47) then
        tmp = t_1
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = y4 * (((k * (y1 * y2)) - (k * (y * b))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y <= -4.4e+157) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -3.8e-89) {
		tmp = t_1;
	} else if (y <= 9.5e-269) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 3.8e-189) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 4.6e-69) {
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	} else if (y <= 5.2e+47) {
		tmp = t_1;
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (((k * (y1 * y2)) - (k * (y * b))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y <= -4.4e+157:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -3.8e-89:
		tmp = t_1
	elif y <= 9.5e-269:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 3.8e-189:
		tmp = y5 * (y0 * ((j * y3) - (k * y2)))
	elif y <= 4.6e-69:
		tmp = (j * y4) * ((t * b) - (y1 * y3))
	elif y <= 5.2e+47:
		tmp = t_1
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(Float64(k * Float64(y1 * y2)) - Float64(k * Float64(y * b))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y <= -4.4e+157)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -3.8e-89)
		tmp = t_1;
	elseif (y <= 9.5e-269)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 3.8e-189)
		tmp = Float64(y5 * Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y <= 4.6e-69)
		tmp = Float64(Float64(j * y4) * Float64(Float64(t * b) - Float64(y1 * y3)));
	elseif (y <= 5.2e+47)
		tmp = t_1;
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = y4 * (((k * (y1 * y2)) - (k * (y * b))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y <= -4.4e+157)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -3.8e-89)
		tmp = t_1;
	elseif (y <= 9.5e-269)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 3.8e-189)
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	elseif (y <= 4.6e-69)
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	elseif (y <= 5.2e+47)
		tmp = t_1;
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	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[(y4 * N[(N[(N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] - N[(k * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+157], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-89], t$95$1, If[LessEqual[y, 9.5e-269], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-189], N[(y5 * N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-69], N[(N[(j * y4), $MachinePrecision] * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+47], t$95$1, N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.4000000000000002e157

   1. Initial program 22.6%

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

   3. Simplified 25.8%

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

   4. Taylor expanded in y around inf 48.6%

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

      1. mul-1-neg 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in y4 around inf 58.4%

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

      1. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -4.4000000000000002e157 < y < -3.8000000000000001e-89 or 4.6000000000000001e-69 < y < 5.20000000000000007e47

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   4. Taylor expanded in y4 around inf 52.4%

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

   5. Taylor expanded in j around 0 51.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

      3. *-commutative 51.8%

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

      4. *-commutative 51.8%

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

   7. Simplified 51.8%

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

   if -3.8000000000000001e-89 < y < 9.5000000000000006e-269

   1. Initial program 29.9%

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

   3. Simplified 39.2%

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

   4. Taylor expanded in y5 around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. mul-1-neg 48.7%

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

      3. mul-1-neg 48.7%

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

      4. sub-neg 48.7%

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

      5. sub-neg 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in t around inf 54.9%

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

      1. associate-*r* 51.3%

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

      2. *-commutative 51.3%

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

   9. Simplified 51.3%

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

   if 9.5000000000000006e-269 < y < 3.80000000000000022e-189

   1. Initial program 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in y5 around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. mul-1-neg 58.2%

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

      3. mul-1-neg 58.2%

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

      4. sub-neg 58.2%

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

      5. sub-neg 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in y0 around inf 63.7%

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

   if 3.80000000000000022e-189 < y < 4.6000000000000001e-69

   1. Initial program 27.4%

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

   3. Simplified 27.4%

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

   4. Taylor expanded in y4 around inf 41.6%

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

   5. Taylor expanded in j around inf 51.4%

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

      1. associate-*r* 47.0%

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

      2. mul-1-neg 47.0%

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

      3. unsub-neg 47.0%

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

      4. *-commutative 47.0%

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

   7. Simplified 47.0%

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

   if 5.20000000000000007e47 < y

   1. Initial program 30.3%

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

   3. Simplified 32.2%

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

   4. Taylor expanded in y5 around inf 43.8%

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

      1. mul-1-neg 43.8%

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

      2. mul-1-neg 43.8%

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

      3. mul-1-neg 43.8%

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

      4. sub-neg 43.8%

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

      5. sub-neg 43.8%

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

   6. Simplified 43.8%

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

   7. Taylor expanded in i around inf 55.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 55.3%

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

   9. Simplified 55.3%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-269}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-189}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(t \cdot b - y1 \cdot y3\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+47}:\\ \;\;\;\;y4 \cdot \left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 10: 30.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot a - k \cdot y4\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \left(b \cdot t_1\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-269}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-188}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(t \cdot b - y1 \cdot y3\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+24}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+80}:\\ \;\;\;\;\left(y \cdot b\right) \cdot t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+147}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x a) (* k y4))))
   (if (<= y -3.5e-18)
     (* y4 (* y (- (* c y3) (* b k))))
     (if (<= y -4.1e-67)
       (* y2 (* k (- (* y1 y4) (* y0 y5))))
       (if (<= y -2e-82)
         (* y (* b t_1))
         (if (<= y 1.45e-269)
           (* (* t y5) (- (* a y2) (* i j)))
           (if (<= y 4.2e-188)
             (* y5 (* y0 (- (* j y3) (* k y2))))
             (if (<= y 2e-69)
               (* (* j y4) (- (* t b) (* y1 y3)))
               (if (<= y 8e+24)
                 (* y4 (+ (* k (* y1 y2)) (* c (- (* y y3) (* t y2)))))
                 (if (<= y 5.5e+47)
                   (* c (* t (- (* z i) (* y2 y4))))
                   (if (<= y 9e+80)
                     (* (* y b) t_1)
                     (if (<= y 4.6e+147)
                       (* y1 (* a (- (* z y3) (* x y2))))
                       (* y5 (* i (- (* y k) (* t j))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * a) - (k * y4);
	double tmp;
	if (y <= -3.5e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -4.1e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -2e-82) {
		tmp = y * (b * t_1);
	} else if (y <= 1.45e-269) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 4.2e-188) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 2e-69) {
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	} else if (y <= 8e+24) {
		tmp = y4 * ((k * (y1 * y2)) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 5.5e+47) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y <= 9e+80) {
		tmp = (y * b) * t_1;
	} else if (y <= 4.6e+147) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: tmp
    t_1 = (x * a) - (k * y4)
    if (y <= (-3.5d-18)) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (y <= (-4.1d-67)) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (y <= (-2d-82)) then
        tmp = y * (b * t_1)
    else if (y <= 1.45d-269) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 4.2d-188) then
        tmp = y5 * (y0 * ((j * y3) - (k * y2)))
    else if (y <= 2d-69) then
        tmp = (j * y4) * ((t * b) - (y1 * y3))
    else if (y <= 8d+24) then
        tmp = y4 * ((k * (y1 * y2)) + (c * ((y * y3) - (t * y2))))
    else if (y <= 5.5d+47) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y <= 9d+80) then
        tmp = (y * b) * t_1
    else if (y <= 4.6d+147) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = (x * a) - (k * y4);
	double tmp;
	if (y <= -3.5e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -4.1e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -2e-82) {
		tmp = y * (b * t_1);
	} else if (y <= 1.45e-269) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 4.2e-188) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 2e-69) {
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	} else if (y <= 8e+24) {
		tmp = y4 * ((k * (y1 * y2)) + (c * ((y * y3) - (t * y2))));
	} else if (y <= 5.5e+47) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y <= 9e+80) {
		tmp = (y * b) * t_1;
	} else if (y <= 4.6e+147) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * a) - (k * y4)
	tmp = 0
	if y <= -3.5e-18:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif y <= -4.1e-67:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif y <= -2e-82:
		tmp = y * (b * t_1)
	elif y <= 1.45e-269:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 4.2e-188:
		tmp = y5 * (y0 * ((j * y3) - (k * y2)))
	elif y <= 2e-69:
		tmp = (j * y4) * ((t * b) - (y1 * y3))
	elif y <= 8e+24:
		tmp = y4 * ((k * (y1 * y2)) + (c * ((y * y3) - (t * y2))))
	elif y <= 5.5e+47:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y <= 9e+80:
		tmp = (y * b) * t_1
	elif y <= 4.6e+147:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * a) - Float64(k * y4))
	tmp = 0.0
	if (y <= -3.5e-18)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -4.1e-67)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y <= -2e-82)
		tmp = Float64(y * Float64(b * t_1));
	elseif (y <= 1.45e-269)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 4.2e-188)
		tmp = Float64(y5 * Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y <= 2e-69)
		tmp = Float64(Float64(j * y4) * Float64(Float64(t * b) - Float64(y1 * y3)));
	elseif (y <= 8e+24)
		tmp = Float64(y4 * Float64(Float64(k * Float64(y1 * y2)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 5.5e+47)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y <= 9e+80)
		tmp = Float64(Float64(y * b) * t_1);
	elseif (y <= 4.6e+147)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = (x * a) - (k * y4);
	tmp = 0.0;
	if (y <= -3.5e-18)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (y <= -4.1e-67)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (y <= -2e-82)
		tmp = y * (b * t_1);
	elseif (y <= 1.45e-269)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 4.2e-188)
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	elseif (y <= 2e-69)
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	elseif (y <= 8e+24)
		tmp = y4 * ((k * (y1 * y2)) + (c * ((y * y3) - (t * y2))));
	elseif (y <= 5.5e+47)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y <= 9e+80)
		tmp = (y * b) * t_1;
	elseif (y <= 4.6e+147)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	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[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-18], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e-67], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-82], N[(y * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-269], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-188], N[(y5 * N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-69], N[(N[(j * y4), $MachinePrecision] * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+24], N[(y4 * N[(N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+47], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+80], N[(N[(y * b), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y, 4.6e+147], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if y < -3.4999999999999999e-18

   1. Initial program 25.4%

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

   3. Simplified 25.4%

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

   4. Taylor expanded in y4 around inf 49.5%

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

   5. Taylor expanded in j around 0 46.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.8%

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

      2. unsub-neg 46.8%

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

      3. *-commutative 46.8%

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

      4. *-commutative 46.8%

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

   7. Simplified 46.8%

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

   8. Taylor expanded in y2 around 0 39.5%

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

      1. +-commutative 39.5%

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

      2. distribute-lft-in 39.5%

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

      3. associate-*r* 39.5%

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

      4. neg-mul-1 39.5%

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

      5. mul-1-neg 39.5%

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

      6. mul-1-neg 39.5%

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

      7. remove-double-neg 39.5%

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

      8. *-commutative 39.5%

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

      9. associate-*r* 39.6%

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

      10. *-commutative 39.6%

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

      11. associate-*r* 41.1%

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

      12. neg-mul-1 41.1%

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

      13. associate-*r* 41.1%

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

      14. distribute-rgt-in 48.5%

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

      15. mul-1-neg 48.5%

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

      16. unsub-neg 48.5%

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

      17. *-commutative 48.5%

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

   10. Simplified 48.5%

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

   if -3.4999999999999999e-18 < y < -4.0999999999999997e-67

   1. Initial program 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in y2 around inf 46.6%

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

   5. Taylor expanded in k around inf 55.0%

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

   if -4.0999999999999997e-67 < y < -2e-82

   1. Initial program 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in y around inf 33.3%

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

      1. mul-1-neg 33.3%

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

   6. Simplified 33.3%

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

   7. Taylor expanded in b around inf 100.0%

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

   if -2e-82 < y < 1.45e-269

   1. Initial program 29.9%

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

   3. Simplified 39.2%

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

   4. Taylor expanded in y5 around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. mul-1-neg 48.7%

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

      3. mul-1-neg 48.7%

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

      4. sub-neg 48.7%

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

      5. sub-neg 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in t around inf 54.9%

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

      1. associate-*r* 51.3%

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

      2. *-commutative 51.3%

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

   9. Simplified 51.3%

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

   if 1.45e-269 < y < 4.1999999999999998e-188

   1. Initial program 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in y5 around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. mul-1-neg 58.2%

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

      3. mul-1-neg 58.2%

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

      4. sub-neg 58.2%

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

      5. sub-neg 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in y0 around inf 63.7%

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

   if 4.1999999999999998e-188 < y < 1.9999999999999999e-69

   1. Initial program 27.4%

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

   3. Simplified 27.4%

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

   4. Taylor expanded in y4 around inf 41.6%

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

   5. Taylor expanded in j around inf 51.4%

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

      1. associate-*r* 47.0%

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

      2. mul-1-neg 47.0%

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

      3. unsub-neg 47.0%

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

      4. *-commutative 47.0%

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

   7. Simplified 47.0%

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

   if 1.9999999999999999e-69 < y < 7.9999999999999999e24

   1. Initial program 17.0%

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

   3. Simplified 17.0%

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

   4. Taylor expanded in y4 around inf 67.1%

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

   5. Taylor expanded in j around 0 62.3%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 62.3%

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

      2. unsub-neg 62.3%

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

      3. *-commutative 62.3%

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

      4. *-commutative 62.3%

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

   7. Simplified 62.3%

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

   8. Taylor expanded in b around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   10. Simplified 50.9%

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

   if 7.9999999999999999e24 < y < 5.4999999999999998e47

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in c around inf 56.8%

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

   5. Taylor expanded in t around inf 57.8%

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

   if 5.4999999999999998e47 < y < 9.00000000000000013e80

   1. Initial program 40.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in y around inf 52.4%

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

      1. mul-1-neg 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in b around inf 61.2%

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

      1. associate-*r* 61.4%

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

   9. Simplified 61.4%

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

   if 9.00000000000000013e80 < y < 4.5999999999999998e147

   1. Initial program 21.9%

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

   3. Simplified 21.9%

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

   4. Taylor expanded in y1 around inf 28.5%

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

      1. mul-1-neg 28.5%

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

      2. mul-1-neg 28.5%

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

      3. sub-neg 28.5%

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

   6. Simplified 28.5%

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

   7. Taylor expanded in a around inf 57.5%

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

   if 4.5999999999999998e147 < y

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in y5 around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. mul-1-neg 51.8%

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

      3. mul-1-neg 51.8%

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

      4. sub-neg 51.8%

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

      5. sub-neg 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in i around inf 69.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 69.1%

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

   9. Simplified 69.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 11 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-269}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-188}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(t \cdot b - y1 \cdot y3\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+24}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+80}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \left(x \cdot a - k \cdot y4\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+147}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 11: 30.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+218}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-242}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+38}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right) + c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+225}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k)))))
        (t_2 (* y2 (* c (- (* x y0) (* t y4))))))
   (if (<= a -2.4e+218)
     (* y2 (* y1 (- (* k y4) (* x a))))
     (if (<= a -1.18e+135)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= a -5.5e+25)
         (* c (* z (- (* t i) (* y0 y3))))
         (if (<= a -1.5e-185)
           t_1
           (if (<= a -2.75e-242)
             (* y (* y4 (- (* c y3) (* b k))))
             (if (<= a -7e-250)
               t_1
               (if (<= a 3.6e+38)
                 (* y4 (+ (* k (- (* y1 y2) (* y b))) (* c (* y y3))))
                 (if (<= a 1.9e+70)
                   t_2
                   (if (<= a 7e+158)
                     (* x (* y (- (* a b) (* c i))))
                     (if (<= a 6.6e+225)
                       t_2
                       (* (* t y5) (- (* a y2) (* i j)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = y2 * (c * ((x * y0) - (t * y4)));
	double tmp;
	if (a <= -2.4e+218) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (a <= -1.18e+135) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (a <= -5.5e+25) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (a <= -1.5e-185) {
		tmp = t_1;
	} else if (a <= -2.75e-242) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (a <= -7e-250) {
		tmp = t_1;
	} else if (a <= 3.6e+38) {
		tmp = y4 * ((k * ((y1 * y2) - (y * b))) + (c * (y * y3)));
	} else if (a <= 1.9e+70) {
		tmp = t_2;
	} else if (a <= 7e+158) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (a <= 6.6e+225) {
		tmp = t_2;
	} else {
		tmp = (t * y5) * ((a * y2) - (i * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * (i * ((x * j) - (z * k)))
    t_2 = y2 * (c * ((x * y0) - (t * y4)))
    if (a <= (-2.4d+218)) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (a <= (-1.18d+135)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (a <= (-5.5d+25)) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (a <= (-1.5d-185)) then
        tmp = t_1
    else if (a <= (-2.75d-242)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (a <= (-7d-250)) then
        tmp = t_1
    else if (a <= 3.6d+38) then
        tmp = y4 * ((k * ((y1 * y2) - (y * b))) + (c * (y * y3)))
    else if (a <= 1.9d+70) then
        tmp = t_2
    else if (a <= 7d+158) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (a <= 6.6d+225) then
        tmp = t_2
    else
        tmp = (t * y5) * ((a * y2) - (i * 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 t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = y2 * (c * ((x * y0) - (t * y4)));
	double tmp;
	if (a <= -2.4e+218) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (a <= -1.18e+135) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (a <= -5.5e+25) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (a <= -1.5e-185) {
		tmp = t_1;
	} else if (a <= -2.75e-242) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (a <= -7e-250) {
		tmp = t_1;
	} else if (a <= 3.6e+38) {
		tmp = y4 * ((k * ((y1 * y2) - (y * b))) + (c * (y * y3)));
	} else if (a <= 1.9e+70) {
		tmp = t_2;
	} else if (a <= 7e+158) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (a <= 6.6e+225) {
		tmp = t_2;
	} else {
		tmp = (t * y5) * ((a * y2) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (i * ((x * j) - (z * k)))
	t_2 = y2 * (c * ((x * y0) - (t * y4)))
	tmp = 0
	if a <= -2.4e+218:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif a <= -1.18e+135:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif a <= -5.5e+25:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif a <= -1.5e-185:
		tmp = t_1
	elif a <= -2.75e-242:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif a <= -7e-250:
		tmp = t_1
	elif a <= 3.6e+38:
		tmp = y4 * ((k * ((y1 * y2) - (y * b))) + (c * (y * y3)))
	elif a <= 1.9e+70:
		tmp = t_2
	elif a <= 7e+158:
		tmp = x * (y * ((a * b) - (c * i)))
	elif a <= 6.6e+225:
		tmp = t_2
	else:
		tmp = (t * y5) * ((a * y2) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (a <= -2.4e+218)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (a <= -1.18e+135)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (a <= -5.5e+25)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (a <= -1.5e-185)
		tmp = t_1;
	elseif (a <= -2.75e-242)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (a <= -7e-250)
		tmp = t_1;
	elseif (a <= 3.6e+38)
		tmp = Float64(y4 * Float64(Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))) + Float64(c * Float64(y * y3))));
	elseif (a <= 1.9e+70)
		tmp = t_2;
	elseif (a <= 7e+158)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (a <= 6.6e+225)
		tmp = t_2;
	else
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * 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)
	t_1 = y1 * (i * ((x * j) - (z * k)));
	t_2 = y2 * (c * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (a <= -2.4e+218)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (a <= -1.18e+135)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (a <= -5.5e+25)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (a <= -1.5e-185)
		tmp = t_1;
	elseif (a <= -2.75e-242)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (a <= -7e-250)
		tmp = t_1;
	elseif (a <= 3.6e+38)
		tmp = y4 * ((k * ((y1 * y2) - (y * b))) + (c * (y * y3)));
	elseif (a <= 1.9e+70)
		tmp = t_2;
	elseif (a <= 7e+158)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (a <= 6.6e+225)
		tmp = t_2;
	else
		tmp = (t * y5) * ((a * y2) - (i * j));
	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[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+218], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.18e+135], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e+25], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-185], t$95$1, If[LessEqual[a, -2.75e-242], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-250], t$95$1, If[LessEqual[a, 3.6e+38], N[(y4 * N[(N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+70], t$95$2, If[LessEqual[a, 7e+158], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e+225], t$95$2, N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if a < -2.39999999999999981e218

   1. Initial program 36.8%

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

   3. Simplified 36.8%

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

   4. Taylor expanded in y2 around inf 63.3%

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

   5. Taylor expanded in y1 around inf 63.4%

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

      1. associate-*r* 63.4%

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

      2. +-commutative 63.4%

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

      3. mul-1-neg 63.4%

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

      4. unsub-neg 63.4%

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

   7. Simplified 63.4%

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

   if -2.39999999999999981e218 < a < -1.18000000000000002e135

   1. Initial program 27.3%

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

   3. Simplified 27.3%

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

   4. Taylor expanded in c around inf 50.6%

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

   5. Taylor expanded in t around inf 55.7%

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

   if -1.18000000000000002e135 < a < -5.50000000000000018e25

   1. Initial program 38.8%

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

   3. Simplified 38.8%

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

   4. Taylor expanded in c around inf 26.6%

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

   5. Taylor expanded in z around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot z\right) \]

      4. *-commutative 52.5%

         \[\leadsto c \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot z\right) \]

      5. *-commutative 52.5%

         \[\leadsto c \cdot \left(\left(t \cdot i - \color{blue}{y3 \cdot y0}\right) \cdot z\right) \]

   7. Simplified 52.5%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot i - y3 \cdot y0\right) \cdot z\right)} \]

   if -5.50000000000000018e25 < a < -1.50000000000000015e-185 or -2.7499999999999999e-242 < a < -6.9999999999999998e-250

   1. Initial program 32.8%

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

   3. Simplified 35.1%

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

   4. Taylor expanded in y1 around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. mul-1-neg 47.2%

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

      3. sub-neg 47.2%

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

   6. Simplified 47.2%

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

   7. Taylor expanded in i around inf 50.0%

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

   if -1.50000000000000015e-185 < a < -2.7499999999999999e-242

   1. Initial program 20.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in y around inf 30.5%

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

      1. mul-1-neg 30.5%

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

   6. Simplified 30.5%

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

   7. Taylor expanded in y4 around inf 70.3%

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

      1. *-commutative 70.3%

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

   9. Simplified 70.3%

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

   if -6.9999999999999998e-250 < a < 3.59999999999999969e38

   1. Initial program 28.0%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in y4 around inf 50.3%

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

   5. Taylor expanded in j around 0 53.4%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

      3. *-commutative 53.4%

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

      4. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   8. Taylor expanded in t around 0 50.9%

      \[\leadsto \color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - \left(k \cdot \left(y \cdot b\right) + -1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right)\right)} \cdot y4 \]
   9. Step-by-step derivation

      1. associate--r+ 50.9%

         \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right) - -1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right)} \cdot y4 \]

      2. distribute-lft-out-- 50.9%

         \[\leadsto \left(\color{blue}{k \cdot \left(y1 \cdot y2 - y \cdot b\right)} - -1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) \cdot y4 \]

      3. *-commutative 50.9%

         \[\leadsto \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right) - -1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) \cdot y4 \]

      4. mul-1-neg 50.9%

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

   10. Simplified 50.9%

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

   if 3.59999999999999969e38 < a < 1.8999999999999999e70 or 7.0000000000000003e158 < a < 6.6000000000000001e225

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y2 around inf 50.0%

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

   5. Taylor expanded in c around inf 71.7%

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

   if 1.8999999999999999e70 < a < 7.0000000000000003e158

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in y around inf 35.6%

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

      1. mul-1-neg 35.6%

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

   6. Simplified 35.6%

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

   7. Taylor expanded in x around inf 71.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 76.9%

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

      2. *-commutative 76.9%

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

   9. Simplified 76.9%

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

   if 6.6000000000000001e225 < a

   1. Initial program 11.1%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in y5 around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. mul-1-neg 55.6%

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

      3. mul-1-neg 55.6%

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

      4. sub-neg 55.6%

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

      5. sub-neg 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in t around inf 61.6%

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

      1. associate-*r* 61.6%

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

      2. *-commutative 61.6%

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

   9. Simplified 61.6%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+218}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+25}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-185}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-242}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-250}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+38}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right) + c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+225}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \end{array} \]

Alternative 12: 32.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ t_2 := y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{if}\;i \leq -2 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-261}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 3.65 \cdot 10^{-41}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y5 (* i (- (* y k) (* t j)))))
        (t_2 (* y2 (* c (- (* x y0) (* t y4))))))
   (if (<= i -2e+97)
     t_1
     (if (<= i -2.3e-66)
       (* c (* y0 (- (* x y2) (* z y3))))
       (if (<= i -7e-156)
         (* y (* b (- (* x a) (* k y4))))
         (if (<= i -5.5e-261)
           t_2
           (if (<= i 4.1e-241)
             (* y (* y4 (- (* c y3) (* b k))))
             (if (<= i 2.5e-169)
               (* a (* t (* y2 y5)))
               (if (<= i 1.7e-100)
                 (* y4 (* k (- (* y1 y2) (* y b))))
                 (if (<= i 3.65e-41)
                   (* (* j y5) (- (* y0 y3) (* t i)))
                   (if (<= i 2.65e+78) t_2 t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y5 * (i * ((y * k) - (t * j)));
	double t_2 = y2 * (c * ((x * y0) - (t * y4)));
	double tmp;
	if (i <= -2e+97) {
		tmp = t_1;
	} else if (i <= -2.3e-66) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (i <= -7e-156) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (i <= -5.5e-261) {
		tmp = t_2;
	} else if (i <= 4.1e-241) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (i <= 2.5e-169) {
		tmp = a * (t * (y2 * y5));
	} else if (i <= 1.7e-100) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (i <= 3.65e-41) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (i <= 2.65e+78) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y5 * (i * ((y * k) - (t * j)))
    t_2 = y2 * (c * ((x * y0) - (t * y4)))
    if (i <= (-2d+97)) then
        tmp = t_1
    else if (i <= (-2.3d-66)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (i <= (-7d-156)) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (i <= (-5.5d-261)) then
        tmp = t_2
    else if (i <= 4.1d-241) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (i <= 2.5d-169) then
        tmp = a * (t * (y2 * y5))
    else if (i <= 1.7d-100) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (i <= 3.65d-41) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (i <= 2.65d+78) then
        tmp = t_2
    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 = y5 * (i * ((y * k) - (t * j)));
	double t_2 = y2 * (c * ((x * y0) - (t * y4)));
	double tmp;
	if (i <= -2e+97) {
		tmp = t_1;
	} else if (i <= -2.3e-66) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (i <= -7e-156) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (i <= -5.5e-261) {
		tmp = t_2;
	} else if (i <= 4.1e-241) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (i <= 2.5e-169) {
		tmp = a * (t * (y2 * y5));
	} else if (i <= 1.7e-100) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (i <= 3.65e-41) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (i <= 2.65e+78) {
		tmp = t_2;
	} 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 = y5 * (i * ((y * k) - (t * j)))
	t_2 = y2 * (c * ((x * y0) - (t * y4)))
	tmp = 0
	if i <= -2e+97:
		tmp = t_1
	elif i <= -2.3e-66:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif i <= -7e-156:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif i <= -5.5e-261:
		tmp = t_2
	elif i <= 4.1e-241:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif i <= 2.5e-169:
		tmp = a * (t * (y2 * y5))
	elif i <= 1.7e-100:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif i <= 3.65e-41:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif i <= 2.65e+78:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * j))))
	t_2 = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))))
	tmp = 0.0
	if (i <= -2e+97)
		tmp = t_1;
	elseif (i <= -2.3e-66)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (i <= -7e-156)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (i <= -5.5e-261)
		tmp = t_2;
	elseif (i <= 4.1e-241)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (i <= 2.5e-169)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (i <= 1.7e-100)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (i <= 3.65e-41)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (i <= 2.65e+78)
		tmp = t_2;
	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 = y5 * (i * ((y * k) - (t * j)));
	t_2 = y2 * (c * ((x * y0) - (t * y4)));
	tmp = 0.0;
	if (i <= -2e+97)
		tmp = t_1;
	elseif (i <= -2.3e-66)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (i <= -7e-156)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (i <= -5.5e-261)
		tmp = t_2;
	elseif (i <= 4.1e-241)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (i <= 2.5e-169)
		tmp = a * (t * (y2 * y5));
	elseif (i <= 1.7e-100)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (i <= 3.65e-41)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (i <= 2.65e+78)
		tmp = t_2;
	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[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2e+97], t$95$1, If[LessEqual[i, -2.3e-66], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7e-156], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.5e-261], t$95$2, If[LessEqual[i, 4.1e-241], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e-169], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e-100], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.65e-41], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.65e+78], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -2.0000000000000001e97 or 2.64999999999999981e78 < i

   1. Initial program 23.6%

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

   3. Simplified 25.6%

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

   4. Taylor expanded in y5 around inf 45.3%

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

      1. mul-1-neg 45.3%

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

      2. mul-1-neg 45.3%

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

      3. mul-1-neg 45.3%

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

      4. sub-neg 45.3%

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

      5. sub-neg 45.3%

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

   6. Simplified 45.3%

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

   7. Taylor expanded in i around inf 55.8%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 55.8%

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

   9. Simplified 55.8%

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

   if -2.0000000000000001e97 < i < -2.29999999999999992e-66

   1. Initial program 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in c around inf 47.3%

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

   5. Taylor expanded in y0 around inf 55.5%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.5%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 55.5%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if -2.29999999999999992e-66 < i < -6.9999999999999999e-156

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in y around inf 22.6%

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

      1. mul-1-neg 22.6%

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

   6. Simplified 22.6%

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

   7. Taylor expanded in b around inf 57.9%

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

   if -6.9999999999999999e-156 < i < -5.50000000000000042e-261 or 3.65000000000000013e-41 < i < 2.64999999999999981e78

   1. Initial program 32.5%

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

   3. Simplified 32.5%

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

   4. Taylor expanded in y2 around inf 47.8%

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

   5. Taylor expanded in c around inf 58.3%

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

   if -5.50000000000000042e-261 < i < 4.0999999999999999e-241

   1. Initial program 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in y around inf 44.5%

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

      1. mul-1-neg 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in y4 around inf 53.9%

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

      1. *-commutative 53.9%

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

   9. Simplified 53.9%

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

   if 4.0999999999999999e-241 < i < 2.5000000000000001e-169

   1. Initial program 24.2%

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

   3. Simplified 35.9%

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

   4. Taylor expanded in y5 around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. mul-1-neg 47.8%

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

      3. mul-1-neg 47.8%

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

      4. sub-neg 47.8%

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

      5. sub-neg 47.8%

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

   6. Simplified 47.8%

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

   7. Taylor expanded in t around inf 31.9%

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

      1. associate-*r* 31.9%

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

      2. *-commutative 31.9%

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

   9. Simplified 31.9%

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

   10. Taylor expanded in a around inf 37.3%

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

   if 2.5000000000000001e-169 < i < 1.69999999999999988e-100

   1. Initial program 47.6%

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

   3. Simplified 47.6%

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

   4. Taylor expanded in y4 around inf 62.4%

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

   5. Taylor expanded in k around inf 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. *-commutative 48.2%

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

   7. Simplified 48.2%

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

   if 1.69999999999999988e-100 < i < 3.65000000000000013e-41

   1. Initial program 27.8%

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

   3. Simplified 36.9%

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

   4. Taylor expanded in y5 around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. mul-1-neg 55.5%

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

      3. mul-1-neg 55.5%

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

      4. sub-neg 55.5%

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

      5. sub-neg 55.5%

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

   6. Simplified 55.5%

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

   7. Taylor expanded in j around -inf 64.5%

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

      1. *-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

      4. *-commutative 64.5%

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

      5. *-commutative 64.5%

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

   9. Simplified 64.5%

      \[\leadsto \color{blue}{\left(j \cdot y5\right) \cdot \left(y3 \cdot y0 - t \cdot i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+97}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq -7 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-261}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 3.65 \cdot 10^{-41}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{+78}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 13: 29.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{if}\;y0 \leq -4.8 \cdot 10^{+256}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.3 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.55 \cdot 10^{+142}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.42 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{+245}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (- (* x i) (* y3 y4))))))
   (if (<= y0 -4.8e+256)
     (* y2 (* x (* c y0)))
     (if (<= y0 -1.95e-35)
       (* c (* z (- (* t i) (* y0 y3))))
       (if (<= y0 -1.3e-165)
         t_1
         (if (<= y0 1.1e-21)
           (* y (* b (- (* x a) (* k y4))))
           (if (<= y0 2e+53)
             (* i (* j (* t (- y5))))
             (if (<= y0 1.55e+142)
               (* c (* t (- (* z i) (* y2 y4))))
               (if (<= y0 1.42e+209)
                 t_1
                 (if (<= y0 2.1e+245)
                   (* (* y1 y2) (* k y4))
                   (* c (* y0 (- (* x y2) (* 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 t_1 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y0 <= -4.8e+256) {
		tmp = y2 * (x * (c * y0));
	} else if (y0 <= -1.95e-35) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y0 <= -1.3e-165) {
		tmp = t_1;
	} else if (y0 <= 1.1e-21) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y0 <= 2e+53) {
		tmp = i * (j * (t * -y5));
	} else if (y0 <= 1.55e+142) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y0 <= 1.42e+209) {
		tmp = t_1;
	} else if (y0 <= 2.1e+245) {
		tmp = (y1 * y2) * (k * y4);
	} else {
		tmp = c * (y0 * ((x * y2) - (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) :: t_1
    real(8) :: tmp
    t_1 = j * (y1 * ((x * i) - (y3 * y4)))
    if (y0 <= (-4.8d+256)) then
        tmp = y2 * (x * (c * y0))
    else if (y0 <= (-1.95d-35)) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (y0 <= (-1.3d-165)) then
        tmp = t_1
    else if (y0 <= 1.1d-21) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (y0 <= 2d+53) then
        tmp = i * (j * (t * -y5))
    else if (y0 <= 1.55d+142) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (y0 <= 1.42d+209) then
        tmp = t_1
    else if (y0 <= 2.1d+245) then
        tmp = (y1 * y2) * (k * y4)
    else
        tmp = c * (y0 * ((x * y2) - (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 t_1 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (y0 <= -4.8e+256) {
		tmp = y2 * (x * (c * y0));
	} else if (y0 <= -1.95e-35) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y0 <= -1.3e-165) {
		tmp = t_1;
	} else if (y0 <= 1.1e-21) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y0 <= 2e+53) {
		tmp = i * (j * (t * -y5));
	} else if (y0 <= 1.55e+142) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (y0 <= 1.42e+209) {
		tmp = t_1;
	} else if (y0 <= 2.1e+245) {
		tmp = (y1 * y2) * (k * y4);
	} else {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y1 * ((x * i) - (y3 * y4)))
	tmp = 0
	if y0 <= -4.8e+256:
		tmp = y2 * (x * (c * y0))
	elif y0 <= -1.95e-35:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif y0 <= -1.3e-165:
		tmp = t_1
	elif y0 <= 1.1e-21:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif y0 <= 2e+53:
		tmp = i * (j * (t * -y5))
	elif y0 <= 1.55e+142:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif y0 <= 1.42e+209:
		tmp = t_1
	elif y0 <= 2.1e+245:
		tmp = (y1 * y2) * (k * y4)
	else:
		tmp = c * (y0 * ((x * y2) - (z * 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(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	tmp = 0.0
	if (y0 <= -4.8e+256)
		tmp = Float64(y2 * Float64(x * Float64(c * y0)));
	elseif (y0 <= -1.95e-35)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y0 <= -1.3e-165)
		tmp = t_1;
	elseif (y0 <= 1.1e-21)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y0 <= 2e+53)
		tmp = Float64(i * Float64(j * Float64(t * Float64(-y5))));
	elseif (y0 <= 1.55e+142)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (y0 <= 1.42e+209)
		tmp = t_1;
	elseif (y0 <= 2.1e+245)
		tmp = Float64(Float64(y1 * y2) * Float64(k * y4));
	else
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - 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)
	t_1 = j * (y1 * ((x * i) - (y3 * y4)));
	tmp = 0.0;
	if (y0 <= -4.8e+256)
		tmp = y2 * (x * (c * y0));
	elseif (y0 <= -1.95e-35)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (y0 <= -1.3e-165)
		tmp = t_1;
	elseif (y0 <= 1.1e-21)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (y0 <= 2e+53)
		tmp = i * (j * (t * -y5));
	elseif (y0 <= 1.55e+142)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (y0 <= 1.42e+209)
		tmp = t_1;
	elseif (y0 <= 2.1e+245)
		tmp = (y1 * y2) * (k * y4);
	else
		tmp = c * (y0 * ((x * y2) - (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_] := Block[{t$95$1 = N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.8e+256], N[(y2 * N[(x * N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.95e-35], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.3e-165], t$95$1, If[LessEqual[y0, 1.1e-21], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2e+53], N[(i * N[(j * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.55e+142], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.42e+209], t$95$1, If[LessEqual[y0, 2.1e+245], N[(N[(y1 * y2), $MachinePrecision] * N[(k * y4), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -4.80000000000000028e256

   1. Initial program 16.7%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in y2 around inf 41.7%

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

   5. Taylor expanded in x around inf 66.7%

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

   6. Taylor expanded in c around inf 75.4%

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

   if -4.80000000000000028e256 < y0 < -1.9499999999999999e-35

   1. Initial program 25.9%

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

   3. Simplified 25.9%

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

   4. Taylor expanded in c around inf 40.5%

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

   5. Taylor expanded in z around inf 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot z\right) \]

      4. *-commutative 45.1%

         \[\leadsto c \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot z\right) \]

      5. *-commutative 45.1%

         \[\leadsto c \cdot \left(\left(t \cdot i - \color{blue}{y3 \cdot y0}\right) \cdot z\right) \]

   7. Simplified 45.1%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot i - y3 \cdot y0\right) \cdot z\right)} \]

   if -1.9499999999999999e-35 < y0 < -1.30000000000000004e-165 or 1.55e142 < y0 < 1.42000000000000004e209

   1. Initial program 30.3%

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

   3. Simplified 39.3%

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

   4. Taylor expanded in y1 around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. mul-1-neg 51.9%

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

      3. sub-neg 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in j around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

      3. *-commutative 55.7%

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

      4. associate-*l* 58.5%

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

      5. mul-1-neg 58.5%

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

      6. unsub-neg 58.5%

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

   9. Simplified 58.5%

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

   if -1.30000000000000004e-165 < y0 < 1.1e-21

   1. Initial program 38.2%

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

   3. Simplified 41.5%

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

   4. Taylor expanded in y around inf 40.3%

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

      1. mul-1-neg 40.3%

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

   6. Simplified 40.3%

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

   7. Taylor expanded in b around inf 39.4%

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

   if 1.1e-21 < y0 < 2e53

   1. Initial program 21.7%

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

   3. Simplified 26.1%

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

   4. Taylor expanded in y5 around inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. mul-1-neg 47.9%

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

      3. mul-1-neg 47.9%

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

      4. sub-neg 47.9%

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

      5. sub-neg 47.9%

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

   6. Simplified 47.9%

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

   7. Taylor expanded in t around inf 48.4%

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

      1. associate-*r* 44.3%

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

      2. *-commutative 44.3%

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

   9. Simplified 44.3%

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

   10. Taylor expanded in a around 0 44.9%

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

       1. mul-1-neg 44.9%

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

       2. *-commutative 44.9%

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

       3. distribute-rgt-neg-in 44.9%

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

       4. *-commutative 44.9%

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

       5. associate-*l* 48.9%

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

       6. *-commutative 48.9%

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

   12. Simplified 48.9%

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

   if 2e53 < y0 < 1.55e142

   1. Initial program 22.4%

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

   3. Simplified 22.4%

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

   4. Taylor expanded in c around inf 35.2%

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

   5. Taylor expanded in t around inf 44.6%

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

   if 1.42000000000000004e209 < y0 < 2.09999999999999996e245

   1. Initial program 16.7%

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

   3. Simplified 16.7%

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

   4. Taylor expanded in y4 around inf 33.3%

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

   5. Taylor expanded in j around 0 33.3%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 33.3%

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

      2. unsub-neg 33.3%

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

      3. *-commutative 33.3%

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

      4. *-commutative 33.3%

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

   7. Simplified 33.3%

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

   8. Taylor expanded in y1 around inf 36.0%

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

      1. associate-*r* 67.6%

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

      2. *-commutative 67.6%

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

      3. *-commutative 67.6%

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

   10. Simplified 67.6%

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

   if 2.09999999999999996e245 < y0

   1. Initial program 23.9%

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

   3. Simplified 23.9%

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

   4. Taylor expanded in c around inf 47.2%

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

   5. Taylor expanded in y0 around inf 65.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 65.2%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 65.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.8 \cdot 10^{+256}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.95 \cdot 10^{-35}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.3 \cdot 10^{-165}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.1 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.55 \cdot 10^{+142}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.42 \cdot 10^{+209}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{+245}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]

Alternative 14: 32.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ t_2 := c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{if}\;z \leq -2.42 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-288}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 1.15:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4)))))
        (t_2 (* c (* z (- (* t i) (* y0 y3))))))
   (if (<= z -2.42e-26)
     t_2
     (if (<= z -9.6e-120)
       t_1
       (if (<= z 4e-288)
         (* y4 (* k (- (* y1 y2) (* y b))))
         (if (<= z 5.4e-66)
           (* y (* y4 (- (* c y3) (* b k))))
           (if (<= z 1.15)
             (* y2 (* c (- (* x y0) (* t y4))))
             (if (<= z 3.2e+35)
               (* y (* b (- (* x a) (* k y4))))
               (if (<= z 9.2e+60)
                 (* y1 (* i (- (* x j) (* z k))))
                 (if (<= z 3.55e+177) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double t_2 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (z <= -2.42e-26) {
		tmp = t_2;
	} else if (z <= -9.6e-120) {
		tmp = t_1;
	} else if (z <= 4e-288) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (z <= 5.4e-66) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 1.15) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (z <= 3.2e+35) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (z <= 9.2e+60) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (z <= 3.55e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    t_2 = c * (z * ((t * i) - (y0 * y3)))
    if (z <= (-2.42d-26)) then
        tmp = t_2
    else if (z <= (-9.6d-120)) then
        tmp = t_1
    else if (z <= 4d-288) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (z <= 5.4d-66) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (z <= 1.15d0) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (z <= 3.2d+35) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (z <= 9.2d+60) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else if (z <= 3.55d+177) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double t_2 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (z <= -2.42e-26) {
		tmp = t_2;
	} else if (z <= -9.6e-120) {
		tmp = t_1;
	} else if (z <= 4e-288) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (z <= 5.4e-66) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 1.15) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (z <= 3.2e+35) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (z <= 9.2e+60) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (z <= 3.55e+177) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * ((z * i) - (y2 * y4)))
	t_2 = c * (z * ((t * i) - (y0 * y3)))
	tmp = 0
	if z <= -2.42e-26:
		tmp = t_2
	elif z <= -9.6e-120:
		tmp = t_1
	elif z <= 4e-288:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif z <= 5.4e-66:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif z <= 1.15:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif z <= 3.2e+35:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif z <= 9.2e+60:
		tmp = y1 * (i * ((x * j) - (z * k)))
	elif z <= 3.55e+177:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	t_2 = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))))
	tmp = 0.0
	if (z <= -2.42e-26)
		tmp = t_2;
	elseif (z <= -9.6e-120)
		tmp = t_1;
	elseif (z <= 4e-288)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (z <= 5.4e-66)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (z <= 1.15)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (z <= 3.2e+35)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (z <= 9.2e+60)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	elseif (z <= 3.55e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (t * ((z * i) - (y2 * y4)));
	t_2 = c * (z * ((t * i) - (y0 * y3)));
	tmp = 0.0;
	if (z <= -2.42e-26)
		tmp = t_2;
	elseif (z <= -9.6e-120)
		tmp = t_1;
	elseif (z <= 4e-288)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (z <= 5.4e-66)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (z <= 1.15)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (z <= 3.2e+35)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (z <= 9.2e+60)
		tmp = y1 * (i * ((x * j) - (z * k)));
	elseif (z <= 3.55e+177)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.42e-26], t$95$2, If[LessEqual[z, -9.6e-120], t$95$1, If[LessEqual[z, 4e-288], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-66], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+35], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+60], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+177], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.42e-26 or 3.54999999999999997e177 < z

   1. Initial program 22.7%

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

   3. Simplified 22.7%

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

   4. Taylor expanded in c around inf 37.5%

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

   5. Taylor expanded in z around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot z\right) \]

      4. *-commutative 53.6%

         \[\leadsto c \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot z\right) \]

      5. *-commutative 53.6%

         \[\leadsto c \cdot \left(\left(t \cdot i - \color{blue}{y3 \cdot y0}\right) \cdot z\right) \]

   7. Simplified 53.6%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot i - y3 \cdot y0\right) \cdot z\right)} \]

   if -2.42e-26 < z < -9.5999999999999998e-120 or 9.20000000000000068e60 < z < 3.54999999999999997e177

   1. Initial program 36.1%

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

   3. Simplified 36.1%

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

   4. Taylor expanded in c around inf 42.4%

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

   5. Taylor expanded in t around inf 58.7%

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

   if -9.5999999999999998e-120 < z < 4.00000000000000023e-288

   1. Initial program 36.4%

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

   3. Simplified 36.4%

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

   4. Taylor expanded in y4 around inf 47.7%

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

   5. Taylor expanded in k around inf 41.1%

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

      1. +-commutative 41.1%

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

      2. mul-1-neg 41.1%

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

      3. unsub-neg 41.1%

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

      4. *-commutative 41.1%

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

   7. Simplified 41.1%

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

   if 4.00000000000000023e-288 < z < 5.39999999999999992e-66

   1. Initial program 30.7%

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

   3. Simplified 32.7%

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

   4. Taylor expanded in y around inf 49.8%

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

      1. mul-1-neg 49.8%

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

   6. Simplified 49.8%

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

   7. Taylor expanded in y4 around inf 50.1%

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

      1. *-commutative 50.1%

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

   9. Simplified 50.1%

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

   if 5.39999999999999992e-66 < z < 1.1499999999999999

   1. Initial program 17.2%

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

   3. Simplified 17.2%

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

   4. Taylor expanded in y2 around inf 58.3%

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

   5. Taylor expanded in c around inf 58.6%

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

   if 1.1499999999999999 < z < 3.19999999999999983e35

   1. Initial program 33.1%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in y around inf 51.6%

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

      1. mul-1-neg 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in b around inf 51.8%

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

   if 3.19999999999999983e35 < z < 9.20000000000000068e60

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y1 around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. mul-1-neg 44.4%

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

      3. sub-neg 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in i around inf 67.5%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.42 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-288}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 1.15:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+60}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+177}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \end{array} \]

Alternative 15: 31.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-270}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-21}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -3.9e-18)
   (* y4 (* y (- (* c y3) (* b k))))
   (if (<= y -7.5e-67)
     (* y2 (* k (- (* y1 y4) (* y0 y5))))
     (if (<= y -2.4e-84)
       (* y (* b (- (* x a) (* k y4))))
       (if (<= y 3.5e-270)
         (* (* t y5) (- (* a y2) (* i j)))
         (if (<= y 8.5e-125)
           (* y5 (* y0 (- (* j y3) (* k y2))))
           (if (<= y 1.52e-21)
             (* y2 (* c (- (* x y0) (* t y4))))
             (if (<= y 8.8e+133)
               (* x (* y (- (* a b) (* c i))))
               (if (<= y 1.5e+148)
                 (* a (* t (* y2 y5)))
                 (* y5 (* i (- (* y k) (* t 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 (y <= -3.9e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -7.5e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -2.4e-84) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y <= 3.5e-270) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 8.5e-125) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 1.52e-21) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= 8.8e+133) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= 1.5e+148) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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 (y <= (-3.9d-18)) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (y <= (-7.5d-67)) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (y <= (-2.4d-84)) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (y <= 3.5d-270) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 8.5d-125) then
        tmp = y5 * (y0 * ((j * y3) - (k * y2)))
    else if (y <= 1.52d-21) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (y <= 8.8d+133) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y <= 1.5d+148) then
        tmp = a * (t * (y2 * y5))
    else
        tmp = y5 * (i * ((y * k) - (t * 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 (y <= -3.9e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -7.5e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -2.4e-84) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y <= 3.5e-270) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 8.5e-125) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 1.52e-21) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= 8.8e+133) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y <= 1.5e+148) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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 y <= -3.9e-18:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif y <= -7.5e-67:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif y <= -2.4e-84:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif y <= 3.5e-270:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 8.5e-125:
		tmp = y5 * (y0 * ((j * y3) - (k * y2)))
	elif y <= 1.52e-21:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif y <= 8.8e+133:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y <= 1.5e+148:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = y5 * (i * ((y * k) - (t * 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 (y <= -3.9e-18)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -7.5e-67)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y <= -2.4e-84)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= 3.5e-270)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 8.5e-125)
		tmp = Float64(y5 * Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y <= 1.52e-21)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y <= 8.8e+133)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y <= 1.5e+148)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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 (y <= -3.9e-18)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (y <= -7.5e-67)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (y <= -2.4e-84)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (y <= 3.5e-270)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 8.5e-125)
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	elseif (y <= 1.52e-21)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (y <= 8.8e+133)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y <= 1.5e+148)
		tmp = a * (t * (y2 * y5));
	else
		tmp = y5 * (i * ((y * k) - (t * 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[y, -3.9e-18], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-67], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-84], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-270], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-125], N[(y5 * N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e-21], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e+133], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+148], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -3.90000000000000005e-18

   1. Initial program 25.4%

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

   3. Simplified 25.4%

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

   4. Taylor expanded in y4 around inf 49.5%

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

   5. Taylor expanded in j around 0 46.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.8%

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

      2. unsub-neg 46.8%

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

      3. *-commutative 46.8%

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

      4. *-commutative 46.8%

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

   7. Simplified 46.8%

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

   8. Taylor expanded in y2 around 0 39.5%

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

      1. +-commutative 39.5%

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

      2. distribute-lft-in 39.5%

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

      3. associate-*r* 39.5%

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

      4. neg-mul-1 39.5%

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

      5. mul-1-neg 39.5%

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

      6. mul-1-neg 39.5%

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

      7. remove-double-neg 39.5%

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

      8. *-commutative 39.5%

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

      9. associate-*r* 39.6%

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

      10. *-commutative 39.6%

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

      11. associate-*r* 41.1%

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

      12. neg-mul-1 41.1%

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

      13. associate-*r* 41.1%

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

      14. distribute-rgt-in 48.5%

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

      15. mul-1-neg 48.5%

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

      16. unsub-neg 48.5%

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

      17. *-commutative 48.5%

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

   10. Simplified 48.5%

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

   if -3.90000000000000005e-18 < y < -7.5000000000000005e-67

   1. Initial program 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in y2 around inf 46.6%

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

   5. Taylor expanded in k around inf 55.0%

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

   if -7.5000000000000005e-67 < y < -2.40000000000000017e-84

   1. Initial program 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in y around inf 33.3%

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

      1. mul-1-neg 33.3%

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

   6. Simplified 33.3%

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

   7. Taylor expanded in b around inf 100.0%

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

   if -2.40000000000000017e-84 < y < 3.49999999999999994e-270

   1. Initial program 29.9%

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

   3. Simplified 39.2%

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

   4. Taylor expanded in y5 around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. mul-1-neg 48.7%

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

      3. mul-1-neg 48.7%

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

      4. sub-neg 48.7%

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

      5. sub-neg 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in t around inf 54.9%

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

      1. associate-*r* 51.3%

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

      2. *-commutative 51.3%

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

   9. Simplified 51.3%

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

   if 3.49999999999999994e-270 < y < 8.5000000000000002e-125

   1. Initial program 46.6%

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

   3. Simplified 46.6%

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

   4. Taylor expanded in y5 around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. mul-1-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 56.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in y0 around inf 53.9%

      \[\leadsto \color{blue}{\left(\left(y3 \cdot j - k \cdot y2\right) \cdot y0\right)} \cdot y5 \]

   if 8.5000000000000002e-125 < y < 1.52000000000000009e-21

   1. Initial program 23.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 50.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 42.3%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x - y4 \cdot t\right)\right)} \cdot y2 \]

   if 1.52000000000000009e-21 < y < 8.8e133

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 42.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 42.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in x around inf 42.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(a \cdot b - c \cdot i\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.6%

         \[\leadsto \color{blue}{\left(y \cdot \left(a \cdot b - c \cdot i\right)\right) \cdot x} \]

      2. *-commutative 45.6%

         \[\leadsto \left(y \cdot \left(a \cdot b - \color{blue}{i \cdot c}\right)\right) \cdot x \]

   9. Simplified 45.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(a \cdot b - i \cdot c\right)\right) \cdot x} \]

   if 8.8e133 < y < 1.50000000000000007e148

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 25.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 25.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 25.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 25.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 25.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 25.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 50.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.0%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 50.0%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 50.0%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 75.6%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if 1.50000000000000007e148 < y

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 51.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 51.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 69.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 69.1%

         \[\leadsto \left(i \cdot \left(\color{blue}{y \cdot k} - t \cdot j\right)\right) \cdot y5 \]

   9. Simplified 69.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 9 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-270}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-21}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+148}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 16: 30.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-269}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-125}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-30}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+147}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* b (- (* x a) (* k y4))))))
   (if (<= y -3.9e-18)
     (* y4 (* y (- (* c y3) (* b k))))
     (if (<= y -3.5e-67)
       (* y2 (* k (- (* y1 y4) (* y0 y5))))
       (if (<= y -3.2e-86)
         t_1
         (if (<= y 1.3e-269)
           (* (* t y5) (- (* a y2) (* i j)))
           (if (<= y 8e-125)
             (* y5 (* y0 (- (* j y3) (* k y2))))
             (if (<= y 1.85e-30)
               (* y2 (* c (- (* x y0) (* t y4))))
               (if (<= y 9e+80)
                 t_1
                 (if (<= y 8.5e+147)
                   (* y1 (* a (- (* z y3) (* x y2))))
                   (* y5 (* i (- (* y k) (* t j))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (b * ((x * a) - (k * y4)));
	double tmp;
	if (y <= -3.9e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -3.5e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -3.2e-86) {
		tmp = t_1;
	} else if (y <= 1.3e-269) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 8e-125) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 1.85e-30) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= 9e+80) {
		tmp = t_1;
	} else if (y <= 8.5e+147) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: tmp
    t_1 = y * (b * ((x * a) - (k * y4)))
    if (y <= (-3.9d-18)) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (y <= (-3.5d-67)) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (y <= (-3.2d-86)) then
        tmp = t_1
    else if (y <= 1.3d-269) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 8d-125) then
        tmp = y5 * (y0 * ((j * y3) - (k * y2)))
    else if (y <= 1.85d-30) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (y <= 9d+80) then
        tmp = t_1
    else if (y <= 8.5d+147) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = y * (b * ((x * a) - (k * y4)));
	double tmp;
	if (y <= -3.9e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -3.5e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -3.2e-86) {
		tmp = t_1;
	} else if (y <= 1.3e-269) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 8e-125) {
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	} else if (y <= 1.85e-30) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (y <= 9e+80) {
		tmp = t_1;
	} else if (y <= 8.5e+147) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (b * ((x * a) - (k * y4)))
	tmp = 0
	if y <= -3.9e-18:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif y <= -3.5e-67:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif y <= -3.2e-86:
		tmp = t_1
	elif y <= 1.3e-269:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 8e-125:
		tmp = y5 * (y0 * ((j * y3) - (k * y2)))
	elif y <= 1.85e-30:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif y <= 9e+80:
		tmp = t_1
	elif y <= 8.5e+147:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (y <= -3.9e-18)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -3.5e-67)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y <= -3.2e-86)
		tmp = t_1;
	elseif (y <= 1.3e-269)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 8e-125)
		tmp = Float64(y5 * Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y <= 1.85e-30)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y <= 9e+80)
		tmp = t_1;
	elseif (y <= 8.5e+147)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = y * (b * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (y <= -3.9e-18)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (y <= -3.5e-67)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (y <= -3.2e-86)
		tmp = t_1;
	elseif (y <= 1.3e-269)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 8e-125)
		tmp = y5 * (y0 * ((j * y3) - (k * y2)));
	elseif (y <= 1.85e-30)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (y <= 9e+80)
		tmp = t_1;
	elseif (y <= 8.5e+147)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	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[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e-18], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-67], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-86], t$95$1, If[LessEqual[y, 1.3e-269], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-125], N[(y5 * N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-30], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+80], t$95$1, If[LessEqual[y, 8.5e+147], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -3.90000000000000005e-18

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 49.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 46.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.8%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 46.8%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 46.8%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 46.8%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 46.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y2 around 0 39.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right) + -1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right)\right)} \cdot y4 \]
   9. Step-by-step derivation

      1. +-commutative 39.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right) + k \cdot \left(y \cdot b\right)\right)}\right) \cdot y4 \]

      2. distribute-lft-in 39.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \cdot y4 \]

      3. associate-*r* 39.5%

         \[\leadsto \left(-1 \cdot \left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) + \color{blue}{\left(-1 \cdot k\right) \cdot \left(y \cdot b\right)}\right) \cdot y4 \]

      4. neg-mul-1 39.5%

         \[\leadsto \left(-1 \cdot \left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) + \color{blue}{\left(-k\right)} \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      5. mul-1-neg 39.5%

         \[\leadsto \left(\color{blue}{\left(--1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right)} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      6. mul-1-neg 39.5%

         \[\leadsto \left(\left(-\color{blue}{\left(-c \cdot \left(y \cdot y3\right)\right)}\right) + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      7. remove-double-neg 39.5%

         \[\leadsto \left(\color{blue}{c \cdot \left(y \cdot y3\right)} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      8. *-commutative 39.5%

         \[\leadsto \left(c \cdot \color{blue}{\left(y3 \cdot y\right)} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      9. associate-*r* 39.6%

         \[\leadsto \left(\color{blue}{\left(c \cdot y3\right) \cdot y} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      10. *-commutative 39.6%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \left(-k\right) \cdot \color{blue}{\left(b \cdot y\right)}\right) \cdot y4 \]

      11. associate-*r* 41.1%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \color{blue}{\left(\left(-k\right) \cdot b\right) \cdot y}\right) \cdot y4 \]

      12. neg-mul-1 41.1%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \left(\color{blue}{\left(-1 \cdot k\right)} \cdot b\right) \cdot y\right) \cdot y4 \]

      13. associate-*r* 41.1%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \color{blue}{\left(-1 \cdot \left(k \cdot b\right)\right)} \cdot y\right) \cdot y4 \]

      14. distribute-rgt-in 48.5%

          \[\leadsto \color{blue}{\left(y \cdot \left(c \cdot y3 + -1 \cdot \left(k \cdot b\right)\right)\right)} \cdot y4 \]

      15. mul-1-neg 48.5%

          \[\leadsto \left(y \cdot \left(c \cdot y3 + \color{blue}{\left(-k \cdot b\right)}\right)\right) \cdot y4 \]

      16. unsub-neg 48.5%

          \[\leadsto \left(y \cdot \color{blue}{\left(c \cdot y3 - k \cdot b\right)}\right) \cdot y4 \]

      17. *-commutative 48.5%

          \[\leadsto \left(y \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right)\right) \cdot y4 \]

   10. Simplified 48.5%

       \[\leadsto \color{blue}{\left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot y4 \]

   if -3.90000000000000005e-18 < y < -3.5e-67

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 46.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 55.0%

      \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \cdot y2 \]

   if -3.5e-67 < y < -3.20000000000000006e-86 or 1.8500000000000002e-30 < y < 9.00000000000000013e80

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 46.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 46.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 50.0%

      \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -3.20000000000000006e-86 < y < 1.3e-269

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 48.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 48.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 51.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 51.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   if 1.3e-269 < y < 8.0000000000000001e-125

   1. Initial program 46.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 56.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 56.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 56.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in y0 around inf 53.9%

      \[\leadsto \color{blue}{\left(\left(y3 \cdot j - k \cdot y2\right) \cdot y0\right)} \cdot y5 \]

   if 8.0000000000000001e-125 < y < 1.8500000000000002e-30

   1. Initial program 20.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 50.7%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x - y4 \cdot t\right)\right)} \cdot y2 \]

   if 9.00000000000000013e80 < y < 8.5000000000000007e147

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 28.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 28.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 28.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 28.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in a around inf 57.5%

      \[\leadsto \color{blue}{\left(\left(y3 \cdot z - y2 \cdot x\right) \cdot a\right)} \cdot y1 \]

   if 8.5000000000000007e147 < y

   1. Initial program 31.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 51.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 51.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 51.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 69.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 69.1%

         \[\leadsto \left(i \cdot \left(\color{blue}{y \cdot k} - t \cdot j\right)\right) \cdot y5 \]

   9. Simplified 69.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-269}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-125}:\\ \;\;\;\;y5 \cdot \left(y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-30}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+147}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 17: 22.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;k \leq -2.4 \cdot 10^{+202}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.95 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;\left(i \cdot y1\right) \cdot \left(x \cdot j\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 27500:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* t (* j (- y5))))))
   (if (<= k -2.4e+202)
     (* y4 (* y1 (* k y2)))
     (if (<= k -1.5e+139)
       (* z (* k (* y1 (- i))))
       (if (<= k -1.95e+26)
         (* k (* y4 (* y1 y2)))
         (if (<= k -3.8e-180)
           (* a (* t (* y2 y5)))
           (if (<= k 5.5e-134)
             t_1
             (if (<= k 2.9e-99)
               (* a (* y2 (* t y5)))
               (if (<= k 7.5e-42)
                 (* (* i y1) (* x j))
                 (if (<= k 2.9e-37)
                   t_1
                   (if (<= k 27500.0)
                     (* y4 (* c (* y y3)))
                     (* y2 (* y1 (* k 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 t_1 = i * (t * (j * -y5));
	double tmp;
	if (k <= -2.4e+202) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -1.5e+139) {
		tmp = z * (k * (y1 * -i));
	} else if (k <= -1.95e+26) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= -3.8e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 5.5e-134) {
		tmp = t_1;
	} else if (k <= 2.9e-99) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 7.5e-42) {
		tmp = (i * y1) * (x * j);
	} else if (k <= 2.9e-37) {
		tmp = t_1;
	} else if (k <= 27500.0) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = y2 * (y1 * (k * 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) :: t_1
    real(8) :: tmp
    t_1 = i * (t * (j * -y5))
    if (k <= (-2.4d+202)) then
        tmp = y4 * (y1 * (k * y2))
    else if (k <= (-1.5d+139)) then
        tmp = z * (k * (y1 * -i))
    else if (k <= (-1.95d+26)) then
        tmp = k * (y4 * (y1 * y2))
    else if (k <= (-3.8d-180)) then
        tmp = a * (t * (y2 * y5))
    else if (k <= 5.5d-134) then
        tmp = t_1
    else if (k <= 2.9d-99) then
        tmp = a * (y2 * (t * y5))
    else if (k <= 7.5d-42) then
        tmp = (i * y1) * (x * j)
    else if (k <= 2.9d-37) then
        tmp = t_1
    else if (k <= 27500.0d0) then
        tmp = y4 * (c * (y * y3))
    else
        tmp = y2 * (y1 * (k * 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 t_1 = i * (t * (j * -y5));
	double tmp;
	if (k <= -2.4e+202) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -1.5e+139) {
		tmp = z * (k * (y1 * -i));
	} else if (k <= -1.95e+26) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= -3.8e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 5.5e-134) {
		tmp = t_1;
	} else if (k <= 2.9e-99) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 7.5e-42) {
		tmp = (i * y1) * (x * j);
	} else if (k <= 2.9e-37) {
		tmp = t_1;
	} else if (k <= 27500.0) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = y2 * (y1 * (k * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (t * (j * -y5))
	tmp = 0
	if k <= -2.4e+202:
		tmp = y4 * (y1 * (k * y2))
	elif k <= -1.5e+139:
		tmp = z * (k * (y1 * -i))
	elif k <= -1.95e+26:
		tmp = k * (y4 * (y1 * y2))
	elif k <= -3.8e-180:
		tmp = a * (t * (y2 * y5))
	elif k <= 5.5e-134:
		tmp = t_1
	elif k <= 2.9e-99:
		tmp = a * (y2 * (t * y5))
	elif k <= 7.5e-42:
		tmp = (i * y1) * (x * j)
	elif k <= 2.9e-37:
		tmp = t_1
	elif k <= 27500.0:
		tmp = y4 * (c * (y * y3))
	else:
		tmp = y2 * (y1 * (k * y4))
	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(t * Float64(j * Float64(-y5))))
	tmp = 0.0
	if (k <= -2.4e+202)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (k <= -1.5e+139)
		tmp = Float64(z * Float64(k * Float64(y1 * Float64(-i))));
	elseif (k <= -1.95e+26)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (k <= -3.8e-180)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (k <= 5.5e-134)
		tmp = t_1;
	elseif (k <= 2.9e-99)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (k <= 7.5e-42)
		tmp = Float64(Float64(i * y1) * Float64(x * j));
	elseif (k <= 2.9e-37)
		tmp = t_1;
	elseif (k <= 27500.0)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	else
		tmp = Float64(y2 * Float64(y1 * Float64(k * 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)
	t_1 = i * (t * (j * -y5));
	tmp = 0.0;
	if (k <= -2.4e+202)
		tmp = y4 * (y1 * (k * y2));
	elseif (k <= -1.5e+139)
		tmp = z * (k * (y1 * -i));
	elseif (k <= -1.95e+26)
		tmp = k * (y4 * (y1 * y2));
	elseif (k <= -3.8e-180)
		tmp = a * (t * (y2 * y5));
	elseif (k <= 5.5e-134)
		tmp = t_1;
	elseif (k <= 2.9e-99)
		tmp = a * (y2 * (t * y5));
	elseif (k <= 7.5e-42)
		tmp = (i * y1) * (x * j);
	elseif (k <= 2.9e-37)
		tmp = t_1;
	elseif (k <= 27500.0)
		tmp = y4 * (c * (y * y3));
	else
		tmp = y2 * (y1 * (k * y4));
	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[(i * N[(t * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.4e+202], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.5e+139], N[(z * N[(k * N[(y1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.95e+26], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -3.8e-180], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.5e-134], t$95$1, If[LessEqual[k, 2.9e-99], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.5e-42], N[(N[(i * y1), $MachinePrecision] * N[(x * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.9e-37], t$95$1, If[LessEqual[k, 27500.0], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y1 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -2.4000000000000002e202

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 57.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 57.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 28.6%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 28.6%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 28.6%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 41.1%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 41.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 44.3%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 44.3%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -2.4000000000000002e202 < k < -1.5e139

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 44.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 44.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 77.9%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 57.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 57.0%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. associate-*r* 57.1%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)} \]

      3. associate-*r* 67.7%

         \[\leadsto -\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   10. Simplified 67.7%

       \[\leadsto \color{blue}{-\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   if -1.5e139 < k < -1.95e26

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 27.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 27.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 27.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -1.95e26 < k < -3.79999999999999999e-180

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 32.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.0%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 28.0%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 32.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -3.79999999999999999e-180 < k < 5.5000000000000002e-134 or 7.49999999999999972e-42 < k < 2.90000000000000005e-37

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 49.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 49.0%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 43.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 43.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 43.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 35.1%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 35.1%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 33.5%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 33.5%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   13. Taylor expanded in i around 0 35.1%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

   if 5.5000000000000002e-134 < k < 2.89999999999999985e-99

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 43.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 43.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 57.8%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 44.0%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 44.0%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 44.2%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 58.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 58.1%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if 2.89999999999999985e-99 < k < 7.49999999999999972e-42

   1. Initial program 42.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 71.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 71.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 71.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 71.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 71.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 58.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 30.6%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto \color{blue}{\left(y1 \cdot i\right) \cdot \left(j \cdot x\right)} \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{\left(y1 \cdot i\right) \cdot \left(j \cdot x\right)} \]

   if 2.90000000000000005e-37 < k < 27500

   1. Initial program 14.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 50.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 50.1%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 50.1%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 50.1%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 50.1%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 43.6%

      \[\leadsto \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \cdot y4 \]

   if 27500 < k

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 37.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.5%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 37.5%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 37.5%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 37.5%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y1 around inf 26.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 32.1%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2\right)} \]

      2. associate-*r* 38.1%

         \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]

   10. Simplified 38.1%

       \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]
3. Recombined 9 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.4 \cdot 10^{+202}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;k \leq -1.95 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.8 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-42}:\\ \;\;\;\;\left(i \cdot y1\right) \cdot \left(x \cdot j\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{-37}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 27500:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \]

Alternative 18: 24.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-304}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-165}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-104}:\\ \;\;\;\;\left(j \cdot \left(t \cdot y5\right)\right) \cdot \left(-i\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-70}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 10^{+116}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* t (- (* z i) (* y2 y4))))))
   (if (<= z -2.9e-25)
     (* c (* y0 (- (* x y2) (* z y3))))
     (if (<= z -2e-119)
       t_1
       (if (<= z -4.1e-304)
         (* y4 (* k (* y1 y2)))
         (if (<= z 7e-165)
           (* y4 (* (* y k) (- b)))
           (if (<= z 6e-104)
             (* (* j (* t y5)) (- i))
             (if (<= z 1.3e-70)
               (* y1 (* i (* x j)))
               (if (<= z 1e+116) (* t (* y5 (* a y2))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (z <= -2.9e-25) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (z <= -2e-119) {
		tmp = t_1;
	} else if (z <= -4.1e-304) {
		tmp = y4 * (k * (y1 * y2));
	} else if (z <= 7e-165) {
		tmp = y4 * ((y * k) * -b);
	} else if (z <= 6e-104) {
		tmp = (j * (t * y5)) * -i;
	} else if (z <= 1.3e-70) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 1e+116) {
		tmp = t * (y5 * (a * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * ((z * i) - (y2 * y4)))
    if (z <= (-2.9d-25)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (z <= (-2d-119)) then
        tmp = t_1
    else if (z <= (-4.1d-304)) then
        tmp = y4 * (k * (y1 * y2))
    else if (z <= 7d-165) then
        tmp = y4 * ((y * k) * -b)
    else if (z <= 6d-104) then
        tmp = (j * (t * y5)) * -i
    else if (z <= 1.3d-70) then
        tmp = y1 * (i * (x * j))
    else if (z <= 1d+116) then
        tmp = t * (y5 * (a * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (t * ((z * i) - (y2 * y4)));
	double tmp;
	if (z <= -2.9e-25) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (z <= -2e-119) {
		tmp = t_1;
	} else if (z <= -4.1e-304) {
		tmp = y4 * (k * (y1 * y2));
	} else if (z <= 7e-165) {
		tmp = y4 * ((y * k) * -b);
	} else if (z <= 6e-104) {
		tmp = (j * (t * y5)) * -i;
	} else if (z <= 1.3e-70) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 1e+116) {
		tmp = t * (y5 * (a * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (t * ((z * i) - (y2 * y4)))
	tmp = 0
	if z <= -2.9e-25:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif z <= -2e-119:
		tmp = t_1
	elif z <= -4.1e-304:
		tmp = y4 * (k * (y1 * y2))
	elif z <= 7e-165:
		tmp = y4 * ((y * k) * -b)
	elif z <= 6e-104:
		tmp = (j * (t * y5)) * -i
	elif z <= 1.3e-70:
		tmp = y1 * (i * (x * j))
	elif z <= 1e+116:
		tmp = t * (y5 * (a * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))))
	tmp = 0.0
	if (z <= -2.9e-25)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (z <= -2e-119)
		tmp = t_1;
	elseif (z <= -4.1e-304)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	elseif (z <= 7e-165)
		tmp = Float64(y4 * Float64(Float64(y * k) * Float64(-b)));
	elseif (z <= 6e-104)
		tmp = Float64(Float64(j * Float64(t * y5)) * Float64(-i));
	elseif (z <= 1.3e-70)
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	elseif (z <= 1e+116)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (t * ((z * i) - (y2 * y4)));
	tmp = 0.0;
	if (z <= -2.9e-25)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (z <= -2e-119)
		tmp = t_1;
	elseif (z <= -4.1e-304)
		tmp = y4 * (k * (y1 * y2));
	elseif (z <= 7e-165)
		tmp = y4 * ((y * k) * -b);
	elseif (z <= 6e-104)
		tmp = (j * (t * y5)) * -i;
	elseif (z <= 1.3e-70)
		tmp = y1 * (i * (x * j));
	elseif (z <= 1e+116)
		tmp = t * (y5 * (a * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-25], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-119], t$95$1, If[LessEqual[z, -4.1e-304], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-165], N[(y4 * N[(N[(y * k), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-104], N[(N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[z, 1.3e-70], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+116], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.9000000000000001e-25

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 40.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 43.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.2%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 43.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if -2.9000000000000001e-25 < z < -2.00000000000000003e-119 or 1.00000000000000002e116 < z

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 38.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 57.3%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y4 \cdot y2\right) \cdot t\right)} \]

   if -2.00000000000000003e-119 < z < -4.10000000000000002e-304

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 38.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 38.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 30.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]

   if -4.10000000000000002e-304 < z < 7.0000000000000003e-165

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 48.9%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 48.9%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 48.9%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 48.9%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 48.9%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \cdot y4 \]
   9. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot b\right)}\right) \cdot y4 \]

      2. associate-*r* 43.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y\right)\right) \cdot b\right)} \cdot y4 \]

      3. neg-mul-1 43.7%

         \[\leadsto \left(\color{blue}{\left(-k \cdot y\right)} \cdot b\right) \cdot y4 \]

      4. *-commutative 43.7%

         \[\leadsto \left(\left(-\color{blue}{y \cdot k}\right) \cdot b\right) \cdot y4 \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{\left(\left(-y \cdot k\right) \cdot b\right)} \cdot y4 \]

   if 7.0000000000000003e-165 < z < 6.0000000000000005e-104

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 69.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 69.2%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 61.6%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 53.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 53.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 53.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 39.2%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 39.2%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. *-commutative 39.2%

          \[\leadsto -\color{blue}{\left(t \cdot \left(j \cdot y5\right)\right) \cdot i} \]

       3. distribute-rgt-neg-in 39.2%

          \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot y5\right)\right) \cdot \left(-i\right)} \]

       4. *-commutative 39.2%

          \[\leadsto \color{blue}{\left(\left(j \cdot y5\right) \cdot t\right)} \cdot \left(-i\right) \]

       5. associate-*l* 46.6%

          \[\leadsto \color{blue}{\left(j \cdot \left(y5 \cdot t\right)\right)} \cdot \left(-i\right) \]

       6. *-commutative 46.6%

          \[\leadsto \left(j \cdot \color{blue}{\left(t \cdot y5\right)}\right) \cdot \left(-i\right) \]

   12. Simplified 46.6%

       \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right) \cdot \left(-i\right)} \]

   if 6.0000000000000005e-104 < z < 1.30000000000000001e-70

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 100.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 100.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 100.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 75.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 75.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]

   if 1.30000000000000001e-70 < z < 1.00000000000000002e116

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.4%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 47.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 35.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 35.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 26.6%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 26.6%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 26.6%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 26.6%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 26.6%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 26.6%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 32.6%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 32.6%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 35.5%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 35.5%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-304}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-165}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-104}:\\ \;\;\;\;\left(j \cdot \left(t \cdot y5\right)\right) \cdot \left(-i\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-70}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 10^{+116}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \end{array} \]

Alternative 19: 27.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-304}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-165}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-105}:\\ \;\;\;\;\left(j \cdot \left(t \cdot y5\right)\right) \cdot \left(-i\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (- (* t i) (* y0 y3))))))
   (if (<= z -3.8e-26)
     t_1
     (if (<= z -1.75e-119)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= z -2.9e-304)
         (* y4 (* k (* y1 y2)))
         (if (<= z 7.5e-165)
           (* y4 (* (* y k) (- b)))
           (if (<= z 4.5e-105)
             (* (* j (* t y5)) (- i))
             (if (<= z 1.65e-72)
               (* y1 (* i (* x j)))
               (if (<= z 2.1e+108) (* t (* y5 (* a y2))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (z <= -3.8e-26) {
		tmp = t_1;
	} else if (z <= -1.75e-119) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (z <= -2.9e-304) {
		tmp = y4 * (k * (y1 * y2));
	} else if (z <= 7.5e-165) {
		tmp = y4 * ((y * k) * -b);
	} else if (z <= 4.5e-105) {
		tmp = (j * (t * y5)) * -i;
	} else if (z <= 1.65e-72) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 2.1e+108) {
		tmp = t * (y5 * (a * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (z * ((t * i) - (y0 * y3)))
    if (z <= (-3.8d-26)) then
        tmp = t_1
    else if (z <= (-1.75d-119)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (z <= (-2.9d-304)) then
        tmp = y4 * (k * (y1 * y2))
    else if (z <= 7.5d-165) then
        tmp = y4 * ((y * k) * -b)
    else if (z <= 4.5d-105) then
        tmp = (j * (t * y5)) * -i
    else if (z <= 1.65d-72) then
        tmp = y1 * (i * (x * j))
    else if (z <= 2.1d+108) then
        tmp = t * (y5 * (a * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (z <= -3.8e-26) {
		tmp = t_1;
	} else if (z <= -1.75e-119) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (z <= -2.9e-304) {
		tmp = y4 * (k * (y1 * y2));
	} else if (z <= 7.5e-165) {
		tmp = y4 * ((y * k) * -b);
	} else if (z <= 4.5e-105) {
		tmp = (j * (t * y5)) * -i;
	} else if (z <= 1.65e-72) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 2.1e+108) {
		tmp = t * (y5 * (a * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (z * ((t * i) - (y0 * y3)))
	tmp = 0
	if z <= -3.8e-26:
		tmp = t_1
	elif z <= -1.75e-119:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif z <= -2.9e-304:
		tmp = y4 * (k * (y1 * y2))
	elif z <= 7.5e-165:
		tmp = y4 * ((y * k) * -b)
	elif z <= 4.5e-105:
		tmp = (j * (t * y5)) * -i
	elif z <= 1.65e-72:
		tmp = y1 * (i * (x * j))
	elif z <= 2.1e+108:
		tmp = t * (y5 * (a * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))))
	tmp = 0.0
	if (z <= -3.8e-26)
		tmp = t_1;
	elseif (z <= -1.75e-119)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (z <= -2.9e-304)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	elseif (z <= 7.5e-165)
		tmp = Float64(y4 * Float64(Float64(y * k) * Float64(-b)));
	elseif (z <= 4.5e-105)
		tmp = Float64(Float64(j * Float64(t * y5)) * Float64(-i));
	elseif (z <= 1.65e-72)
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	elseif (z <= 2.1e+108)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (z * ((t * i) - (y0 * y3)));
	tmp = 0.0;
	if (z <= -3.8e-26)
		tmp = t_1;
	elseif (z <= -1.75e-119)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (z <= -2.9e-304)
		tmp = y4 * (k * (y1 * y2));
	elseif (z <= 7.5e-165)
		tmp = y4 * ((y * k) * -b);
	elseif (z <= 4.5e-105)
		tmp = (j * (t * y5)) * -i;
	elseif (z <= 1.65e-72)
		tmp = y1 * (i * (x * j));
	elseif (z <= 2.1e+108)
		tmp = t * (y5 * (a * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-26], t$95$1, If[LessEqual[z, -1.75e-119], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-304], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-165], N[(y4 * N[(N[(y * k), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-105], N[(N[(j * N[(t * y5), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[z, 1.65e-72], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+108], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -3.80000000000000015e-26 or 2.1000000000000001e108 < z

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 35.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 51.8%

      \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right) \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 51.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)} \cdot z\right) \]

      2. mul-1-neg 51.8%

         \[\leadsto c \cdot \left(\left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right) \cdot z\right) \]

      3. unsub-neg 51.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot z\right) \]

      4. *-commutative 51.8%

         \[\leadsto c \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot z\right) \]

      5. *-commutative 51.8%

         \[\leadsto c \cdot \left(\left(t \cdot i - \color{blue}{y3 \cdot y0}\right) \cdot z\right) \]

   7. Simplified 51.8%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot i - y3 \cdot y0\right) \cdot z\right)} \]

   if -3.80000000000000015e-26 < z < -1.75e-119

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 58.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 63.8%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y4 \cdot y2\right) \cdot t\right)} \]

   if -1.75e-119 < z < -2.9e-304

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 38.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 38.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 38.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 30.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]

   if -2.9e-304 < z < 7.5000000000000002e-165

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 48.9%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 48.9%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 48.9%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 48.9%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 48.9%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \cdot y4 \]
   9. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot b\right)}\right) \cdot y4 \]

      2. associate-*r* 43.7%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y\right)\right) \cdot b\right)} \cdot y4 \]

      3. neg-mul-1 43.7%

         \[\leadsto \left(\color{blue}{\left(-k \cdot y\right)} \cdot b\right) \cdot y4 \]

      4. *-commutative 43.7%

         \[\leadsto \left(\left(-\color{blue}{y \cdot k}\right) \cdot b\right) \cdot y4 \]

   10. Simplified 43.7%

       \[\leadsto \color{blue}{\left(\left(-y \cdot k\right) \cdot b\right)} \cdot y4 \]

   if 7.5000000000000002e-165 < z < 4.4999999999999997e-105

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 69.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 69.2%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 69.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 61.6%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 53.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 53.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 53.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 39.2%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 39.2%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. *-commutative 39.2%

          \[\leadsto -\color{blue}{\left(t \cdot \left(j \cdot y5\right)\right) \cdot i} \]

       3. distribute-rgt-neg-in 39.2%

          \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot y5\right)\right) \cdot \left(-i\right)} \]

       4. *-commutative 39.2%

          \[\leadsto \color{blue}{\left(\left(j \cdot y5\right) \cdot t\right)} \cdot \left(-i\right) \]

       5. associate-*l* 46.6%

          \[\leadsto \color{blue}{\left(j \cdot \left(y5 \cdot t\right)\right)} \cdot \left(-i\right) \]

       6. *-commutative 46.6%

          \[\leadsto \left(j \cdot \color{blue}{\left(t \cdot y5\right)}\right) \cdot \left(-i\right) \]

   12. Simplified 46.6%

       \[\leadsto \color{blue}{\left(j \cdot \left(t \cdot y5\right)\right) \cdot \left(-i\right)} \]

   if 4.4999999999999997e-105 < z < 1.65e-72

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 100.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 100.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 100.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 75.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 75.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]

   if 1.65e-72 < z < 2.1000000000000001e108

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.4%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.4%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.4%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 47.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 35.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 35.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 26.6%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 26.6%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 26.6%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 26.6%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 26.6%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 26.6%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 32.6%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 32.6%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 35.5%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 35.5%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-304}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-165}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-105}:\\ \;\;\;\;\left(j \cdot \left(t \cdot y5\right)\right) \cdot \left(-i\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \end{array} \]

Alternative 20: 32.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ t_2 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{if}\;i \leq -1.66 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-261}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* y4 (- (* c y3) (* b k)))))
        (t_2 (* y5 (* i (- (* y k) (* t j))))))
   (if (<= i -1.66e+100)
     t_2
     (if (<= i -1.45e-67)
       (* c (* y0 (- (* x y2) (* z y3))))
       (if (<= i -7.8e-156)
         (* y (* b (- (* x a) (* k y4))))
         (if (<= i -5.4e-261)
           (* y2 (* c (- (* x y0) (* t y4))))
           (if (<= i 4.5e-241)
             t_1
             (if (<= i 1.05e-168)
               (* a (* t (* y2 y5)))
               (if (<= i 1.6e+81) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * ((c * y3) - (b * k)));
	double t_2 = y5 * (i * ((y * k) - (t * j)));
	double tmp;
	if (i <= -1.66e+100) {
		tmp = t_2;
	} else if (i <= -1.45e-67) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (i <= -7.8e-156) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (i <= -5.4e-261) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (i <= 4.5e-241) {
		tmp = t_1;
	} else if (i <= 1.05e-168) {
		tmp = a * (t * (y2 * y5));
	} else if (i <= 1.6e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (y4 * ((c * y3) - (b * k)))
    t_2 = y5 * (i * ((y * k) - (t * j)))
    if (i <= (-1.66d+100)) then
        tmp = t_2
    else if (i <= (-1.45d-67)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (i <= (-7.8d-156)) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (i <= (-5.4d-261)) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else if (i <= 4.5d-241) then
        tmp = t_1
    else if (i <= 1.05d-168) then
        tmp = a * (t * (y2 * y5))
    else if (i <= 1.6d+81) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (y4 * ((c * y3) - (b * k)));
	double t_2 = y5 * (i * ((y * k) - (t * j)));
	double tmp;
	if (i <= -1.66e+100) {
		tmp = t_2;
	} else if (i <= -1.45e-67) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (i <= -7.8e-156) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (i <= -5.4e-261) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else if (i <= 4.5e-241) {
		tmp = t_1;
	} else if (i <= 1.05e-168) {
		tmp = a * (t * (y2 * y5));
	} else if (i <= 1.6e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (y4 * ((c * y3) - (b * k)))
	t_2 = y5 * (i * ((y * k) - (t * j)))
	tmp = 0
	if i <= -1.66e+100:
		tmp = t_2
	elif i <= -1.45e-67:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif i <= -7.8e-156:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif i <= -5.4e-261:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	elif i <= 4.5e-241:
		tmp = t_1
	elif i <= 1.05e-168:
		tmp = a * (t * (y2 * y5))
	elif i <= 1.6e+81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))))
	t_2 = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * j))))
	tmp = 0.0
	if (i <= -1.66e+100)
		tmp = t_2;
	elseif (i <= -1.45e-67)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (i <= -7.8e-156)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (i <= -5.4e-261)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (i <= 4.5e-241)
		tmp = t_1;
	elseif (i <= 1.05e-168)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (i <= 1.6e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y * (y4 * ((c * y3) - (b * k)));
	t_2 = y5 * (i * ((y * k) - (t * j)));
	tmp = 0.0;
	if (i <= -1.66e+100)
		tmp = t_2;
	elseif (i <= -1.45e-67)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (i <= -7.8e-156)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (i <= -5.4e-261)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	elseif (i <= 4.5e-241)
		tmp = t_1;
	elseif (i <= 1.05e-168)
		tmp = a * (t * (y2 * y5));
	elseif (i <= 1.6e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.66e+100], t$95$2, If[LessEqual[i, -1.45e-67], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.8e-156], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.4e-261], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.5e-241], t$95$1, If[LessEqual[i, 1.05e-168], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e+81], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.66e100 or 1.6e81 < i

   1. Initial program 23.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 45.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 45.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 45.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 45.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 45.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 45.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 56.4%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto \left(i \cdot \left(\color{blue}{y \cdot k} - t \cdot j\right)\right) \cdot y5 \]

   9. Simplified 56.4%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]

   if -1.66e100 < i < -1.45000000000000002e-67

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 55.5%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 55.5%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 55.5%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if -1.45000000000000002e-67 < i < -7.8000000000000002e-156

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 22.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 22.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 22.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 57.9%

      \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -7.8000000000000002e-156 < i < -5.3999999999999998e-261

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 40.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 65.8%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x - y4 \cdot t\right)\right)} \cdot y2 \]

   if -5.3999999999999998e-261 < i < 4.4999999999999999e-241 or 1.04999999999999997e-168 < i < 1.6e81

   1. Initial program 36.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 37.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 37.4%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 42.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot c} - k \cdot b\right)\right) \]

   9. Simplified 42.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(y3 \cdot c - k \cdot b\right)\right)} \]

   if 4.4999999999999999e-241 < i < 1.04999999999999997e-168

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 31.9%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 31.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 31.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 37.3%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.66 \cdot 10^{+100}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-261}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 21: 30.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;y \leq -2.06 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -2050000000000:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-268}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* b (- (* x a) (* k y4))))))
   (if (<= y -2.06e+77)
     (* y (* y4 (- (* c y3) (* b k))))
     (if (<= y -2050000000000.0)
       (* j (* y1 (- (* x i) (* y3 y4))))
       (if (<= y -5.5e-15)
         t_1
         (if (<= y -7e-67)
           (* y2 (* k (- (* y1 y4) (* y0 y5))))
           (if (<= y -1.95e-81)
             t_1
             (if (<= y 4.6e-268)
               (* (* t y5) (- (* a y2) (* i j)))
               (if (<= y 2.6e+47)
                 (* y2 (* c (- (* x y0) (* t y4))))
                 (* y5 (* i (- (* y k) (* t j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y * (b * ((x * a) - (k * y4)));
	double tmp;
	if (y <= -2.06e+77) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -2050000000000.0) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y <= -5.5e-15) {
		tmp = t_1;
	} else if (y <= -7e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -1.95e-81) {
		tmp = t_1;
	} else if (y <= 4.6e-268) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 2.6e+47) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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) :: t_1
    real(8) :: tmp
    t_1 = y * (b * ((x * a) - (k * y4)))
    if (y <= (-2.06d+77)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (y <= (-2050000000000.0d0)) then
        tmp = j * (y1 * ((x * i) - (y3 * y4)))
    else if (y <= (-5.5d-15)) then
        tmp = t_1
    else if (y <= (-7d-67)) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (y <= (-1.95d-81)) then
        tmp = t_1
    else if (y <= 4.6d-268) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 2.6d+47) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else
        tmp = y5 * (i * ((y * k) - (t * 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 t_1 = y * (b * ((x * a) - (k * y4)));
	double tmp;
	if (y <= -2.06e+77) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (y <= -2050000000000.0) {
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	} else if (y <= -5.5e-15) {
		tmp = t_1;
	} else if (y <= -7e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -1.95e-81) {
		tmp = t_1;
	} else if (y <= 4.6e-268) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 2.6e+47) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y * (b * ((x * a) - (k * y4)))
	tmp = 0
	if y <= -2.06e+77:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif y <= -2050000000000.0:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	elif y <= -5.5e-15:
		tmp = t_1
	elif y <= -7e-67:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif y <= -1.95e-81:
		tmp = t_1
	elif y <= 4.6e-268:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 2.6e+47:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	else:
		tmp = y5 * (i * ((y * k) - (t * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (y <= -2.06e+77)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -2050000000000.0)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y <= -5.5e-15)
		tmp = t_1;
	elseif (y <= -7e-67)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y <= -1.95e-81)
		tmp = t_1;
	elseif (y <= 4.6e-268)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 2.6e+47)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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)
	t_1 = y * (b * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (y <= -2.06e+77)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (y <= -2050000000000.0)
		tmp = j * (y1 * ((x * i) - (y3 * y4)));
	elseif (y <= -5.5e-15)
		tmp = t_1;
	elseif (y <= -7e-67)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (y <= -1.95e-81)
		tmp = t_1;
	elseif (y <= 4.6e-268)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 2.6e+47)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	else
		tmp = y5 * (i * ((y * k) - (t * j)));
	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[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.06e+77], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2050000000000.0], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e-15], t$95$1, If[LessEqual[y, -7e-67], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-81], t$95$1, If[LessEqual[y, 4.6e-268], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+47], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.06e77

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 44.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 44.6%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 53.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 53.9%

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot c} - k \cdot b\right)\right) \]

   9. Simplified 53.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(y3 \cdot c - k \cdot b\right)\right)} \]

   if -2.06e77 < y < -2.05e12

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 57.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 57.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 57.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 57.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 58.9%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right)} \]

      2. *-commutative 58.9%

         \[\leadsto \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right) \cdot y1} \]

      3. *-commutative 58.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \cdot y1 \]

      4. associate-*l* 65.0%

         \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot y1\right)} \]

      5. mul-1-neg 65.0%

         \[\leadsto j \cdot \left(\left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \cdot y1\right) \]

      6. unsub-neg 65.0%

         \[\leadsto j \cdot \left(\color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \cdot y1\right) \]

   9. Simplified 65.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x - y4 \cdot y3\right) \cdot y1\right)} \]

   if -2.05e12 < y < -5.5000000000000002e-15 or -7.0000000000000001e-67 < y < -1.94999999999999992e-81

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 26.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 26.2%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 26.2%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 87.5%

      \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -5.5000000000000002e-15 < y < -7.0000000000000001e-67

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 44.1%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 51.0%

      \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \cdot y2 \]

   if -1.94999999999999992e-81 < y < 4.60000000000000021e-268

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 48.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 48.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 51.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 51.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   if 4.60000000000000021e-268 < y < 2.60000000000000003e47

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 47.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 37.5%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x - y4 \cdot t\right)\right)} \cdot y2 \]

   if 2.60000000000000003e47 < y

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 43.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 43.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 55.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 55.3%

         \[\leadsto \left(i \cdot \left(\color{blue}{y \cdot k} - t \cdot j\right)\right) \cdot y5 \]

   9. Simplified 55.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -2050000000000:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-268}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 22: 21.0% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -8.5 \cdot 10^{+202}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.12 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;k \leq -9.8 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.32 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-96}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-16} \lor \neg \left(k \leq 4.1 \cdot 10^{+135}\right):\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-c\right) \cdot \left(y0 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -8.5e+202)
   (* y4 (* y1 (* k y2)))
   (if (<= k -1.12e+139)
     (* z (* k (* y1 (- i))))
     (if (<= k -9.8e+26)
       (* k (* y4 (* y1 y2)))
       (if (<= k -1.32e-180)
         (* a (* t (* y2 y5)))
         (if (<= k 4.8e-134)
           (* i (* t (* j (- y5))))
           (if (<= k 4.4e-96)
             (* a (* y2 (* t y5)))
             (if (or (<= k 2.8e-16) (not (<= k 4.1e+135)))
               (* k (* y (* b (- y4))))
               (* (- c) (* y0 (* 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 (k <= -8.5e+202) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -1.12e+139) {
		tmp = z * (k * (y1 * -i));
	} else if (k <= -9.8e+26) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= -1.32e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 4.8e-134) {
		tmp = i * (t * (j * -y5));
	} else if (k <= 4.4e-96) {
		tmp = a * (y2 * (t * y5));
	} else if ((k <= 2.8e-16) || !(k <= 4.1e+135)) {
		tmp = k * (y * (b * -y4));
	} else {
		tmp = -c * (y0 * (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 (k <= (-8.5d+202)) then
        tmp = y4 * (y1 * (k * y2))
    else if (k <= (-1.12d+139)) then
        tmp = z * (k * (y1 * -i))
    else if (k <= (-9.8d+26)) then
        tmp = k * (y4 * (y1 * y2))
    else if (k <= (-1.32d-180)) then
        tmp = a * (t * (y2 * y5))
    else if (k <= 4.8d-134) then
        tmp = i * (t * (j * -y5))
    else if (k <= 4.4d-96) then
        tmp = a * (y2 * (t * y5))
    else if ((k <= 2.8d-16) .or. (.not. (k <= 4.1d+135))) then
        tmp = k * (y * (b * -y4))
    else
        tmp = -c * (y0 * (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 (k <= -8.5e+202) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -1.12e+139) {
		tmp = z * (k * (y1 * -i));
	} else if (k <= -9.8e+26) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= -1.32e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 4.8e-134) {
		tmp = i * (t * (j * -y5));
	} else if (k <= 4.4e-96) {
		tmp = a * (y2 * (t * y5));
	} else if ((k <= 2.8e-16) || !(k <= 4.1e+135)) {
		tmp = k * (y * (b * -y4));
	} else {
		tmp = -c * (y0 * (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 k <= -8.5e+202:
		tmp = y4 * (y1 * (k * y2))
	elif k <= -1.12e+139:
		tmp = z * (k * (y1 * -i))
	elif k <= -9.8e+26:
		tmp = k * (y4 * (y1 * y2))
	elif k <= -1.32e-180:
		tmp = a * (t * (y2 * y5))
	elif k <= 4.8e-134:
		tmp = i * (t * (j * -y5))
	elif k <= 4.4e-96:
		tmp = a * (y2 * (t * y5))
	elif (k <= 2.8e-16) or not (k <= 4.1e+135):
		tmp = k * (y * (b * -y4))
	else:
		tmp = -c * (y0 * (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 (k <= -8.5e+202)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (k <= -1.12e+139)
		tmp = Float64(z * Float64(k * Float64(y1 * Float64(-i))));
	elseif (k <= -9.8e+26)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (k <= -1.32e-180)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (k <= 4.8e-134)
		tmp = Float64(i * Float64(t * Float64(j * Float64(-y5))));
	elseif (k <= 4.4e-96)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif ((k <= 2.8e-16) || !(k <= 4.1e+135))
		tmp = Float64(k * Float64(y * Float64(b * Float64(-y4))));
	else
		tmp = Float64(Float64(-c) * Float64(y0 * 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 (k <= -8.5e+202)
		tmp = y4 * (y1 * (k * y2));
	elseif (k <= -1.12e+139)
		tmp = z * (k * (y1 * -i));
	elseif (k <= -9.8e+26)
		tmp = k * (y4 * (y1 * y2));
	elseif (k <= -1.32e-180)
		tmp = a * (t * (y2 * y5));
	elseif (k <= 4.8e-134)
		tmp = i * (t * (j * -y5));
	elseif (k <= 4.4e-96)
		tmp = a * (y2 * (t * y5));
	elseif ((k <= 2.8e-16) || ~((k <= 4.1e+135)))
		tmp = k * (y * (b * -y4));
	else
		tmp = -c * (y0 * (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[k, -8.5e+202], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.12e+139], N[(z * N[(k * N[(y1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -9.8e+26], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.32e-180], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.8e-134], N[(i * N[(t * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.4e-96], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[k, 2.8e-16], N[Not[LessEqual[k, 4.1e+135]], $MachinePrecision]], N[(k * N[(y * N[(b * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-c) * N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if k < -8.5000000000000003e202

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 57.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 57.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 28.6%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 28.6%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 28.6%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 41.1%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 41.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 44.3%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 44.3%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -8.5000000000000003e202 < k < -1.12e139

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 44.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 44.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 77.9%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 57.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 57.0%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. associate-*r* 57.1%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)} \]

      3. associate-*r* 67.7%

         \[\leadsto -\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   10. Simplified 67.7%

       \[\leadsto \color{blue}{-\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   if -1.12e139 < k < -9.79999999999999947e26

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 27.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 27.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 27.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -9.79999999999999947e26 < k < -1.32000000000000004e-180

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 32.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.0%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 28.0%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 32.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -1.32000000000000004e-180 < k < 4.80000000000000019e-134

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 40.1%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 41.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 41.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 41.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 32.7%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 32.7%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 31.0%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 31.0%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   13. Taylor expanded in i around 0 32.7%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

   if 4.80000000000000019e-134 < k < 4.39999999999999959e-96

   1. Initial program 49.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 59.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 40.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 40.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 40.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 40.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 40.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 40.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 41.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.5%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 31.5%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 31.5%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 31.7%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 41.4%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 41.4%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if 4.39999999999999959e-96 < k < 2.8000000000000001e-16 or 4.1e135 < k

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 65.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 65.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 65.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 65.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 65.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 65.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around 0 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 45.8%

         \[\leadsto \color{blue}{-k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 45.8%

         \[\leadsto \color{blue}{k \cdot \left(-y4 \cdot \left(y \cdot b\right)\right)} \]

      3. *-commutative 45.8%

         \[\leadsto k \cdot \left(-\color{blue}{\left(y \cdot b\right) \cdot y4}\right) \]

      4. associate-*l* 47.7%

         \[\leadsto k \cdot \left(-\color{blue}{y \cdot \left(b \cdot y4\right)}\right) \]

   10. Simplified 47.7%

       \[\leadsto \color{blue}{k \cdot \left(-y \cdot \left(b \cdot y4\right)\right)} \]

   if 2.8000000000000001e-16 < k < 4.1e135

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 39.9%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 39.9%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around 0 36.8%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.8%

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y3 \cdot z\right)\right)} \]

      2. neg-mul-1 36.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y3 \cdot z\right)\right) \]

   10. Simplified 36.8%

       \[\leadsto c \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8.5 \cdot 10^{+202}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.12 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;k \leq -9.8 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.32 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-96}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{-16} \lor \neg \left(k \leq 4.1 \cdot 10^{+135}\right):\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-c\right) \cdot \left(y0 \cdot \left(z \cdot y3\right)\right)\\ \end{array} \]

Alternative 23: 22.2% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(-y5\right)\\ \mathbf{if}\;y2 \leq -7.2 \cdot 10^{+190}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.7 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -25000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.16 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.3 \cdot 10^{-275}:\\ \;\;\;\;\left(t \cdot i\right) \cdot t_1\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{-186}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-124}:\\ \;\;\;\;i \cdot \left(t \cdot t_1\right)\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (- y5))))
   (if (<= y2 -7.2e+190)
     (* y4 (* k (* y1 y2)))
     (if (<= y2 -2.7e+144)
       (* t (* y5 (* a y2)))
       (if (<= y2 -25000.0)
         (* y4 (* y1 (* k y2)))
         (if (<= y2 -1.16e-23)
           (* c (* (* t y4) (- y2)))
           (if (<= y2 -2.3e-275)
             (* (* t i) t_1)
             (if (<= y2 2.2e-186)
               (* y4 (* c (* y y3)))
               (if (<= y2 3.2e-124)
                 (* i (* t t_1))
                 (if (<= y2 4.6e+17)
                   (* z (* k (* y1 (- i))))
                   (* c (* y0 (* x y2)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * -y5;
	double tmp;
	if (y2 <= -7.2e+190) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y2 <= -2.7e+144) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -25000.0) {
		tmp = y4 * (y1 * (k * y2));
	} else if (y2 <= -1.16e-23) {
		tmp = c * ((t * y4) * -y2);
	} else if (y2 <= -2.3e-275) {
		tmp = (t * i) * t_1;
	} else if (y2 <= 2.2e-186) {
		tmp = y4 * (c * (y * y3));
	} else if (y2 <= 3.2e-124) {
		tmp = i * (t * t_1);
	} else if (y2 <= 4.6e+17) {
		tmp = z * (k * (y1 * -i));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * -y5
    if (y2 <= (-7.2d+190)) then
        tmp = y4 * (k * (y1 * y2))
    else if (y2 <= (-2.7d+144)) then
        tmp = t * (y5 * (a * y2))
    else if (y2 <= (-25000.0d0)) then
        tmp = y4 * (y1 * (k * y2))
    else if (y2 <= (-1.16d-23)) then
        tmp = c * ((t * y4) * -y2)
    else if (y2 <= (-2.3d-275)) then
        tmp = (t * i) * t_1
    else if (y2 <= 2.2d-186) then
        tmp = y4 * (c * (y * y3))
    else if (y2 <= 3.2d-124) then
        tmp = i * (t * t_1)
    else if (y2 <= 4.6d+17) then
        tmp = z * (k * (y1 * -i))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * -y5;
	double tmp;
	if (y2 <= -7.2e+190) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y2 <= -2.7e+144) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -25000.0) {
		tmp = y4 * (y1 * (k * y2));
	} else if (y2 <= -1.16e-23) {
		tmp = c * ((t * y4) * -y2);
	} else if (y2 <= -2.3e-275) {
		tmp = (t * i) * t_1;
	} else if (y2 <= 2.2e-186) {
		tmp = y4 * (c * (y * y3));
	} else if (y2 <= 3.2e-124) {
		tmp = i * (t * t_1);
	} else if (y2 <= 4.6e+17) {
		tmp = z * (k * (y1 * -i));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * -y5
	tmp = 0
	if y2 <= -7.2e+190:
		tmp = y4 * (k * (y1 * y2))
	elif y2 <= -2.7e+144:
		tmp = t * (y5 * (a * y2))
	elif y2 <= -25000.0:
		tmp = y4 * (y1 * (k * y2))
	elif y2 <= -1.16e-23:
		tmp = c * ((t * y4) * -y2)
	elif y2 <= -2.3e-275:
		tmp = (t * i) * t_1
	elif y2 <= 2.2e-186:
		tmp = y4 * (c * (y * y3))
	elif y2 <= 3.2e-124:
		tmp = i * (t * t_1)
	elif y2 <= 4.6e+17:
		tmp = z * (k * (y1 * -i))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(-y5))
	tmp = 0.0
	if (y2 <= -7.2e+190)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	elseif (y2 <= -2.7e+144)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (y2 <= -25000.0)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (y2 <= -1.16e-23)
		tmp = Float64(c * Float64(Float64(t * y4) * Float64(-y2)));
	elseif (y2 <= -2.3e-275)
		tmp = Float64(Float64(t * i) * t_1);
	elseif (y2 <= 2.2e-186)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (y2 <= 3.2e-124)
		tmp = Float64(i * Float64(t * t_1));
	elseif (y2 <= 4.6e+17)
		tmp = Float64(z * Float64(k * Float64(y1 * Float64(-i))));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * -y5;
	tmp = 0.0;
	if (y2 <= -7.2e+190)
		tmp = y4 * (k * (y1 * y2));
	elseif (y2 <= -2.7e+144)
		tmp = t * (y5 * (a * y2));
	elseif (y2 <= -25000.0)
		tmp = y4 * (y1 * (k * y2));
	elseif (y2 <= -1.16e-23)
		tmp = c * ((t * y4) * -y2);
	elseif (y2 <= -2.3e-275)
		tmp = (t * i) * t_1;
	elseif (y2 <= 2.2e-186)
		tmp = y4 * (c * (y * y3));
	elseif (y2 <= 3.2e-124)
		tmp = i * (t * t_1);
	elseif (y2 <= 4.6e+17)
		tmp = z * (k * (y1 * -i));
	else
		tmp = c * (y0 * (x * y2));
	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[(j * (-y5)), $MachinePrecision]}, If[LessEqual[y2, -7.2e+190], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.7e+144], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -25000.0], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.16e-23], N[(c * N[(N[(t * y4), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.3e-275], N[(N[(t * i), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y2, 2.2e-186], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.2e-124], N[(i * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.6e+17], N[(z * N[(k * N[(y1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -7.19999999999999957e190

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 54.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 54.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 57.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]

   if -7.19999999999999957e190 < y2 < -2.70000000000000015e144

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 42.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 59.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 59.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 58.7%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 58.7%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 58.7%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 58.7%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 58.7%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 58.7%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 58.7%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 58.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 66.8%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 66.8%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   if -2.70000000000000015e144 < y2 < -25000

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 41.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 33.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 33.0%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 33.0%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 33.2%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 33.2%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 33.2%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 33.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 33.2%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -25000 < y2 < -1.1599999999999999e-23

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 43.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 43.1%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 43.1%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 43.1%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 43.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in t around inf 57.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 57.7%

         \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 57.7%

         \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      3. *-commutative 57.7%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      4. *-commutative 57.7%

         \[\leadsto c \cdot \left(-\color{blue}{\left(y2 \cdot t\right)} \cdot y4\right) \]

      5. associate-*l* 57.7%

         \[\leadsto c \cdot \left(-\color{blue}{y2 \cdot \left(t \cdot y4\right)}\right) \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{c \cdot \left(-y2 \cdot \left(t \cdot y4\right)\right)} \]

   if -1.1599999999999999e-23 < y2 < -2.2999999999999999e-275

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 49.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 49.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 49.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 49.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 49.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 49.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 31.6%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 31.5%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 31.5%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 31.5%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 23.8%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 23.8%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 27.7%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 27.7%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   if -2.2999999999999999e-275 < y2 < 2.20000000000000013e-186

   1. Initial program 15.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 56.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 44.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 44.5%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 44.5%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 44.5%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 44.5%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 44.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 32.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \cdot y4 \]

   if 2.20000000000000013e-186 < y2 < 3.20000000000000004e-124

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 40.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 40.5%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 40.8%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.2%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 28.2%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 28.2%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 34.6%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 34.6%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 28.3%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 28.3%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   13. Taylor expanded in i around 0 34.6%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

   if 3.20000000000000004e-124 < y2 < 4.6e17

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 46.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 46.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 46.4%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 42.3%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 34.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 34.4%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. associate-*r* 34.4%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)} \]

      3. associate-*r* 38.4%

         \[\leadsto -\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   10. Simplified 38.4%

       \[\leadsto \color{blue}{-\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   if 4.6e17 < y2

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 41.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 41.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   8. Taylor expanded in x around inf 34.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.2 \cdot 10^{+190}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.7 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -25000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.16 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y2 \leq -2.3 \cdot 10^{-275}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.2 \cdot 10^{-186}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-124}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 24: 22.3% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(-y5\right)\\ \mathbf{if}\;k \leq -7.2 \cdot 10^{+201}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -2.5 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-198}:\\ \;\;\;\;i \cdot \left(t \cdot t_1\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 0.000215:\\ \;\;\;\;t \cdot \left(i \cdot t_1\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+128}:\\ \;\;\;\;\left(-c\right) \cdot \left(y0 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (- y5))))
   (if (<= k -7.2e+201)
     (* y4 (* y1 (* k y2)))
     (if (<= k -1.5e+139)
       (* z (* k (* y1 (- i))))
       (if (<= k -4e+26)
         (* k (* y4 (* y1 y2)))
         (if (<= k -2.5e-180)
           (* a (* t (* y2 y5)))
           (if (<= k 1.25e-198)
             (* i (* t t_1))
             (if (<= k 2.4e-48)
               (* c (* y4 (* y y3)))
               (if (<= k 0.000215)
                 (* t (* i t_1))
                 (if (<= k 5e+128)
                   (* (- c) (* y0 (* z y3)))
                   (* y2 (* y1 (* k 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 t_1 = j * -y5;
	double tmp;
	if (k <= -7.2e+201) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -1.5e+139) {
		tmp = z * (k * (y1 * -i));
	} else if (k <= -4e+26) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= -2.5e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 1.25e-198) {
		tmp = i * (t * t_1);
	} else if (k <= 2.4e-48) {
		tmp = c * (y4 * (y * y3));
	} else if (k <= 0.000215) {
		tmp = t * (i * t_1);
	} else if (k <= 5e+128) {
		tmp = -c * (y0 * (z * y3));
	} else {
		tmp = y2 * (y1 * (k * 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) :: t_1
    real(8) :: tmp
    t_1 = j * -y5
    if (k <= (-7.2d+201)) then
        tmp = y4 * (y1 * (k * y2))
    else if (k <= (-1.5d+139)) then
        tmp = z * (k * (y1 * -i))
    else if (k <= (-4d+26)) then
        tmp = k * (y4 * (y1 * y2))
    else if (k <= (-2.5d-180)) then
        tmp = a * (t * (y2 * y5))
    else if (k <= 1.25d-198) then
        tmp = i * (t * t_1)
    else if (k <= 2.4d-48) then
        tmp = c * (y4 * (y * y3))
    else if (k <= 0.000215d0) then
        tmp = t * (i * t_1)
    else if (k <= 5d+128) then
        tmp = -c * (y0 * (z * y3))
    else
        tmp = y2 * (y1 * (k * 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 t_1 = j * -y5;
	double tmp;
	if (k <= -7.2e+201) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -1.5e+139) {
		tmp = z * (k * (y1 * -i));
	} else if (k <= -4e+26) {
		tmp = k * (y4 * (y1 * y2));
	} else if (k <= -2.5e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 1.25e-198) {
		tmp = i * (t * t_1);
	} else if (k <= 2.4e-48) {
		tmp = c * (y4 * (y * y3));
	} else if (k <= 0.000215) {
		tmp = t * (i * t_1);
	} else if (k <= 5e+128) {
		tmp = -c * (y0 * (z * y3));
	} else {
		tmp = y2 * (y1 * (k * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * -y5
	tmp = 0
	if k <= -7.2e+201:
		tmp = y4 * (y1 * (k * y2))
	elif k <= -1.5e+139:
		tmp = z * (k * (y1 * -i))
	elif k <= -4e+26:
		tmp = k * (y4 * (y1 * y2))
	elif k <= -2.5e-180:
		tmp = a * (t * (y2 * y5))
	elif k <= 1.25e-198:
		tmp = i * (t * t_1)
	elif k <= 2.4e-48:
		tmp = c * (y4 * (y * y3))
	elif k <= 0.000215:
		tmp = t * (i * t_1)
	elif k <= 5e+128:
		tmp = -c * (y0 * (z * y3))
	else:
		tmp = y2 * (y1 * (k * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(-y5))
	tmp = 0.0
	if (k <= -7.2e+201)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (k <= -1.5e+139)
		tmp = Float64(z * Float64(k * Float64(y1 * Float64(-i))));
	elseif (k <= -4e+26)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (k <= -2.5e-180)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (k <= 1.25e-198)
		tmp = Float64(i * Float64(t * t_1));
	elseif (k <= 2.4e-48)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (k <= 0.000215)
		tmp = Float64(t * Float64(i * t_1));
	elseif (k <= 5e+128)
		tmp = Float64(Float64(-c) * Float64(y0 * Float64(z * y3)));
	else
		tmp = Float64(y2 * Float64(y1 * Float64(k * 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)
	t_1 = j * -y5;
	tmp = 0.0;
	if (k <= -7.2e+201)
		tmp = y4 * (y1 * (k * y2));
	elseif (k <= -1.5e+139)
		tmp = z * (k * (y1 * -i));
	elseif (k <= -4e+26)
		tmp = k * (y4 * (y1 * y2));
	elseif (k <= -2.5e-180)
		tmp = a * (t * (y2 * y5));
	elseif (k <= 1.25e-198)
		tmp = i * (t * t_1);
	elseif (k <= 2.4e-48)
		tmp = c * (y4 * (y * y3));
	elseif (k <= 0.000215)
		tmp = t * (i * t_1);
	elseif (k <= 5e+128)
		tmp = -c * (y0 * (z * y3));
	else
		tmp = y2 * (y1 * (k * y4));
	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[(j * (-y5)), $MachinePrecision]}, If[LessEqual[k, -7.2e+201], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.5e+139], N[(z * N[(k * N[(y1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4e+26], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.5e-180], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.25e-198], N[(i * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.4e-48], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 0.000215], N[(t * N[(i * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5e+128], N[((-c) * N[(y0 * N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y1 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if k < -7.19999999999999951e201

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 20.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 57.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 57.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 57.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 28.6%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 28.6%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 28.6%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 41.1%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 41.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 44.3%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 44.3%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -7.19999999999999951e201 < k < -1.5e139

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 44.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 44.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 44.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 77.9%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 57.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 57.0%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. associate-*r* 57.1%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)} \]

      3. associate-*r* 67.7%

         \[\leadsto -\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   10. Simplified 67.7%

       \[\leadsto \color{blue}{-\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   if -1.5e139 < k < -4.00000000000000019e26

   1. Initial program 34.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 27.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 27.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 27.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 27.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -4.00000000000000019e26 < k < -2.5000000000000001e-180

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 32.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.0%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 28.0%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 32.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -2.5000000000000001e-180 < k < 1.25e-198

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.0%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 45.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 47.4%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 39.6%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 39.6%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 37.3%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 37.3%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   13. Taylor expanded in i around 0 39.6%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

   if 1.25e-198 < k < 2.4e-48

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 26.3%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 26.3%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 26.3%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 26.3%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 26.3%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 26.3%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 26.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 26.1%

         \[\leadsto c \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y4\right)} \]

   10. Simplified 26.1%

       \[\leadsto \color{blue}{c \cdot \left(\left(y \cdot y3\right) \cdot y4\right)} \]

   if 2.4e-48 < k < 2.14999999999999995e-4

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 31.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 31.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 31.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 31.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 31.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 31.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 31.5%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 46.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.7%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 46.7%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 46.7%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 32.2%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 32.2%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 32.2%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 32.2%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   13. Taylor expanded in i around 0 32.2%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 32.2%

          \[\leadsto -i \cdot \left(t \cdot \color{blue}{\left(y5 \cdot j\right)}\right) \]

       2. *-commutative 32.2%

          \[\leadsto -\color{blue}{\left(t \cdot \left(y5 \cdot j\right)\right) \cdot i} \]

       3. associate-*l* 39.5%

          \[\leadsto -\color{blue}{t \cdot \left(\left(y5 \cdot j\right) \cdot i\right)} \]

       4. *-commutative 39.5%

          \[\leadsto -t \cdot \left(\color{blue}{\left(j \cdot y5\right)} \cdot i\right) \]

   15. Simplified 39.5%

       \[\leadsto -\color{blue}{t \cdot \left(\left(j \cdot y5\right) \cdot i\right)} \]

   if 2.14999999999999995e-4 < k < 5e128

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around 0 39.3%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 39.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(y3 \cdot z\right)\right)} \]

      2. neg-mul-1 39.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(y3 \cdot z\right)\right) \]

   10. Simplified 39.3%

       \[\leadsto c \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(y3 \cdot z\right)\right)} \]

   if 5e128 < k

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 42.7%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.7%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 42.7%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 42.7%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 42.7%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 42.7%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y1 around inf 36.7%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 43.5%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2\right)} \]

      2. associate-*r* 48.6%

         \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]

   10. Simplified 48.6%

       \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]
3. Recombined 9 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7.2 \cdot 10^{+201}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+26}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -2.5 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.25 \cdot 10^{-198}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 0.000215:\\ \;\;\;\;t \cdot \left(i \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{+128}:\\ \;\;\;\;\left(-c\right) \cdot \left(y0 \cdot \left(z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \]

Alternative 25: 30.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-208}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+212} \lor \neg \left(t \leq 2.8 \cdot 10^{+256}\right):\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y1 (- (* x i) (* y3 y4))))))
   (if (<= t -1.35e+49)
     (* c (* t (- (* z i) (* y2 y4))))
     (if (<= t -6.5e-122)
       t_1
       (if (<= t -1.3e-208)
         (* k (* y (* b (- y4))))
         (if (<= t 1.35e-171)
           t_1
           (if (or (<= t 3.6e+212) (not (<= t 2.8e+256)))
             (* c (* z (- (* t i) (* y0 y3))))
             (* c (* (* t y4) (- y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (t <= -1.35e+49) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -6.5e-122) {
		tmp = t_1;
	} else if (t <= -1.3e-208) {
		tmp = k * (y * (b * -y4));
	} else if (t <= 1.35e-171) {
		tmp = t_1;
	} else if ((t <= 3.6e+212) || !(t <= 2.8e+256)) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else {
		tmp = c * ((t * y4) * -y2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y1 * ((x * i) - (y3 * y4)))
    if (t <= (-1.35d+49)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= (-6.5d-122)) then
        tmp = t_1
    else if (t <= (-1.3d-208)) then
        tmp = k * (y * (b * -y4))
    else if (t <= 1.35d-171) then
        tmp = t_1
    else if ((t <= 3.6d+212) .or. (.not. (t <= 2.8d+256))) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else
        tmp = c * ((t * y4) * -y2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y1 * ((x * i) - (y3 * y4)));
	double tmp;
	if (t <= -1.35e+49) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -6.5e-122) {
		tmp = t_1;
	} else if (t <= -1.3e-208) {
		tmp = k * (y * (b * -y4));
	} else if (t <= 1.35e-171) {
		tmp = t_1;
	} else if ((t <= 3.6e+212) || !(t <= 2.8e+256)) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else {
		tmp = c * ((t * y4) * -y2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y1 * ((x * i) - (y3 * y4)))
	tmp = 0
	if t <= -1.35e+49:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= -6.5e-122:
		tmp = t_1
	elif t <= -1.3e-208:
		tmp = k * (y * (b * -y4))
	elif t <= 1.35e-171:
		tmp = t_1
	elif (t <= 3.6e+212) or not (t <= 2.8e+256):
		tmp = c * (z * ((t * i) - (y0 * y3)))
	else:
		tmp = c * ((t * y4) * -y2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * y4))))
	tmp = 0.0
	if (t <= -1.35e+49)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= -6.5e-122)
		tmp = t_1;
	elseif (t <= -1.3e-208)
		tmp = Float64(k * Float64(y * Float64(b * Float64(-y4))));
	elseif (t <= 1.35e-171)
		tmp = t_1;
	elseif ((t <= 3.6e+212) || !(t <= 2.8e+256))
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	else
		tmp = Float64(c * Float64(Float64(t * y4) * Float64(-y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y1 * ((x * i) - (y3 * y4)));
	tmp = 0.0;
	if (t <= -1.35e+49)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= -6.5e-122)
		tmp = t_1;
	elseif (t <= -1.3e-208)
		tmp = k * (y * (b * -y4));
	elseif (t <= 1.35e-171)
		tmp = t_1;
	elseif ((t <= 3.6e+212) || ~((t <= 2.8e+256)))
		tmp = c * (z * ((t * i) - (y0 * y3)));
	else
		tmp = c * ((t * y4) * -y2);
	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[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+49], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-122], t$95$1, If[LessEqual[t, -1.3e-208], N[(k * N[(y * N[(b * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-171], t$95$1, If[Or[LessEqual[t, 3.6e+212], N[Not[LessEqual[t, 2.8e+256]], $MachinePrecision]], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * y4), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.35000000000000005e49

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 22.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 42.2%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y4 \cdot y2\right) \cdot t\right)} \]

   if -1.35000000000000005e49 < t < -6.49999999999999965e-122 or -1.30000000000000008e-208 < t < 1.35000000000000007e-171

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 39.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 39.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 39.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 39.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 37.7%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 37.7%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right)} \]

      2. *-commutative 37.7%

         \[\leadsto \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right) \cdot y1} \]

      3. *-commutative 37.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \cdot y1 \]

      4. associate-*l* 36.5%

         \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot y1\right)} \]

      5. mul-1-neg 36.5%

         \[\leadsto j \cdot \left(\left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \cdot y1\right) \]

      6. unsub-neg 36.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \cdot y1\right) \]

   9. Simplified 36.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x - y4 \cdot y3\right) \cdot y1\right)} \]

   if -6.49999999999999965e-122 < t < -1.30000000000000008e-208

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 51.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 51.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 51.4%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 51.4%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 51.4%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around 0 51.3%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.3%

         \[\leadsto \color{blue}{-k \cdot \left(y4 \cdot \left(y \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 51.3%

         \[\leadsto \color{blue}{k \cdot \left(-y4 \cdot \left(y \cdot b\right)\right)} \]

      3. *-commutative 51.3%

         \[\leadsto k \cdot \left(-\color{blue}{\left(y \cdot b\right) \cdot y4}\right) \]

      4. associate-*l* 51.3%

         \[\leadsto k \cdot \left(-\color{blue}{y \cdot \left(b \cdot y4\right)}\right) \]

   10. Simplified 51.3%

       \[\leadsto \color{blue}{k \cdot \left(-y \cdot \left(b \cdot y4\right)\right)} \]

   if 1.35000000000000007e-171 < t < 3.6e212 or 2.79999999999999988e256 < t

   1. Initial program 35.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 42.7%

      \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right) \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 42.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)} \cdot z\right) \]

      2. mul-1-neg 42.7%

         \[\leadsto c \cdot \left(\left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right) \cdot z\right) \]

      3. unsub-neg 42.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot z\right) \]

      4. *-commutative 42.7%

         \[\leadsto c \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot z\right) \]

      5. *-commutative 42.7%

         \[\leadsto c \cdot \left(\left(t \cdot i - \color{blue}{y3 \cdot y0}\right) \cdot z\right) \]

   7. Simplified 42.7%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot i - y3 \cdot y0\right) \cdot z\right)} \]

   if 3.6e212 < t < 2.79999999999999988e256

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 11.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 33.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 56.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 56.2%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 56.2%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 56.2%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 56.2%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 56.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in t around inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 67.1%

         \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 67.1%

         \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      3. *-commutative 67.1%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      4. *-commutative 67.1%

         \[\leadsto c \cdot \left(-\color{blue}{\left(y2 \cdot t\right)} \cdot y4\right) \]

      5. associate-*l* 77.9%

         \[\leadsto c \cdot \left(-\color{blue}{y2 \cdot \left(t \cdot y4\right)}\right) \]

   10. Simplified 77.9%

       \[\leadsto \color{blue}{c \cdot \left(-y2 \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-208}:\\ \;\;\;\;k \cdot \left(y \cdot \left(b \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+212} \lor \neg \left(t \leq 2.8 \cdot 10^{+256}\right):\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \end{array} \]

Alternative 26: 31.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ t_2 := y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-130}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (- (* t i) (* y0 y3)))))
        (t_2 (* y (* b (- (* x a) (* k y4))))))
   (if (<= z -1.75e-27)
     t_1
     (if (<= z -9e-130)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= z -3.9e-302)
         t_2
         (if (<= z 4.8e-91)
           (* y (* y4 (- (* c y3) (* b k))))
           (if (<= z 4.6e+37)
             t_2
             (if (<= z 2.15e+158)
               (* j (* y1 (- (* x i) (* y3 y4))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (z * ((t * i) - (y0 * y3)));
	double t_2 = y * (b * ((x * a) - (k * y4)));
	double tmp;
	if (z <= -1.75e-27) {
		tmp = t_1;
	} else if (z <= -9e-130) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (z <= -3.9e-302) {
		tmp = t_2;
	} else if (z <= 4.8e-91) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 4.6e+37) {
		tmp = t_2;
	} else if (z <= 2.15e+158) {
		tmp = j * (y1 * ((x * i) - (y3 * 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) :: t_2
    real(8) :: tmp
    t_1 = c * (z * ((t * i) - (y0 * y3)))
    t_2 = y * (b * ((x * a) - (k * y4)))
    if (z <= (-1.75d-27)) then
        tmp = t_1
    else if (z <= (-9d-130)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (z <= (-3.9d-302)) then
        tmp = t_2
    else if (z <= 4.8d-91) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (z <= 4.6d+37) then
        tmp = t_2
    else if (z <= 2.15d+158) then
        tmp = j * (y1 * ((x * i) - (y3 * 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 = c * (z * ((t * i) - (y0 * y3)));
	double t_2 = y * (b * ((x * a) - (k * y4)));
	double tmp;
	if (z <= -1.75e-27) {
		tmp = t_1;
	} else if (z <= -9e-130) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (z <= -3.9e-302) {
		tmp = t_2;
	} else if (z <= 4.8e-91) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 4.6e+37) {
		tmp = t_2;
	} else if (z <= 2.15e+158) {
		tmp = j * (y1 * ((x * i) - (y3 * 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 = c * (z * ((t * i) - (y0 * y3)))
	t_2 = y * (b * ((x * a) - (k * y4)))
	tmp = 0
	if z <= -1.75e-27:
		tmp = t_1
	elif z <= -9e-130:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif z <= -3.9e-302:
		tmp = t_2
	elif z <= 4.8e-91:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif z <= 4.6e+37:
		tmp = t_2
	elif z <= 2.15e+158:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))))
	t_2 = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))))
	tmp = 0.0
	if (z <= -1.75e-27)
		tmp = t_1;
	elseif (z <= -9e-130)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (z <= -3.9e-302)
		tmp = t_2;
	elseif (z <= 4.8e-91)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (z <= 4.6e+37)
		tmp = t_2;
	elseif (z <= 2.15e+158)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * 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 = c * (z * ((t * i) - (y0 * y3)));
	t_2 = y * (b * ((x * a) - (k * y4)));
	tmp = 0.0;
	if (z <= -1.75e-27)
		tmp = t_1;
	elseif (z <= -9e-130)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (z <= -3.9e-302)
		tmp = t_2;
	elseif (z <= 4.8e-91)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (z <= 4.6e+37)
		tmp = t_2;
	elseif (z <= 2.15e+158)
		tmp = j * (y1 * ((x * i) - (y3 * 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[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e-27], t$95$1, If[LessEqual[z, -9e-130], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-302], t$95$2, If[LessEqual[z, 4.8e-91], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+37], t$95$2, If[LessEqual[z, 2.15e+158], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7500000000000001e-27 or 2.15e158 < z

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 36.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 52.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right) \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)} \cdot z\right) \]

      2. mul-1-neg 52.9%

         \[\leadsto c \cdot \left(\left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right) \cdot z\right) \]

      3. unsub-neg 52.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot z\right) \]

      4. *-commutative 52.9%

         \[\leadsto c \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot z\right) \]

      5. *-commutative 52.9%

         \[\leadsto c \cdot \left(\left(t \cdot i - \color{blue}{y3 \cdot y0}\right) \cdot z\right) \]

   7. Simplified 52.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot i - y3 \cdot y0\right) \cdot z\right)} \]

   if -1.7500000000000001e-27 < z < -9e-130

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 52.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y4 \cdot y2\right) \cdot t\right)} \]

   if -9e-130 < z < -3.8999999999999999e-302 or 4.80000000000000022e-91 < z < 4.60000000000000005e37

   1. Initial program 36.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 29.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 29.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 29.9%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 39.2%

      \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -3.8999999999999999e-302 < z < 4.80000000000000022e-91

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 47.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 48.3%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot c} - k \cdot b\right)\right) \]

   9. Simplified 48.3%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(y3 \cdot c - k \cdot b\right)\right)} \]

   if 4.60000000000000005e37 < z < 2.15e158

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right)} \]

      2. *-commutative 47.7%

         \[\leadsto \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right) \cdot y1} \]

      3. *-commutative 47.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \cdot y1 \]

      4. associate-*l* 47.7%

         \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot y1\right)} \]

      5. mul-1-neg 47.7%

         \[\leadsto j \cdot \left(\left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \cdot y1\right) \]

      6. unsub-neg 47.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \cdot y1\right) \]

   9. Simplified 47.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x - y4 \cdot y3\right) \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-130}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \end{array} \]

Alternative 27: 31.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-287}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* z (- (* t i) (* y0 y3))))))
   (if (<= z -1.55e-27)
     t_1
     (if (<= z -9.5e-120)
       (* c (* t (- (* z i) (* y2 y4))))
       (if (<= z 3.3e-287)
         (* y4 (* k (- (* y1 y2) (* y b))))
         (if (<= z 5.2e-90)
           (* y (* y4 (- (* c y3) (* b k))))
           (if (<= z 2.5e+37)
             (* y (* b (- (* x a) (* k y4))))
             (if (<= z 6.5e+155) (* j (* y1 (- (* x i) (* y3 y4)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (z <= -1.55e-27) {
		tmp = t_1;
	} else if (z <= -9.5e-120) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (z <= 3.3e-287) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (z <= 5.2e-90) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 2.5e+37) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (z <= 6.5e+155) {
		tmp = j * (y1 * ((x * i) - (y3 * 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 = c * (z * ((t * i) - (y0 * y3)))
    if (z <= (-1.55d-27)) then
        tmp = t_1
    else if (z <= (-9.5d-120)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (z <= 3.3d-287) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (z <= 5.2d-90) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (z <= 2.5d+37) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (z <= 6.5d+155) then
        tmp = j * (y1 * ((x * i) - (y3 * 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 = c * (z * ((t * i) - (y0 * y3)));
	double tmp;
	if (z <= -1.55e-27) {
		tmp = t_1;
	} else if (z <= -9.5e-120) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (z <= 3.3e-287) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (z <= 5.2e-90) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 2.5e+37) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (z <= 6.5e+155) {
		tmp = j * (y1 * ((x * i) - (y3 * 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 = c * (z * ((t * i) - (y0 * y3)))
	tmp = 0
	if z <= -1.55e-27:
		tmp = t_1
	elif z <= -9.5e-120:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif z <= 3.3e-287:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif z <= 5.2e-90:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif z <= 2.5e+37:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif z <= 6.5e+155:
		tmp = j * (y1 * ((x * i) - (y3 * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))))
	tmp = 0.0
	if (z <= -1.55e-27)
		tmp = t_1;
	elseif (z <= -9.5e-120)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (z <= 3.3e-287)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (z <= 5.2e-90)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (z <= 2.5e+37)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (z <= 6.5e+155)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(y3 * 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 = c * (z * ((t * i) - (y0 * y3)));
	tmp = 0.0;
	if (z <= -1.55e-27)
		tmp = t_1;
	elseif (z <= -9.5e-120)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (z <= 3.3e-287)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (z <= 5.2e-90)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (z <= 2.5e+37)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (z <= 6.5e+155)
		tmp = j * (y1 * ((x * i) - (y3 * 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[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e-27], t$95$1, If[LessEqual[z, -9.5e-120], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-287], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-90], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+37], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+155], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.5499999999999999e-27 or 6.50000000000000046e155 < z

   1. Initial program 21.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 36.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in z around inf 52.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right) \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)} \cdot z\right) \]

      2. mul-1-neg 52.9%

         \[\leadsto c \cdot \left(\left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right) \cdot z\right) \]

      3. unsub-neg 52.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot z\right) \]

      4. *-commutative 52.9%

         \[\leadsto c \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot z\right) \]

      5. *-commutative 52.9%

         \[\leadsto c \cdot \left(\left(t \cdot i - \color{blue}{y3 \cdot y0}\right) \cdot z\right) \]

   7. Simplified 52.9%

      \[\leadsto c \cdot \color{blue}{\left(\left(t \cdot i - y3 \cdot y0\right) \cdot z\right)} \]

   if -1.5499999999999999e-27 < z < -9.49999999999999937e-120

   1. Initial program 42.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 58.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 63.8%

      \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y4 \cdot y2\right) \cdot t\right)} \]

   if -9.49999999999999937e-120 < z < 3.29999999999999973e-287

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.1%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 41.1%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 41.1%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 41.1%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 41.1%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   if 3.29999999999999973e-287 < z < 5.2000000000000001e-90

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 48.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.7%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 48.7%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 49.0%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot c} - k \cdot b\right)\right) \]

   9. Simplified 49.0%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(y3 \cdot c - k \cdot b\right)\right)} \]

   if 5.2000000000000001e-90 < z < 2.49999999999999994e37

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 31.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 31.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 31.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 49.2%

      \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if 2.49999999999999994e37 < z < 6.50000000000000046e155

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right)} \]

      2. *-commutative 47.7%

         \[\leadsto \color{blue}{\left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot j\right) \cdot y1} \]

      3. *-commutative 47.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \cdot y1 \]

      4. associate-*l* 47.7%

         \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right) \cdot y1\right)} \]

      5. mul-1-neg 47.7%

         \[\leadsto j \cdot \left(\left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \cdot y1\right) \]

      6. unsub-neg 47.7%

         \[\leadsto j \cdot \left(\color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \cdot y1\right) \]

   9. Simplified 47.7%

      \[\leadsto \color{blue}{j \cdot \left(\left(i \cdot x - y4 \cdot y3\right) \cdot y1\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-287}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \end{array} \]

Alternative 28: 22.5% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -8.2 \cdot 10^{+188}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -350:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-24}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y2 \leq -9.2 \cdot 10^{-180}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -8.2e+188)
   (* y4 (* k (* y1 y2)))
   (if (<= y2 -4e+139)
     (* t (* y5 (* a y2)))
     (if (<= y2 -350.0)
       (* y4 (* y1 (* k y2)))
       (if (<= y2 -3.8e-24)
         (* c (* (* t y4) (- y2)))
         (if (<= y2 -9.2e-180)
           (* (* t i) (* j (- y5)))
           (if (<= y2 3.5e-124)
             (* y4 (* k (* y (- b))))
             (if (<= y2 1.35e+16)
               (* z (* k (* y1 (- i))))
               (* c (* y0 (* x y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.2e+188) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y2 <= -4e+139) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -350.0) {
		tmp = y4 * (y1 * (k * y2));
	} else if (y2 <= -3.8e-24) {
		tmp = c * ((t * y4) * -y2);
	} else if (y2 <= -9.2e-180) {
		tmp = (t * i) * (j * -y5);
	} else if (y2 <= 3.5e-124) {
		tmp = y4 * (k * (y * -b));
	} else if (y2 <= 1.35e+16) {
		tmp = z * (k * (y1 * -i));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-8.2d+188)) then
        tmp = y4 * (k * (y1 * y2))
    else if (y2 <= (-4d+139)) then
        tmp = t * (y5 * (a * y2))
    else if (y2 <= (-350.0d0)) then
        tmp = y4 * (y1 * (k * y2))
    else if (y2 <= (-3.8d-24)) then
        tmp = c * ((t * y4) * -y2)
    else if (y2 <= (-9.2d-180)) then
        tmp = (t * i) * (j * -y5)
    else if (y2 <= 3.5d-124) then
        tmp = y4 * (k * (y * -b))
    else if (y2 <= 1.35d+16) then
        tmp = z * (k * (y1 * -i))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.2e+188) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y2 <= -4e+139) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -350.0) {
		tmp = y4 * (y1 * (k * y2));
	} else if (y2 <= -3.8e-24) {
		tmp = c * ((t * y4) * -y2);
	} else if (y2 <= -9.2e-180) {
		tmp = (t * i) * (j * -y5);
	} else if (y2 <= 3.5e-124) {
		tmp = y4 * (k * (y * -b));
	} else if (y2 <= 1.35e+16) {
		tmp = z * (k * (y1 * -i));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -8.2e+188:
		tmp = y4 * (k * (y1 * y2))
	elif y2 <= -4e+139:
		tmp = t * (y5 * (a * y2))
	elif y2 <= -350.0:
		tmp = y4 * (y1 * (k * y2))
	elif y2 <= -3.8e-24:
		tmp = c * ((t * y4) * -y2)
	elif y2 <= -9.2e-180:
		tmp = (t * i) * (j * -y5)
	elif y2 <= 3.5e-124:
		tmp = y4 * (k * (y * -b))
	elif y2 <= 1.35e+16:
		tmp = z * (k * (y1 * -i))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -8.2e+188)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	elseif (y2 <= -4e+139)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (y2 <= -350.0)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (y2 <= -3.8e-24)
		tmp = Float64(c * Float64(Float64(t * y4) * Float64(-y2)));
	elseif (y2 <= -9.2e-180)
		tmp = Float64(Float64(t * i) * Float64(j * Float64(-y5)));
	elseif (y2 <= 3.5e-124)
		tmp = Float64(y4 * Float64(k * Float64(y * Float64(-b))));
	elseif (y2 <= 1.35e+16)
		tmp = Float64(z * Float64(k * Float64(y1 * Float64(-i))));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -8.2e+188)
		tmp = y4 * (k * (y1 * y2));
	elseif (y2 <= -4e+139)
		tmp = t * (y5 * (a * y2));
	elseif (y2 <= -350.0)
		tmp = y4 * (y1 * (k * y2));
	elseif (y2 <= -3.8e-24)
		tmp = c * ((t * y4) * -y2);
	elseif (y2 <= -9.2e-180)
		tmp = (t * i) * (j * -y5);
	elseif (y2 <= 3.5e-124)
		tmp = y4 * (k * (y * -b));
	elseif (y2 <= 1.35e+16)
		tmp = z * (k * (y1 * -i));
	else
		tmp = c * (y0 * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -8.2e+188], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4e+139], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -350.0], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.8e-24], N[(c * N[(N[(t * y4), $MachinePrecision] * (-y2)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9.2e-180], N[(N[(t * i), $MachinePrecision] * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.5e-124], N[(y4 * N[(k * N[(y * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.35e+16], N[(z * N[(k * N[(y1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -8.2e188

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 54.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 54.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 57.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]

   if -8.2e188 < y2 < -4.00000000000000013e139

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 42.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 59.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 59.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 58.7%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 58.7%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 58.7%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 58.7%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 58.7%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 58.7%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 58.7%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 58.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 66.8%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 66.8%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   if -4.00000000000000013e139 < y2 < -350

   1. Initial program 23.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 41.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 41.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 33.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 33.0%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 33.0%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 33.2%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 33.2%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 33.2%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 33.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 33.2%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -350 < y2 < -3.80000000000000026e-24

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 43.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 43.1%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 43.1%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 43.1%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 43.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in t around inf 57.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 57.7%

         \[\leadsto \color{blue}{-c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. distribute-rgt-neg-in 57.7%

         \[\leadsto \color{blue}{c \cdot \left(-y4 \cdot \left(t \cdot y2\right)\right)} \]

      3. *-commutative 57.7%

         \[\leadsto c \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot y4}\right) \]

      4. *-commutative 57.7%

         \[\leadsto c \cdot \left(-\color{blue}{\left(y2 \cdot t\right)} \cdot y4\right) \]

      5. associate-*l* 57.7%

         \[\leadsto c \cdot \left(-\color{blue}{y2 \cdot \left(t \cdot y4\right)}\right) \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{c \cdot \left(-y2 \cdot \left(t \cdot y4\right)\right)} \]

   if -3.80000000000000026e-24 < y2 < -9.19999999999999985e-180

   1. Initial program 39.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 46.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 46.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 46.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 46.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 46.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 46.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 39.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.7%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 39.7%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 39.7%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 33.4%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 33.4%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 39.6%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 39.6%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   if -9.19999999999999985e-180 < y2 < 3.4999999999999999e-124

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 49.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 33.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 33.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around 0 33.1%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 33.1%

         \[\leadsto y4 \cdot \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)} \]

      2. *-commutative 33.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y \cdot b\right) \cdot k}\right) \]

      3. distribute-rgt-neg-in 33.1%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot \left(-k\right)\right)} \]

   10. Simplified 33.1%

       \[\leadsto y4 \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot \left(-k\right)\right)} \]

   if 3.4999999999999999e-124 < y2 < 1.35e16

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 46.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 46.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 46.4%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 42.3%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 34.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 34.4%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. associate-*r* 34.4%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)} \]

      3. associate-*r* 38.4%

         \[\leadsto -\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   10. Simplified 38.4%

       \[\leadsto \color{blue}{-\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   if 1.35e16 < y2

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 41.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 41.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   8. Taylor expanded in x around inf 34.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.2 \cdot 10^{+188}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -4 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -350:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-24}:\\ \;\;\;\;c \cdot \left(\left(t \cdot y4\right) \cdot \left(-y2\right)\right)\\ \mathbf{elif}\;y2 \leq -9.2 \cdot 10^{-180}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.35 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 29: 22.8% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.8 \cdot 10^{+190}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1 \cdot 10^{+28}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y2 \leq -9.5 \cdot 10^{-179}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-123}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.8e+190)
   (* y4 (* k (* y1 y2)))
   (if (<= y2 -6e+137)
     (* t (* y5 (* a y2)))
     (if (<= y2 -1e+28)
       (* k (* y4 (* y1 y2)))
       (if (<= y2 -1.9e-22)
         (* y4 (* (* y k) (- b)))
         (if (<= y2 -9.5e-179)
           (* (* t i) (* j (- y5)))
           (if (<= y2 2e-123)
             (* y4 (* k (* y (- b))))
             (if (<= y2 1.25e+17)
               (* z (* k (* y1 (- i))))
               (* c (* y0 (* x y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.8e+190) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y2 <= -6e+137) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -1e+28) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= -1.9e-22) {
		tmp = y4 * ((y * k) * -b);
	} else if (y2 <= -9.5e-179) {
		tmp = (t * i) * (j * -y5);
	} else if (y2 <= 2e-123) {
		tmp = y4 * (k * (y * -b));
	} else if (y2 <= 1.25e+17) {
		tmp = z * (k * (y1 * -i));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.8d+190)) then
        tmp = y4 * (k * (y1 * y2))
    else if (y2 <= (-6d+137)) then
        tmp = t * (y5 * (a * y2))
    else if (y2 <= (-1d+28)) then
        tmp = k * (y4 * (y1 * y2))
    else if (y2 <= (-1.9d-22)) then
        tmp = y4 * ((y * k) * -b)
    else if (y2 <= (-9.5d-179)) then
        tmp = (t * i) * (j * -y5)
    else if (y2 <= 2d-123) then
        tmp = y4 * (k * (y * -b))
    else if (y2 <= 1.25d+17) then
        tmp = z * (k * (y1 * -i))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.8e+190) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y2 <= -6e+137) {
		tmp = t * (y5 * (a * y2));
	} else if (y2 <= -1e+28) {
		tmp = k * (y4 * (y1 * y2));
	} else if (y2 <= -1.9e-22) {
		tmp = y4 * ((y * k) * -b);
	} else if (y2 <= -9.5e-179) {
		tmp = (t * i) * (j * -y5);
	} else if (y2 <= 2e-123) {
		tmp = y4 * (k * (y * -b));
	} else if (y2 <= 1.25e+17) {
		tmp = z * (k * (y1 * -i));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.8e+190:
		tmp = y4 * (k * (y1 * y2))
	elif y2 <= -6e+137:
		tmp = t * (y5 * (a * y2))
	elif y2 <= -1e+28:
		tmp = k * (y4 * (y1 * y2))
	elif y2 <= -1.9e-22:
		tmp = y4 * ((y * k) * -b)
	elif y2 <= -9.5e-179:
		tmp = (t * i) * (j * -y5)
	elif y2 <= 2e-123:
		tmp = y4 * (k * (y * -b))
	elif y2 <= 1.25e+17:
		tmp = z * (k * (y1 * -i))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.8e+190)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	elseif (y2 <= -6e+137)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (y2 <= -1e+28)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	elseif (y2 <= -1.9e-22)
		tmp = Float64(y4 * Float64(Float64(y * k) * Float64(-b)));
	elseif (y2 <= -9.5e-179)
		tmp = Float64(Float64(t * i) * Float64(j * Float64(-y5)));
	elseif (y2 <= 2e-123)
		tmp = Float64(y4 * Float64(k * Float64(y * Float64(-b))));
	elseif (y2 <= 1.25e+17)
		tmp = Float64(z * Float64(k * Float64(y1 * Float64(-i))));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.8e+190)
		tmp = y4 * (k * (y1 * y2));
	elseif (y2 <= -6e+137)
		tmp = t * (y5 * (a * y2));
	elseif (y2 <= -1e+28)
		tmp = k * (y4 * (y1 * y2));
	elseif (y2 <= -1.9e-22)
		tmp = y4 * ((y * k) * -b);
	elseif (y2 <= -9.5e-179)
		tmp = (t * i) * (j * -y5);
	elseif (y2 <= 2e-123)
		tmp = y4 * (k * (y * -b));
	elseif (y2 <= 1.25e+17)
		tmp = z * (k * (y1 * -i));
	else
		tmp = c * (y0 * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.8e+190], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -6e+137], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1e+28], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.9e-22], N[(y4 * N[(N[(y * k), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9.5e-179], N[(N[(t * i), $MachinePrecision] * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2e-123], N[(y4 * N[(k * N[(y * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.25e+17], N[(z * N[(k * N[(y1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -1.79999999999999989e190

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 25.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 54.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 54.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 54.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 57.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]

   if -1.79999999999999989e190 < y2 < -6.0000000000000002e137

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 42.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 59.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 59.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 58.7%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 58.7%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 58.7%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 58.7%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 58.7%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 58.7%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 58.7%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 58.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 66.8%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 66.8%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   if -6.0000000000000002e137 < y2 < -9.99999999999999958e27

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 41.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 41.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 41.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 41.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 41.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -9.99999999999999958e27 < y2 < -1.90000000000000012e-22

   1. Initial program 18.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 18.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 36.6%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.6%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 36.6%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 36.6%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 36.6%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in b around inf 37.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \cdot y4 \]
   9. Step-by-step derivation

      1. associate-*r* 46.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot b\right)}\right) \cdot y4 \]

      2. associate-*r* 46.2%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y\right)\right) \cdot b\right)} \cdot y4 \]

      3. neg-mul-1 46.2%

         \[\leadsto \left(\color{blue}{\left(-k \cdot y\right)} \cdot b\right) \cdot y4 \]

      4. *-commutative 46.2%

         \[\leadsto \left(\left(-\color{blue}{y \cdot k}\right) \cdot b\right) \cdot y4 \]

   10. Simplified 46.2%

       \[\leadsto \color{blue}{\left(\left(-y \cdot k\right) \cdot b\right)} \cdot y4 \]

   if -1.90000000000000012e-22 < y2 < -9.50000000000000037e-179

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 44.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 44.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 44.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 44.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 44.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 38.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 38.5%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 32.4%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 32.4%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 38.4%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 38.4%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   if -9.50000000000000037e-179 < y2 < 2.0000000000000001e-123

   1. Initial program 24.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 49.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 33.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 33.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 33.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around 0 33.1%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 33.1%

         \[\leadsto y4 \cdot \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)} \]

      2. *-commutative 33.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y \cdot b\right) \cdot k}\right) \]

      3. distribute-rgt-neg-in 33.1%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot \left(-k\right)\right)} \]

   10. Simplified 33.1%

       \[\leadsto y4 \cdot \color{blue}{\left(\left(y \cdot b\right) \cdot \left(-k\right)\right)} \]

   if 2.0000000000000001e-123 < y2 < 1.25e17

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 46.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 46.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 46.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 46.4%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 42.3%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around 0 34.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 34.4%

         \[\leadsto \color{blue}{-k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

      2. associate-*r* 34.4%

         \[\leadsto -k \cdot \color{blue}{\left(\left(y1 \cdot i\right) \cdot z\right)} \]

      3. associate-*r* 38.4%

         \[\leadsto -\color{blue}{\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   10. Simplified 38.4%

       \[\leadsto \color{blue}{-\left(k \cdot \left(y1 \cdot i\right)\right) \cdot z} \]

   if 1.25e17 < y2

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 41.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 41.1%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   8. Taylor expanded in x around inf 34.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.8 \cdot 10^{+190}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -6 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1 \cdot 10^{+28}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -1.9 \cdot 10^{-22}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y2 \leq -9.5 \cdot 10^{-179}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(j \cdot \left(-y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-123}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(k \cdot \left(y1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 30: 23.1% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{if}\;k \leq -8.6 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-43}:\\ \;\;\;\;\left(i \cdot y1\right) \cdot \left(x \cdot j\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5000:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* t (* j (- y5))))))
   (if (<= k -8.6e+26)
     (* y4 (* y1 (* k y2)))
     (if (<= k -2.4e-180)
       (* a (* t (* y2 y5)))
       (if (<= k 7.5e-134)
         t_1
         (if (<= k 1.95e-106)
           (* a (* y2 (* t y5)))
           (if (<= k 9.5e-43)
             (* (* i y1) (* x j))
             (if (<= k 3e-37)
               t_1
               (if (<= k 5000.0)
                 (* y4 (* c (* y y3)))
                 (* y2 (* y1 (* k 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 t_1 = i * (t * (j * -y5));
	double tmp;
	if (k <= -8.6e+26) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -2.4e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 7.5e-134) {
		tmp = t_1;
	} else if (k <= 1.95e-106) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 9.5e-43) {
		tmp = (i * y1) * (x * j);
	} else if (k <= 3e-37) {
		tmp = t_1;
	} else if (k <= 5000.0) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = y2 * (y1 * (k * 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) :: t_1
    real(8) :: tmp
    t_1 = i * (t * (j * -y5))
    if (k <= (-8.6d+26)) then
        tmp = y4 * (y1 * (k * y2))
    else if (k <= (-2.4d-180)) then
        tmp = a * (t * (y2 * y5))
    else if (k <= 7.5d-134) then
        tmp = t_1
    else if (k <= 1.95d-106) then
        tmp = a * (y2 * (t * y5))
    else if (k <= 9.5d-43) then
        tmp = (i * y1) * (x * j)
    else if (k <= 3d-37) then
        tmp = t_1
    else if (k <= 5000.0d0) then
        tmp = y4 * (c * (y * y3))
    else
        tmp = y2 * (y1 * (k * 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 t_1 = i * (t * (j * -y5));
	double tmp;
	if (k <= -8.6e+26) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= -2.4e-180) {
		tmp = a * (t * (y2 * y5));
	} else if (k <= 7.5e-134) {
		tmp = t_1;
	} else if (k <= 1.95e-106) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 9.5e-43) {
		tmp = (i * y1) * (x * j);
	} else if (k <= 3e-37) {
		tmp = t_1;
	} else if (k <= 5000.0) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = y2 * (y1 * (k * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (t * (j * -y5))
	tmp = 0
	if k <= -8.6e+26:
		tmp = y4 * (y1 * (k * y2))
	elif k <= -2.4e-180:
		tmp = a * (t * (y2 * y5))
	elif k <= 7.5e-134:
		tmp = t_1
	elif k <= 1.95e-106:
		tmp = a * (y2 * (t * y5))
	elif k <= 9.5e-43:
		tmp = (i * y1) * (x * j)
	elif k <= 3e-37:
		tmp = t_1
	elif k <= 5000.0:
		tmp = y4 * (c * (y * y3))
	else:
		tmp = y2 * (y1 * (k * y4))
	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(t * Float64(j * Float64(-y5))))
	tmp = 0.0
	if (k <= -8.6e+26)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (k <= -2.4e-180)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	elseif (k <= 7.5e-134)
		tmp = t_1;
	elseif (k <= 1.95e-106)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (k <= 9.5e-43)
		tmp = Float64(Float64(i * y1) * Float64(x * j));
	elseif (k <= 3e-37)
		tmp = t_1;
	elseif (k <= 5000.0)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	else
		tmp = Float64(y2 * Float64(y1 * Float64(k * 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)
	t_1 = i * (t * (j * -y5));
	tmp = 0.0;
	if (k <= -8.6e+26)
		tmp = y4 * (y1 * (k * y2));
	elseif (k <= -2.4e-180)
		tmp = a * (t * (y2 * y5));
	elseif (k <= 7.5e-134)
		tmp = t_1;
	elseif (k <= 1.95e-106)
		tmp = a * (y2 * (t * y5));
	elseif (k <= 9.5e-43)
		tmp = (i * y1) * (x * j);
	elseif (k <= 3e-37)
		tmp = t_1;
	elseif (k <= 5000.0)
		tmp = y4 * (c * (y * y3));
	else
		tmp = y2 * (y1 * (k * y4));
	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[(i * N[(t * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -8.6e+26], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -2.4e-180], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.5e-134], t$95$1, If[LessEqual[k, 1.95e-106], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.5e-43], N[(N[(i * y1), $MachinePrecision] * N[(x * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3e-37], t$95$1, If[LessEqual[k, 5000.0], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y1 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -8.5999999999999996e26

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 40.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 40.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 27.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 27.5%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 33.3%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 33.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 34.7%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 34.7%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 34.7%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -8.5999999999999996e26 < k < -2.39999999999999979e-180

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 32.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.0%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 28.0%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 28.0%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 32.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

   if -2.39999999999999979e-180 < k < 7.50000000000000048e-134 or 9.50000000000000044e-43 < k < 3e-37

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 49.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.0%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 49.0%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 49.0%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 43.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 43.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 43.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around 0 35.1%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 35.1%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. associate-*r* 33.5%

          \[\leadsto -\color{blue}{\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   12. Simplified 33.5%

       \[\leadsto \color{blue}{-\left(i \cdot t\right) \cdot \left(j \cdot y5\right)} \]

   13. Taylor expanded in i around 0 35.1%

       \[\leadsto -\color{blue}{i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

   if 7.50000000000000048e-134 < k < 1.95000000000000005e-106

   1. Initial program 28.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 43.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 43.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 43.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 57.8%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 44.0%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 44.0%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 44.2%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 58.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 58.1%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if 1.95000000000000005e-106 < k < 9.50000000000000044e-43

   1. Initial program 42.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 71.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 71.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 71.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 71.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 71.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 58.4%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 30.6%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.0%

         \[\leadsto \color{blue}{\left(y1 \cdot i\right) \cdot \left(j \cdot x\right)} \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{\left(y1 \cdot i\right) \cdot \left(j \cdot x\right)} \]

   if 3e-37 < k < 5e3

   1. Initial program 14.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 14.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 50.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 50.1%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 50.1%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 50.1%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 50.1%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 50.1%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 43.6%

      \[\leadsto \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \cdot y4 \]

   if 5e3 < k

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 37.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.5%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 37.5%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 37.5%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 37.5%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y1 around inf 26.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 32.1%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2\right)} \]

      2. associate-*r* 38.1%

         \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]

   10. Simplified 38.1%

       \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]
3. Recombined 7 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8.6 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -2.4 \cdot 10^{-180}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{-134}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-43}:\\ \;\;\;\;\left(i \cdot y1\right) \cdot \left(x \cdot j\right)\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-37}:\\ \;\;\;\;i \cdot \left(t \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;k \leq 5000:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \]

Alternative 31: 31.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-271}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -4e-18)
   (* y4 (* y (- (* c y3) (* b k))))
   (if (<= y -5.8e-67)
     (* y2 (* k (- (* y1 y4) (* y0 y5))))
     (if (<= y -1.7e-81)
       (* y (* b (- (* x a) (* k y4))))
       (if (<= y 2.2e-271)
         (* (* t y5) (- (* a y2) (* i j)))
         (if (<= y 5e+47)
           (* y2 (* c (- (* x y0) (* t y4))))
           (* y5 (* i (- (* y k) (* t 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 (y <= -4e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -5.8e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -1.7e-81) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y <= 2.2e-271) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 5e+47) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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 (y <= (-4d-18)) then
        tmp = y4 * (y * ((c * y3) - (b * k)))
    else if (y <= (-5.8d-67)) then
        tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
    else if (y <= (-1.7d-81)) then
        tmp = y * (b * ((x * a) - (k * y4)))
    else if (y <= 2.2d-271) then
        tmp = (t * y5) * ((a * y2) - (i * j))
    else if (y <= 5d+47) then
        tmp = y2 * (c * ((x * y0) - (t * y4)))
    else
        tmp = y5 * (i * ((y * k) - (t * 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 (y <= -4e-18) {
		tmp = y4 * (y * ((c * y3) - (b * k)));
	} else if (y <= -5.8e-67) {
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	} else if (y <= -1.7e-81) {
		tmp = y * (b * ((x * a) - (k * y4)));
	} else if (y <= 2.2e-271) {
		tmp = (t * y5) * ((a * y2) - (i * j));
	} else if (y <= 5e+47) {
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	} else {
		tmp = y5 * (i * ((y * k) - (t * 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 y <= -4e-18:
		tmp = y4 * (y * ((c * y3) - (b * k)))
	elif y <= -5.8e-67:
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)))
	elif y <= -1.7e-81:
		tmp = y * (b * ((x * a) - (k * y4)))
	elif y <= 2.2e-271:
		tmp = (t * y5) * ((a * y2) - (i * j))
	elif y <= 5e+47:
		tmp = y2 * (c * ((x * y0) - (t * y4)))
	else:
		tmp = y5 * (i * ((y * k) - (t * 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 (y <= -4e-18)
		tmp = Float64(y4 * Float64(y * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (y <= -5.8e-67)
		tmp = Float64(y2 * Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y <= -1.7e-81)
		tmp = Float64(y * Float64(b * Float64(Float64(x * a) - Float64(k * y4))));
	elseif (y <= 2.2e-271)
		tmp = Float64(Float64(t * y5) * Float64(Float64(a * y2) - Float64(i * j)));
	elseif (y <= 5e+47)
		tmp = Float64(y2 * Float64(c * Float64(Float64(x * y0) - Float64(t * y4))));
	else
		tmp = Float64(y5 * Float64(i * Float64(Float64(y * k) - Float64(t * 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 (y <= -4e-18)
		tmp = y4 * (y * ((c * y3) - (b * k)));
	elseif (y <= -5.8e-67)
		tmp = y2 * (k * ((y1 * y4) - (y0 * y5)));
	elseif (y <= -1.7e-81)
		tmp = y * (b * ((x * a) - (k * y4)));
	elseif (y <= 2.2e-271)
		tmp = (t * y5) * ((a * y2) - (i * j));
	elseif (y <= 5e+47)
		tmp = y2 * (c * ((x * y0) - (t * y4)));
	else
		tmp = y5 * (i * ((y * k) - (t * 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[y, -4e-18], N[(y4 * N[(y * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-67], N[(y2 * N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-81], N[(y * N[(b * N[(N[(x * a), $MachinePrecision] - N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-271], N[(N[(t * y5), $MachinePrecision] * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+47], N[(y2 * N[(c * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.0000000000000003e-18

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 49.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 46.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.8%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 46.8%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 46.8%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 46.8%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 46.8%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y2 around 0 39.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right) + -1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right)\right)} \cdot y4 \]
   9. Step-by-step derivation

      1. +-commutative 39.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right) + k \cdot \left(y \cdot b\right)\right)}\right) \cdot y4 \]

      2. distribute-lft-in 39.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \cdot y4 \]

      3. associate-*r* 39.5%

         \[\leadsto \left(-1 \cdot \left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) + \color{blue}{\left(-1 \cdot k\right) \cdot \left(y \cdot b\right)}\right) \cdot y4 \]

      4. neg-mul-1 39.5%

         \[\leadsto \left(-1 \cdot \left(-1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right) + \color{blue}{\left(-k\right)} \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      5. mul-1-neg 39.5%

         \[\leadsto \left(\color{blue}{\left(--1 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\right)} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      6. mul-1-neg 39.5%

         \[\leadsto \left(\left(-\color{blue}{\left(-c \cdot \left(y \cdot y3\right)\right)}\right) + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      7. remove-double-neg 39.5%

         \[\leadsto \left(\color{blue}{c \cdot \left(y \cdot y3\right)} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      8. *-commutative 39.5%

         \[\leadsto \left(c \cdot \color{blue}{\left(y3 \cdot y\right)} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      9. associate-*r* 39.6%

         \[\leadsto \left(\color{blue}{\left(c \cdot y3\right) \cdot y} + \left(-k\right) \cdot \left(y \cdot b\right)\right) \cdot y4 \]

      10. *-commutative 39.6%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \left(-k\right) \cdot \color{blue}{\left(b \cdot y\right)}\right) \cdot y4 \]

      11. associate-*r* 41.1%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \color{blue}{\left(\left(-k\right) \cdot b\right) \cdot y}\right) \cdot y4 \]

      12. neg-mul-1 41.1%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \left(\color{blue}{\left(-1 \cdot k\right)} \cdot b\right) \cdot y\right) \cdot y4 \]

      13. associate-*r* 41.1%

          \[\leadsto \left(\left(c \cdot y3\right) \cdot y + \color{blue}{\left(-1 \cdot \left(k \cdot b\right)\right)} \cdot y\right) \cdot y4 \]

      14. distribute-rgt-in 48.5%

          \[\leadsto \color{blue}{\left(y \cdot \left(c \cdot y3 + -1 \cdot \left(k \cdot b\right)\right)\right)} \cdot y4 \]

      15. mul-1-neg 48.5%

          \[\leadsto \left(y \cdot \left(c \cdot y3 + \color{blue}{\left(-k \cdot b\right)}\right)\right) \cdot y4 \]

      16. unsub-neg 48.5%

          \[\leadsto \left(y \cdot \color{blue}{\left(c \cdot y3 - k \cdot b\right)}\right) \cdot y4 \]

      17. *-commutative 48.5%

          \[\leadsto \left(y \cdot \left(c \cdot y3 - \color{blue}{b \cdot k}\right)\right) \cdot y4 \]

   10. Simplified 48.5%

       \[\leadsto \color{blue}{\left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)} \cdot y4 \]

   if -4.0000000000000003e-18 < y < -5.8000000000000001e-67

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 46.6%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in k around inf 55.0%

      \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right)} \cdot y2 \]

   if -5.8000000000000001e-67 < y < -1.6999999999999999e-81

   1. Initial program 66.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y around inf 33.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.3%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right) \]

   6. Simplified 33.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

   7. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(b \cdot \left(a \cdot x - k \cdot y4\right)\right)} \]

   if -1.6999999999999999e-81 < y < 2.1999999999999999e-271

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 48.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 48.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 48.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 51.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 51.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   if 2.1999999999999999e-271 < y < 5.00000000000000022e47

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 47.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in c around inf 37.5%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x - y4 \cdot t\right)\right)} \cdot y2 \]

   if 5.00000000000000022e47 < y

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 43.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 43.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 43.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in i around inf 55.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(k \cdot y - t \cdot j\right)\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 55.3%

         \[\leadsto \left(i \cdot \left(\color{blue}{y \cdot k} - t \cdot j\right)\right) \cdot y5 \]

   9. Simplified 55.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(y \cdot k - t \cdot j\right)\right)} \cdot y5 \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-18}:\\ \;\;\;\;y4 \cdot \left(y \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-67}:\\ \;\;\;\;y2 \cdot \left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \left(b \cdot \left(x \cdot a - k \cdot y4\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-271}:\\ \;\;\;\;\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+47}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \end{array} \]

Alternative 32: 21.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ t_2 := k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* x (* i j)))) (t_2 (* k (* y4 (* y1 y2)))))
   (if (<= i -2.6e+120)
     t_1
     (if (<= i -5.2e-28)
       t_2
       (if (<= i 1.15e-305)
         (* t (* y5 (* a y2)))
         (if (<= i 3.1e-232)
           t_2
           (if (<= i 1.42e+106) (* a (* y2 (* t y5))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (x * (i * j));
	double t_2 = k * (y4 * (y1 * y2));
	double tmp;
	if (i <= -2.6e+120) {
		tmp = t_1;
	} else if (i <= -5.2e-28) {
		tmp = t_2;
	} else if (i <= 1.15e-305) {
		tmp = t * (y5 * (a * y2));
	} else if (i <= 3.1e-232) {
		tmp = t_2;
	} else if (i <= 1.42e+106) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y1 * (x * (i * j))
    t_2 = k * (y4 * (y1 * y2))
    if (i <= (-2.6d+120)) then
        tmp = t_1
    else if (i <= (-5.2d-28)) then
        tmp = t_2
    else if (i <= 1.15d-305) then
        tmp = t * (y5 * (a * y2))
    else if (i <= 3.1d-232) then
        tmp = t_2
    else if (i <= 1.42d+106) then
        tmp = a * (y2 * (t * y5))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (x * (i * j));
	double t_2 = k * (y4 * (y1 * y2));
	double tmp;
	if (i <= -2.6e+120) {
		tmp = t_1;
	} else if (i <= -5.2e-28) {
		tmp = t_2;
	} else if (i <= 1.15e-305) {
		tmp = t * (y5 * (a * y2));
	} else if (i <= 3.1e-232) {
		tmp = t_2;
	} else if (i <= 1.42e+106) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (x * (i * j))
	t_2 = k * (y4 * (y1 * y2))
	tmp = 0
	if i <= -2.6e+120:
		tmp = t_1
	elif i <= -5.2e-28:
		tmp = t_2
	elif i <= 1.15e-305:
		tmp = t * (y5 * (a * y2))
	elif i <= 3.1e-232:
		tmp = t_2
	elif i <= 1.42e+106:
		tmp = a * (y2 * (t * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(x * Float64(i * j)))
	t_2 = Float64(k * Float64(y4 * Float64(y1 * y2)))
	tmp = 0.0
	if (i <= -2.6e+120)
		tmp = t_1;
	elseif (i <= -5.2e-28)
		tmp = t_2;
	elseif (i <= 1.15e-305)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	elseif (i <= 3.1e-232)
		tmp = t_2;
	elseif (i <= 1.42e+106)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (x * (i * j));
	t_2 = k * (y4 * (y1 * y2));
	tmp = 0.0;
	if (i <= -2.6e+120)
		tmp = t_1;
	elseif (i <= -5.2e-28)
		tmp = t_2;
	elseif (i <= 1.15e-305)
		tmp = t * (y5 * (a * y2));
	elseif (i <= 3.1e-232)
		tmp = t_2;
	elseif (i <= 1.42e+106)
		tmp = a * (y2 * (t * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(x * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+120], t$95$1, If[LessEqual[i, -5.2e-28], t$95$2, If[LessEqual[i, 1.15e-305], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e-232], t$95$2, If[LessEqual[i, 1.42e+106], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.5999999999999999e120 or 1.4200000000000001e106 < i

   1. Initial program 25.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 43.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 43.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 43.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 47.7%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   8. Taylor expanded in j around inf 31.0%

      \[\leadsto y1 \cdot \color{blue}{\left(i \cdot \left(j \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto y1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot x\right)} \]

      2. *-commutative 37.5%

         \[\leadsto y1 \cdot \left(\color{blue}{\left(j \cdot i\right)} \cdot x\right) \]

   10. Simplified 37.5%

       \[\leadsto y1 \cdot \color{blue}{\left(\left(j \cdot i\right) \cdot x\right)} \]

   if -2.5999999999999999e120 < i < -5.2e-28 or 1.15e-305 < i < 3.0999999999999999e-232

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 30.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 43.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 43.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 43.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 43.5%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 43.5%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 43.5%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 35.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if -5.2e-28 < i < 1.15e-305

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 43.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 43.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 43.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 43.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 43.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 43.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 30.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 22.8%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 22.8%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 22.8%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 21.2%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 21.2%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 21.2%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 21.2%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 21.2%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 21.2%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 28.4%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 28.4%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 30.3%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 30.3%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   if 3.0999999999999999e-232 < i < 1.4200000000000001e106

   1. Initial program 30.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 41.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 41.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 41.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 41.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 41.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 31.3%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 28.5%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 28.5%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 28.5%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 27.1%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 27.1%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 27.1%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+120}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-28}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-232}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j\right)\right)\\ \end{array} \]

Alternative 33: 26.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-113}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.72 \cdot 10^{-128}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y0 (- (* x y2) (* z y3))))))
   (if (<= c -1.6e+57)
     t_1
     (if (<= c -2.15e-113)
       (* y2 (* y1 (* k y4)))
       (if (<= c 1.72e-128) (* y4 (* (* y k) (- b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (c <= -1.6e+57) {
		tmp = t_1;
	} else if (c <= -2.15e-113) {
		tmp = y2 * (y1 * (k * y4));
	} else if (c <= 1.72e-128) {
		tmp = y4 * ((y * k) * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (y0 * ((x * y2) - (z * y3)))
    if (c <= (-1.6d+57)) then
        tmp = t_1
    else if (c <= (-2.15d-113)) then
        tmp = y2 * (y1 * (k * y4))
    else if (c <= 1.72d-128) then
        tmp = y4 * ((y * k) * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y0 * ((x * y2) - (z * y3)));
	double tmp;
	if (c <= -1.6e+57) {
		tmp = t_1;
	} else if (c <= -2.15e-113) {
		tmp = y2 * (y1 * (k * y4));
	} else if (c <= 1.72e-128) {
		tmp = y4 * ((y * k) * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y0 * ((x * y2) - (z * y3)))
	tmp = 0
	if c <= -1.6e+57:
		tmp = t_1
	elif c <= -2.15e-113:
		tmp = y2 * (y1 * (k * y4))
	elif c <= 1.72e-128:
		tmp = y4 * ((y * k) * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))))
	tmp = 0.0
	if (c <= -1.6e+57)
		tmp = t_1;
	elseif (c <= -2.15e-113)
		tmp = Float64(y2 * Float64(y1 * Float64(k * y4)));
	elseif (c <= 1.72e-128)
		tmp = Float64(y4 * Float64(Float64(y * k) * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y0 * ((x * y2) - (z * y3)));
	tmp = 0.0;
	if (c <= -1.6e+57)
		tmp = t_1;
	elseif (c <= -2.15e-113)
		tmp = y2 * (y1 * (k * y4));
	elseif (c <= 1.72e-128)
		tmp = y4 * ((y * k) * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.6e+57], t$95$1, If[LessEqual[c, -2.15e-113], N[(y2 * N[(y1 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.72e-128], N[(y4 * N[(N[(y * k), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.60000000000000015e57 or 1.71999999999999992e-128 < c

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 35.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 35.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if -1.60000000000000015e57 < c < -2.15e-113

   1. Initial program 19.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 50.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 42.6%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.6%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 42.6%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 42.6%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 42.6%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 42.6%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y1 around inf 32.7%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.2%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2\right)} \]

      2. associate-*r* 40.5%

         \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]

   10. Simplified 40.5%

       \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]

   if -2.15e-113 < c < 1.71999999999999992e-128

   1. Initial program 38.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 36.4%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.4%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 36.4%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 36.4%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 36.4%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 36.4%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in b around inf 30.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right)} \cdot y4 \]
   9. Step-by-step derivation

      1. associate-*r* 31.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(k \cdot y\right) \cdot b\right)}\right) \cdot y4 \]

      2. associate-*r* 31.3%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(k \cdot y\right)\right) \cdot b\right)} \cdot y4 \]

      3. neg-mul-1 31.3%

         \[\leadsto \left(\color{blue}{\left(-k \cdot y\right)} \cdot b\right) \cdot y4 \]

      4. *-commutative 31.3%

         \[\leadsto \left(\left(-\color{blue}{y \cdot k}\right) \cdot b\right) \cdot y4 \]

   10. Simplified 31.3%

       \[\leadsto \color{blue}{\left(\left(-y \cdot k\right) \cdot b\right)} \cdot y4 \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+57}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-113}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 1.72 \cdot 10^{-128}:\\ \;\;\;\;y4 \cdot \left(\left(y \cdot k\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]

Alternative 34: 22.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{if}\;k \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 6.3 \cdot 10^{+16}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y1 (* k y2)))))
   (if (<= k -3.2e+26)
     t_1
     (if (<= k 5.5e-167)
       (* a (* y2 (* t y5)))
       (if (<= k 6.3e+16)
         (* y4 (* c (* y y3)))
         (if (<= k 1.05e+115) (* t (* y5 (* a y2))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y1 * (k * y2));
	double tmp;
	if (k <= -3.2e+26) {
		tmp = t_1;
	} else if (k <= 5.5e-167) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 6.3e+16) {
		tmp = y4 * (c * (y * y3));
	} else if (k <= 1.05e+115) {
		tmp = t * (y5 * (a * y2));
	} 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 = y4 * (y1 * (k * y2))
    if (k <= (-3.2d+26)) then
        tmp = t_1
    else if (k <= 5.5d-167) then
        tmp = a * (y2 * (t * y5))
    else if (k <= 6.3d+16) then
        tmp = y4 * (c * (y * y3))
    else if (k <= 1.05d+115) then
        tmp = t * (y5 * (a * y2))
    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 = y4 * (y1 * (k * y2));
	double tmp;
	if (k <= -3.2e+26) {
		tmp = t_1;
	} else if (k <= 5.5e-167) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 6.3e+16) {
		tmp = y4 * (c * (y * y3));
	} else if (k <= 1.05e+115) {
		tmp = t * (y5 * (a * y2));
	} 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 = y4 * (y1 * (k * y2))
	tmp = 0
	if k <= -3.2e+26:
		tmp = t_1
	elif k <= 5.5e-167:
		tmp = a * (y2 * (t * y5))
	elif k <= 6.3e+16:
		tmp = y4 * (c * (y * y3))
	elif k <= 1.05e+115:
		tmp = t * (y5 * (a * y2))
	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(y4 * Float64(y1 * Float64(k * y2)))
	tmp = 0.0
	if (k <= -3.2e+26)
		tmp = t_1;
	elseif (k <= 5.5e-167)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (k <= 6.3e+16)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (k <= 1.05e+115)
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	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 = y4 * (y1 * (k * y2));
	tmp = 0.0;
	if (k <= -3.2e+26)
		tmp = t_1;
	elseif (k <= 5.5e-167)
		tmp = a * (y2 * (t * y5));
	elseif (k <= 6.3e+16)
		tmp = y4 * (c * (y * y3));
	elseif (k <= 1.05e+115)
		tmp = t * (y5 * (a * y2));
	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[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.2e+26], t$95$1, If[LessEqual[k, 5.5e-167], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.3e+16], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.05e+115], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -3.20000000000000029e26 or 1.05000000000000002e115 < k

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 52.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 52.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 29.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 29.9%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 35.0%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 35.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 35.9%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 35.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 35.9%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -3.20000000000000029e26 < k < 5.5000000000000003e-167

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 37.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 36.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 36.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 27.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 27.5%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 27.5%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if 5.5000000000000003e-167 < k < 6.3e16

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 39.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 39.2%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 39.2%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 39.2%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 39.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 34.2%

      \[\leadsto \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \cdot y4 \]

   if 6.3e16 < k < 1.05000000000000002e115

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 42.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 32.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.2%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 32.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 32.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 32.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 32.2%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 32.2%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 27.2%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 22.2%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 22.2%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 22.2%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 22.2%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 22.2%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 22.2%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 22.2%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 22.2%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 22.2%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 27.2%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 27.2%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 27.2%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 27.2%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 6.3 \cdot 10^{+16}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 35: 22.9% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{if}\;k \leq -6.2 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+28}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+128}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y1 (* k y2)))))
   (if (<= k -6.2e+28)
     t_1
     (if (<= k 3.7e-167)
       (* a (* y2 (* t y5)))
       (if (<= k 8e+28)
         (* y4 (* c (* y y3)))
         (if (<= k 4e+128) (* y2 (* c (* x y0))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y1 * (k * y2));
	double tmp;
	if (k <= -6.2e+28) {
		tmp = t_1;
	} else if (k <= 3.7e-167) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 8e+28) {
		tmp = y4 * (c * (y * y3));
	} else if (k <= 4e+128) {
		tmp = y2 * (c * (x * y0));
	} 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 = y4 * (y1 * (k * y2))
    if (k <= (-6.2d+28)) then
        tmp = t_1
    else if (k <= 3.7d-167) then
        tmp = a * (y2 * (t * y5))
    else if (k <= 8d+28) then
        tmp = y4 * (c * (y * y3))
    else if (k <= 4d+128) then
        tmp = y2 * (c * (x * y0))
    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 = y4 * (y1 * (k * y2));
	double tmp;
	if (k <= -6.2e+28) {
		tmp = t_1;
	} else if (k <= 3.7e-167) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 8e+28) {
		tmp = y4 * (c * (y * y3));
	} else if (k <= 4e+128) {
		tmp = y2 * (c * (x * y0));
	} 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 = y4 * (y1 * (k * y2))
	tmp = 0
	if k <= -6.2e+28:
		tmp = t_1
	elif k <= 3.7e-167:
		tmp = a * (y2 * (t * y5))
	elif k <= 8e+28:
		tmp = y4 * (c * (y * y3))
	elif k <= 4e+128:
		tmp = y2 * (c * (x * y0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(y1 * Float64(k * y2)))
	tmp = 0.0
	if (k <= -6.2e+28)
		tmp = t_1;
	elseif (k <= 3.7e-167)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (k <= 8e+28)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (k <= 4e+128)
		tmp = Float64(y2 * Float64(c * Float64(x * y0)));
	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 = y4 * (y1 * (k * y2));
	tmp = 0.0;
	if (k <= -6.2e+28)
		tmp = t_1;
	elseif (k <= 3.7e-167)
		tmp = a * (y2 * (t * y5));
	elseif (k <= 8e+28)
		tmp = y4 * (c * (y * y3));
	elseif (k <= 4e+128)
		tmp = y2 * (c * (x * y0));
	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[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -6.2e+28], t$95$1, If[LessEqual[k, 3.7e-167], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8e+28], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4e+128], N[(y2 * N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -6.2000000000000001e28 or 4.0000000000000003e128 < k

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 53.8%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 53.8%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 53.8%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 53.8%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 53.8%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 53.8%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 31.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 31.0%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 31.0%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 36.3%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 36.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 37.2%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 37.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 37.2%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -6.2000000000000001e28 < k < 3.7000000000000003e-167

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 37.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 36.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 36.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 27.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 27.5%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 27.5%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if 3.7000000000000003e-167 < k < 7.99999999999999967e28

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 38.2%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 38.2%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 38.2%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 33.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \cdot y4 \]

   if 7.99999999999999967e28 < k < 4.0000000000000003e128

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 32.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in x around inf 28.4%

      \[\leadsto \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x\right)} \cdot y2 \]

   6. Taylor expanded in c around inf 23.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x\right)\right)} \cdot y2 \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6.2 \cdot 10^{+28}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 3.7 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+28}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+128}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \end{array} \]

Alternative 36: 22.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -3.7 \cdot 10^{+28}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{+129}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -3.7e+28)
   (* y4 (* y1 (* k y2)))
   (if (<= k 1.05e-167)
     (* a (* y2 (* t y5)))
     (if (<= k 1.7e+26)
       (* y4 (* c (* y y3)))
       (if (<= k 8.2e+129) (* y2 (* c (* x y0))) (* (* y1 y2) (* k 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 (k <= -3.7e+28) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= 1.05e-167) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 1.7e+26) {
		tmp = y4 * (c * (y * y3));
	} else if (k <= 8.2e+129) {
		tmp = y2 * (c * (x * y0));
	} else {
		tmp = (y1 * y2) * (k * 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 (k <= (-3.7d+28)) then
        tmp = y4 * (y1 * (k * y2))
    else if (k <= 1.05d-167) then
        tmp = a * (y2 * (t * y5))
    else if (k <= 1.7d+26) then
        tmp = y4 * (c * (y * y3))
    else if (k <= 8.2d+129) then
        tmp = y2 * (c * (x * y0))
    else
        tmp = (y1 * y2) * (k * 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 (k <= -3.7e+28) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= 1.05e-167) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 1.7e+26) {
		tmp = y4 * (c * (y * y3));
	} else if (k <= 8.2e+129) {
		tmp = y2 * (c * (x * y0));
	} else {
		tmp = (y1 * y2) * (k * 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 k <= -3.7e+28:
		tmp = y4 * (y1 * (k * y2))
	elif k <= 1.05e-167:
		tmp = a * (y2 * (t * y5))
	elif k <= 1.7e+26:
		tmp = y4 * (c * (y * y3))
	elif k <= 8.2e+129:
		tmp = y2 * (c * (x * y0))
	else:
		tmp = (y1 * y2) * (k * 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 (k <= -3.7e+28)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (k <= 1.05e-167)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (k <= 1.7e+26)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (k <= 8.2e+129)
		tmp = Float64(y2 * Float64(c * Float64(x * y0)));
	else
		tmp = Float64(Float64(y1 * y2) * Float64(k * 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 (k <= -3.7e+28)
		tmp = y4 * (y1 * (k * y2));
	elseif (k <= 1.05e-167)
		tmp = a * (y2 * (t * y5));
	elseif (k <= 1.7e+26)
		tmp = y4 * (c * (y * y3));
	elseif (k <= 8.2e+129)
		tmp = y2 * (c * (x * y0));
	else
		tmp = (y1 * y2) * (k * 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[k, -3.7e+28], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.05e-167], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.7e+26], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.2e+129], N[(y2 * N[(c * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y1 * y2), $MachinePrecision] * N[(k * y4), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -3.6999999999999999e28

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 40.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 40.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 27.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 27.5%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 33.3%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 33.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 34.7%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 34.7%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 34.7%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -3.6999999999999999e28 < k < 1.05000000000000009e-167

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 37.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 36.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 36.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 27.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 27.5%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 27.5%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if 1.05000000000000009e-167 < k < 1.7000000000000001e26

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 38.2%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 38.2%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 38.2%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 33.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \cdot y4 \]

   if 1.7000000000000001e26 < k < 8.2000000000000005e129

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y2 around inf 32.4%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in x around inf 28.4%

      \[\leadsto \color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x\right)} \cdot y2 \]

   6. Taylor expanded in c around inf 23.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot x\right)\right)} \cdot y2 \]

   if 8.2000000000000005e129 < k

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 42.7%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.7%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 42.7%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 42.7%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 42.7%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 42.7%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y1 around inf 36.7%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 43.5%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2\right)} \]

      2. *-commutative 43.5%

         \[\leadsto \color{blue}{\left(y1 \cdot y2\right) \cdot \left(k \cdot y4\right)} \]

      3. *-commutative 43.5%

         \[\leadsto \color{blue}{\left(y2 \cdot y1\right)} \cdot \left(k \cdot y4\right) \]

   10. Simplified 43.5%

       \[\leadsto \color{blue}{\left(y2 \cdot y1\right) \cdot \left(k \cdot y4\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.7 \cdot 10^{+28}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 1.7 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{+129}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y1 \cdot y2\right) \cdot \left(k \cdot y4\right)\\ \end{array} \]

Alternative 37: 23.1% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -8.6 \cdot 10^{+27}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 16500:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -8.6e+27)
   (* y4 (* y1 (* k y2)))
   (if (<= k 6e-168)
     (* a (* y2 (* t y5)))
     (if (<= k 16500.0) (* y4 (* c (* y y3))) (* y2 (* y1 (* k 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 (k <= -8.6e+27) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= 6e-168) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 16500.0) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = y2 * (y1 * (k * 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 (k <= (-8.6d+27)) then
        tmp = y4 * (y1 * (k * y2))
    else if (k <= 6d-168) then
        tmp = a * (y2 * (t * y5))
    else if (k <= 16500.0d0) then
        tmp = y4 * (c * (y * y3))
    else
        tmp = y2 * (y1 * (k * 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 (k <= -8.6e+27) {
		tmp = y4 * (y1 * (k * y2));
	} else if (k <= 6e-168) {
		tmp = a * (y2 * (t * y5));
	} else if (k <= 16500.0) {
		tmp = y4 * (c * (y * y3));
	} else {
		tmp = y2 * (y1 * (k * 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 k <= -8.6e+27:
		tmp = y4 * (y1 * (k * y2))
	elif k <= 6e-168:
		tmp = a * (y2 * (t * y5))
	elif k <= 16500.0:
		tmp = y4 * (c * (y * y3))
	else:
		tmp = y2 * (y1 * (k * 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 (k <= -8.6e+27)
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	elseif (k <= 6e-168)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (k <= 16500.0)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	else
		tmp = Float64(y2 * Float64(y1 * Float64(k * 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 (k <= -8.6e+27)
		tmp = y4 * (y1 * (k * y2));
	elseif (k <= 6e-168)
		tmp = a * (y2 * (t * y5));
	elseif (k <= 16500.0)
		tmp = y4 * (c * (y * y3));
	else
		tmp = y2 * (y1 * (k * 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[k, -8.6e+27], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6e-168], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 16500.0], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(y1 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -8.60000000000000017e27

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 40.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 40.7%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 40.7%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 27.5%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 27.5%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 33.3%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 33.3%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 34.7%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 34.7%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 34.7%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -8.60000000000000017e27 < k < 5.99999999999999983e-168

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 47.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 47.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 37.4%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 36.3%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 36.3%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 27.5%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 27.5%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 27.5%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if 5.99999999999999983e-168 < k < 16500

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 35.9%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 35.9%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 35.9%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 35.9%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 35.9%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 33.3%

      \[\leadsto \color{blue}{\left(c \cdot \left(y \cdot y3\right)\right)} \cdot y4 \]

   if 16500 < k

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 37.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.5%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 37.5%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 37.5%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 37.5%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y1 around inf 26.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 32.1%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y1 \cdot y2\right)} \]

      2. associate-*r* 38.1%

         \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]

   10. Simplified 38.1%

       \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y1\right) \cdot y2} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -8.6 \cdot 10^{+27}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 16500:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4\right)\right)\\ \end{array} \]

Alternative 38: 22.0% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+21} \lor \neg \left(t \leq 1.65 \cdot 10^{-25}\right):\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= t -1.05e+21) (not (<= t 1.65e-25)))
   (* a (* y2 (* t y5)))
   (* c (* y0 (* x y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((t <= -1.05e+21) || !(t <= 1.65e-25)) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((t <= (-1.05d+21)) .or. (.not. (t <= 1.65d-25))) then
        tmp = a * (y2 * (t * y5))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((t <= -1.05e+21) || !(t <= 1.65e-25)) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (t <= -1.05e+21) or not (t <= 1.65e-25):
		tmp = a * (y2 * (t * y5))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((t <= -1.05e+21) || !(t <= 1.65e-25))
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((t <= -1.05e+21) || ~((t <= 1.65e-25)))
		tmp = a * (y2 * (t * y5));
	else
		tmp = c * (y0 * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[t, -1.05e+21], N[Not[LessEqual[t, 1.65e-25]], $MachinePrecision]], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e21 or 1.6499999999999999e-25 < t

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 42.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 42.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 42.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 42.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 42.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 36.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.9%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 35.9%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 35.9%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 28.1%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 30.2%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 30.2%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if -1.05e21 < t < 1.6499999999999999e-25

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 37.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y0 around inf 29.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 29.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

   7. Simplified 29.6%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   8. Taylor expanded in x around inf 21.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+21} \lor \neg \left(t \leq 1.65 \cdot 10^{-25}\right):\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 39: 22.2% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.25 \cdot 10^{+30} \lor \neg \left(y5 \leq 1.05 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y5 -1.25e+30) (not (<= y5 1.05e+70)))
   (* a (* y2 (* t y5)))
   (* k (* y4 (* y1 y2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -1.25e+30) || !(y5 <= 1.05e+70)) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = k * (y4 * (y1 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y5 <= (-1.25d+30)) .or. (.not. (y5 <= 1.05d+70))) then
        tmp = a * (y2 * (t * y5))
    else
        tmp = k * (y4 * (y1 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -1.25e+30) || !(y5 <= 1.05e+70)) {
		tmp = a * (y2 * (t * y5));
	} else {
		tmp = k * (y4 * (y1 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y5 <= -1.25e+30) or not (y5 <= 1.05e+70):
		tmp = a * (y2 * (t * y5))
	else:
		tmp = k * (y4 * (y1 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y5 <= -1.25e+30) || !(y5 <= 1.05e+70))
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	else
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y5 <= -1.25e+30) || ~((y5 <= 1.05e+70)))
		tmp = a * (y2 * (t * y5));
	else
		tmp = k * (y4 * (y1 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y5, -1.25e+30], N[Not[LessEqual[y5, 1.05e+70]], $MachinePrecision]], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y5 < -1.25e30 or 1.05000000000000004e70 < y5

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 55.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 55.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 55.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 55.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 55.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 55.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 52.0%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 46.4%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 46.4%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 32.1%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 33.0%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 33.0%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if -1.25e30 < y5 < 1.05000000000000004e70

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 31.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 31.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 22.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.25 \cdot 10^{+30} \lor \neg \left(y5 \leq 1.05 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]

Alternative 40: 21.2% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -5 \cdot 10^{+29} \lor \neg \left(k \leq 7 \cdot 10^{+115}\right):\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= k -5e+29) (not (<= k 7e+115)))
   (* y4 (* k (* y1 y2)))
   (* a (* y2 (* t y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((k <= -5e+29) || !(k <= 7e+115)) {
		tmp = y4 * (k * (y1 * y2));
	} else {
		tmp = a * (y2 * (t * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((k <= (-5d+29)) .or. (.not. (k <= 7d+115))) then
        tmp = y4 * (k * (y1 * y2))
    else
        tmp = a * (y2 * (t * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((k <= -5e+29) || !(k <= 7e+115)) {
		tmp = y4 * (k * (y1 * y2));
	} else {
		tmp = a * (y2 * (t * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (k <= -5e+29) or not (k <= 7e+115):
		tmp = y4 * (k * (y1 * y2))
	else:
		tmp = a * (y2 * (t * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((k <= -5e+29) || !(k <= 7e+115))
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	else
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((k <= -5e+29) || ~((k <= 7e+115)))
		tmp = y4 * (k * (y1 * y2));
	else
		tmp = a * (y2 * (t * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[k, -5e+29], N[Not[LessEqual[k, 7e+115]], $MachinePrecision]], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -5.0000000000000001e29 or 7.00000000000000011e115 < k

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 52.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 52.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 35.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]

   if -5.0000000000000001e29 < k < 7.00000000000000011e115

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 42.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 36.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.6%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 34.6%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 34.6%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 23.9%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 24.6%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 24.6%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5 \cdot 10^{+29} \lor \neg \left(k \leq 7 \cdot 10^{+115}\right):\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \]

Alternative 41: 22.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -7.2 \cdot 10^{+28} \lor \neg \left(k \leq 1.95 \cdot 10^{+112}\right):\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= k -7.2e+28) (not (<= k 1.95e+112)))
   (* y4 (* y1 (* k y2)))
   (* a (* y2 (* t y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((k <= -7.2e+28) || !(k <= 1.95e+112)) {
		tmp = y4 * (y1 * (k * y2));
	} else {
		tmp = a * (y2 * (t * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((k <= (-7.2d+28)) .or. (.not. (k <= 1.95d+112))) then
        tmp = y4 * (y1 * (k * y2))
    else
        tmp = a * (y2 * (t * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((k <= -7.2e+28) || !(k <= 1.95e+112)) {
		tmp = y4 * (y1 * (k * y2));
	} else {
		tmp = a * (y2 * (t * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (k <= -7.2e+28) or not (k <= 1.95e+112):
		tmp = y4 * (y1 * (k * y2))
	else:
		tmp = a * (y2 * (t * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((k <= -7.2e+28) || !(k <= 1.95e+112))
		tmp = Float64(y4 * Float64(y1 * Float64(k * y2)));
	else
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((k <= -7.2e+28) || ~((k <= 1.95e+112)))
		tmp = y4 * (y1 * (k * y2));
	else
		tmp = a * (y2 * (t * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[k, -7.2e+28], N[Not[LessEqual[k, 1.95e+112]], $MachinePrecision]], N[(y4 * N[(y1 * N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -7.1999999999999999e28 or 1.94999999999999984e112 < k

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 52.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 52.0%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 52.0%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 29.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y1 \cdot y2\right)\right) \cdot k} \]

      2. *-commutative 29.9%

         \[\leadsto \left(y4 \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \cdot k \]

      3. associate-*l* 35.0%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y2 \cdot y1\right) \cdot k\right)} \]

      4. *-commutative 35.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y1 \cdot y2\right)} \cdot k\right) \]

      5. associate-*l* 35.9%

         \[\leadsto y4 \cdot \color{blue}{\left(y1 \cdot \left(y2 \cdot k\right)\right)} \]

      6. *-commutative 35.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \color{blue}{\left(k \cdot y2\right)}\right) \]

   10. Simplified 35.9%

       \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)} \]

   if -7.1999999999999999e28 < k < 1.94999999999999984e112

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 42.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 42.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 36.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.6%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 34.6%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 34.6%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 23.9%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 24.6%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 24.6%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7.2 \cdot 10^{+28} \lor \neg \left(k \leq 1.95 \cdot 10^{+112}\right):\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \end{array} \]

Alternative 42: 21.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.22 \cdot 10^{+70}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -3.6e+30)
   (* a (* y2 (* t y5)))
   (if (<= y5 1.22e+70) (* k (* y4 (* y1 y2))) (* t (* y5 (* a y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -3.6e+30) {
		tmp = a * (y2 * (t * y5));
	} else if (y5 <= 1.22e+70) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-3.6d+30)) then
        tmp = a * (y2 * (t * y5))
    else if (y5 <= 1.22d+70) then
        tmp = k * (y4 * (y1 * y2))
    else
        tmp = t * (y5 * (a * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -3.6e+30) {
		tmp = a * (y2 * (t * y5));
	} else if (y5 <= 1.22e+70) {
		tmp = k * (y4 * (y1 * y2));
	} else {
		tmp = t * (y5 * (a * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -3.6e+30:
		tmp = a * (y2 * (t * y5))
	elif y5 <= 1.22e+70:
		tmp = k * (y4 * (y1 * y2))
	else:
		tmp = t * (y5 * (a * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -3.6e+30)
		tmp = Float64(a * Float64(y2 * Float64(t * y5)));
	elseif (y5 <= 1.22e+70)
		tmp = Float64(k * Float64(y4 * Float64(y1 * y2)));
	else
		tmp = Float64(t * Float64(y5 * Float64(a * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -3.6e+30)
		tmp = a * (y2 * (t * y5));
	elseif (y5 <= 1.22e+70)
		tmp = k * (y4 * (y1 * y2));
	else
		tmp = t * (y5 * (a * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -3.6e+30], N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.22e+70], N[(k * N[(y4 * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y5 * N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -3.6000000000000002e30

   1. Initial program 22.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 53.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 53.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 53.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 53.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 53.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 46.5%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.1%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 45.1%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 45.1%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 30.8%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.3%

          \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 32.3%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

   if -3.6000000000000002e30 < y5 < 1.22e70

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 40.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 31.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

      4. *-commutative 31.3%

         \[\leadsto y4 \cdot \left(k \cdot \left(\color{blue}{y2 \cdot y1} - y \cdot b\right)\right) \]

   7. Simplified 31.3%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1 - y \cdot b\right)\right)} \]

   8. Taylor expanded in y2 around inf 22.4%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)} \]

   if 1.22e70 < y5

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 59.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 59.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 59.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 59.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 59.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 59.5%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 59.7%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 48.2%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 48.2%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 48.2%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 33.9%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 33.9%

          \[\leadsto \color{blue}{{\left(a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)\right)}^{1}} \]

       2. *-commutative 33.9%

          \[\leadsto {\color{blue}{\left(\left(t \cdot \left(y5 \cdot y2\right)\right) \cdot a\right)}}^{1} \]

       3. *-commutative 33.9%

          \[\leadsto {\left(\left(t \cdot \color{blue}{\left(y2 \cdot y5\right)}\right) \cdot a\right)}^{1} \]

   12. Applied egg-rr 33.9%

       \[\leadsto \color{blue}{{\left(\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 33.9%

          \[\leadsto \color{blue}{\left(t \cdot \left(y2 \cdot y5\right)\right) \cdot a} \]

       2. associate-*l* 39.8%

          \[\leadsto \color{blue}{t \cdot \left(\left(y2 \cdot y5\right) \cdot a\right)} \]

       3. *-commutative 39.8%

          \[\leadsto t \cdot \left(\color{blue}{\left(y5 \cdot y2\right)} \cdot a\right) \]

       4. associate-*l* 37.9%

          \[\leadsto t \cdot \color{blue}{\left(y5 \cdot \left(y2 \cdot a\right)\right)} \]

   14. Simplified 37.9%

       \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(y2 \cdot a\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 1.22 \cdot 10^{+70}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2\right)\right)\\ \end{array} \]

Alternative 43: 19.3% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y4 \leq -1.1 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y4 -1.1e-56) (* c (* y (* y3 y4))) (* a (* t (* y2 y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.1e-56) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y4 <= (-1.1d-56)) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = a * (t * (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y4 <= -1.1e-56) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * (t * (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y4 <= -1.1e-56:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = a * (t * (y2 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y4 <= -1.1e-56)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y4 <= -1.1e-56)
		tmp = c * (y * (y3 * y4));
	else
		tmp = a * (t * (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y4, -1.1e-56], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y4 < -1.10000000000000002e-56

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 48.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around 0 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y1 \cdot y2\right) + -1 \cdot \left(k \cdot \left(y \cdot b\right)\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4} \]
   6. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto \left(\left(k \cdot \left(y1 \cdot y2\right) + \color{blue}{\left(-k \cdot \left(y \cdot b\right)\right)}\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      2. unsub-neg 38.2%

         \[\leadsto \left(\color{blue}{\left(k \cdot \left(y1 \cdot y2\right) - k \cdot \left(y \cdot b\right)\right)} - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      3. *-commutative 38.2%

         \[\leadsto \left(\left(k \cdot \color{blue}{\left(y2 \cdot y1\right)} - k \cdot \left(y \cdot b\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \cdot y4 \]

      4. *-commutative 38.2%

         \[\leadsto \left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \color{blue}{\left(t \cdot y2 - y \cdot y3\right) \cdot c}\right) \cdot y4 \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(k \cdot \left(y2 \cdot y1\right) - k \cdot \left(y \cdot b\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot c\right) \cdot y4} \]

   8. Taylor expanded in y3 around inf 21.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 21.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y4\right)} \]

      2. associate-*l* 24.5%

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   10. Simplified 24.5%

       \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -1.10000000000000002e-56 < y4

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 46.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 46.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 46.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 46.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 46.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 46.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in t around inf 35.6%

      \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 33.8%

         \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

      2. *-commutative 33.8%

         \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

   9. Simplified 33.8%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

   10. Taylor expanded in a around inf 23.2%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.1 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \end{array} \]

Alternative 44: 16.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* t (* y2 y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (t * (y2 * y5))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (t * (y2 * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(t * Float64(y2 * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (t * (y2 * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.4%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 34.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in y5 around inf 42.3%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
5. Step-by-step derivation

   1. mul-1-neg 42.3%

      \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

   2. mul-1-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

   3. mul-1-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

   4. sub-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

   5. sub-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

6. Simplified 42.3%

   \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

7. Taylor expanded in t around inf 32.3%

   \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
8. Step-by-step derivation

   1. associate-*r* 28.6%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   2. *-commutative 28.6%

      \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

9. Simplified 28.6%

   \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

10. Taylor expanded in a around inf 19.4%

    \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]

11. Final simplification 19.4%

    \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

Alternative 45: 16.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y2 (* t y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y2 * (t * y5));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y2 * (t * y5))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y2 * (t * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y2 * (t * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y2 * Float64(t * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y2 * (t * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y2 * N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.4%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 34.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in y5 around inf 42.3%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
5. Step-by-step derivation

   1. mul-1-neg 42.3%

      \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

   2. mul-1-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

   3. mul-1-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

   4. sub-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

   5. sub-neg 42.3%

      \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

6. Simplified 42.3%

   \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

7. Taylor expanded in t around inf 32.3%

   \[\leadsto \color{blue}{t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]
8. Step-by-step derivation

   1. associate-*r* 28.6%

      \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   2. *-commutative 28.6%

      \[\leadsto \left(t \cdot y5\right) \cdot \left(a \cdot y2 - \color{blue}{j \cdot i}\right) \]

9. Simplified 28.6%

   \[\leadsto \color{blue}{\left(t \cdot y5\right) \cdot \left(a \cdot y2 - j \cdot i\right)} \]

10. Taylor expanded in a around inf 19.4%

    \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(y5 \cdot y2\right)\right)} \]
11. Step-by-step derivation

    1. associate-*r* 19.8%

       \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot y5\right) \cdot y2\right)} \]

12. Simplified 19.8%

    \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5\right) \cdot y2\right)} \]

13. Final simplification 19.8%

    \[\leadsto a \cdot \left(y2 \cdot \left(t \cdot y5\right)\right) \]

Developer target: 26.7% accurate, 0.8× 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 2023196 
(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

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* 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)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* 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 -1.2000065055686116e-105) (+ (+ (- (* (- (* 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 6.718963124057495e-279) (+ (- (- (- (* (* 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 4.77962681403792e-222) (+ (+ (- (* (- (* 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 2.2852241541266835e-175) (+ (- (- (- (* (* 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)))))