Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.5% → 38.5%

Time: 2.0min

Alternatives: 44

Speedup: 4.5×

• 88.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.5% 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: 38.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := t \cdot y2 - y \cdot y3\\ t_3 := x \cdot y - z \cdot t\\ t_4 := b \cdot y4 - i \cdot y5\\ t_5 := y \cdot k - t \cdot j\\ t_6 := y0 \cdot y5 - y1 \cdot y4\\ t_7 := x \cdot j - z \cdot k\\ \mathbf{if}\;i \leq -1.8 \cdot 10^{+235}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot t_4 + y2 \cdot t_1\right)\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(b \cdot t_3 + \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + y5 \cdot t_2\right)\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot t_6 + t \cdot t_4\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot t_5 + \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + t_2 \cdot t_1\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-44}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot t_7 + y5 \cdot t_5\right) - c \cdot t_3\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;y3 \cdot \left(\left(j \cdot t_6 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right) - y \cdot t_1\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+242}:\\ \;\;\;\;y1 \cdot \left(i \cdot t_7\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - i \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2 (- (* t y2) (* y y3)))
        (t_3 (- (* x y) (* z t)))
        (t_4 (- (* b y4) (* i y5)))
        (t_5 (- (* y k) (* t j)))
        (t_6 (- (* y0 y5) (* y1 y4)))
        (t_7 (- (* x j) (* z k))))
   (if (<= i -1.8e+235)
     (* (* j y1) (- (* x i) (* y3 y4)))
     (if (<= i -1e-83)
       (* t (+ (* z (- (* c i) (* a b))) (+ (* j t_4) (* y2 t_1))))
       (if (<= i 1.6e-263)
         (* a (+ (* b t_3) (+ (* y1 (- (* z y3) (* x y2))) (* y5 t_2))))
         (if (<= i 1.15e-192)
           (* j (+ (+ (* y3 t_6) (* t t_4)) (* x (- (* i y1) (* b y0)))))
           (if (<= i 4.5e-77)
             (+
              (* (* i y5) t_5)
              (+
               (* (- (* y1 y4) (* y0 y5)) (- (* k y2) (* j y3)))
               (* t_2 t_1)))
             (if (<= i 7.5e-44)
               (* i (- (+ (* y1 t_7) (* y5 t_5)) (* c t_3)))
               (if (<= i 3.5e+22)
                 (*
                  y
                  (+
                   (* k (- (* i y5) (* b y4)))
                   (+ (* x (- (* a b) (* c i))) (* y3 (- (* c y4) (* a y5))))))
                 (if (<= i 9.2e+46)
                   (*
                    y3
                    (- (+ (* j t_6) (* z (- (* a y1) (* c y0)))) (* y t_1)))
                   (if (<= i 3.1e+101)
                     (* c (* i (- (* z t) (* x y))))
                     (if (<= i 8.5e+242)
                       (* y1 (* i t_7))
                       (* c (- (* x (* y0 y2)) (* i t_3)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = (x * y) - (z * t);
	double t_4 = (b * y4) - (i * y5);
	double t_5 = (y * k) - (t * j);
	double t_6 = (y0 * y5) - (y1 * y4);
	double t_7 = (x * j) - (z * k);
	double tmp;
	if (i <= -1.8e+235) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (i <= -1e-83) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_1)));
	} else if (i <= 1.6e-263) {
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * t_2)));
	} else if (i <= 1.15e-192) {
		tmp = j * (((y3 * t_6) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	} else if (i <= 4.5e-77) {
		tmp = ((i * y5) * t_5) + ((((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3))) + (t_2 * t_1));
	} else if (i <= 7.5e-44) {
		tmp = i * (((y1 * t_7) + (y5 * t_5)) - (c * t_3));
	} else if (i <= 3.5e+22) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	} else if (i <= 9.2e+46) {
		tmp = y3 * (((j * t_6) + (z * ((a * y1) - (c * y0)))) - (y * t_1));
	} else if (i <= 3.1e+101) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (i <= 8.5e+242) {
		tmp = y1 * (i * t_7);
	} else {
		tmp = c * ((x * (y0 * y2)) - (i * t_3));
	}
	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) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (a * y5) - (c * y4)
    t_2 = (t * y2) - (y * y3)
    t_3 = (x * y) - (z * t)
    t_4 = (b * y4) - (i * y5)
    t_5 = (y * k) - (t * j)
    t_6 = (y0 * y5) - (y1 * y4)
    t_7 = (x * j) - (z * k)
    if (i <= (-1.8d+235)) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (i <= (-1d-83)) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_1)))
    else if (i <= 1.6d-263) then
        tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * t_2)))
    else if (i <= 1.15d-192) then
        tmp = j * (((y3 * t_6) + (t * t_4)) + (x * ((i * y1) - (b * y0))))
    else if (i <= 4.5d-77) then
        tmp = ((i * y5) * t_5) + ((((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3))) + (t_2 * t_1))
    else if (i <= 7.5d-44) then
        tmp = i * (((y1 * t_7) + (y5 * t_5)) - (c * t_3))
    else if (i <= 3.5d+22) then
        tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
    else if (i <= 9.2d+46) then
        tmp = y3 * (((j * t_6) + (z * ((a * y1) - (c * y0)))) - (y * t_1))
    else if (i <= 3.1d+101) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (i <= 8.5d+242) then
        tmp = y1 * (i * t_7)
    else
        tmp = c * ((x * (y0 * y2)) - (i * t_3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = (x * y) - (z * t);
	double t_4 = (b * y4) - (i * y5);
	double t_5 = (y * k) - (t * j);
	double t_6 = (y0 * y5) - (y1 * y4);
	double t_7 = (x * j) - (z * k);
	double tmp;
	if (i <= -1.8e+235) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (i <= -1e-83) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_1)));
	} else if (i <= 1.6e-263) {
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * t_2)));
	} else if (i <= 1.15e-192) {
		tmp = j * (((y3 * t_6) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	} else if (i <= 4.5e-77) {
		tmp = ((i * y5) * t_5) + ((((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3))) + (t_2 * t_1));
	} else if (i <= 7.5e-44) {
		tmp = i * (((y1 * t_7) + (y5 * t_5)) - (c * t_3));
	} else if (i <= 3.5e+22) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	} else if (i <= 9.2e+46) {
		tmp = y3 * (((j * t_6) + (z * ((a * y1) - (c * y0)))) - (y * t_1));
	} else if (i <= 3.1e+101) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (i <= 8.5e+242) {
		tmp = y1 * (i * t_7);
	} else {
		tmp = c * ((x * (y0 * y2)) - (i * t_3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = (t * y2) - (y * y3)
	t_3 = (x * y) - (z * t)
	t_4 = (b * y4) - (i * y5)
	t_5 = (y * k) - (t * j)
	t_6 = (y0 * y5) - (y1 * y4)
	t_7 = (x * j) - (z * k)
	tmp = 0
	if i <= -1.8e+235:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif i <= -1e-83:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_1)))
	elif i <= 1.6e-263:
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * t_2)))
	elif i <= 1.15e-192:
		tmp = j * (((y3 * t_6) + (t * t_4)) + (x * ((i * y1) - (b * y0))))
	elif i <= 4.5e-77:
		tmp = ((i * y5) * t_5) + ((((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3))) + (t_2 * t_1))
	elif i <= 7.5e-44:
		tmp = i * (((y1 * t_7) + (y5 * t_5)) - (c * t_3))
	elif i <= 3.5e+22:
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
	elif i <= 9.2e+46:
		tmp = y3 * (((j * t_6) + (z * ((a * y1) - (c * y0)))) - (y * t_1))
	elif i <= 3.1e+101:
		tmp = c * (i * ((z * t) - (x * y)))
	elif i <= 8.5e+242:
		tmp = y1 * (i * t_7)
	else:
		tmp = c * ((x * (y0 * y2)) - (i * t_3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	t_5 = Float64(Float64(y * k) - Float64(t * j))
	t_6 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_7 = Float64(Float64(x * j) - Float64(z * k))
	tmp = 0.0
	if (i <= -1.8e+235)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (i <= -1e-83)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * t_4) + Float64(y2 * t_1))));
	elseif (i <= 1.6e-263)
		tmp = Float64(a * Float64(Float64(b * t_3) + Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(y5 * t_2))));
	elseif (i <= 1.15e-192)
		tmp = Float64(j * Float64(Float64(Float64(y3 * t_6) + Float64(t * t_4)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (i <= 4.5e-77)
		tmp = Float64(Float64(Float64(i * y5) * t_5) + Float64(Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(t_2 * t_1)));
	elseif (i <= 7.5e-44)
		tmp = Float64(i * Float64(Float64(Float64(y1 * t_7) + Float64(y5 * t_5)) - Float64(c * t_3)));
	elseif (i <= 3.5e+22)
		tmp = Float64(y * Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (i <= 9.2e+46)
		tmp = Float64(y3 * Float64(Float64(Float64(j * t_6) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))) - Float64(y * t_1)));
	elseif (i <= 3.1e+101)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (i <= 8.5e+242)
		tmp = Float64(y1 * Float64(i * t_7));
	else
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(i * t_3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = (t * y2) - (y * y3);
	t_3 = (x * y) - (z * t);
	t_4 = (b * y4) - (i * y5);
	t_5 = (y * k) - (t * j);
	t_6 = (y0 * y5) - (y1 * y4);
	t_7 = (x * j) - (z * k);
	tmp = 0.0;
	if (i <= -1.8e+235)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (i <= -1e-83)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_1)));
	elseif (i <= 1.6e-263)
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * t_2)));
	elseif (i <= 1.15e-192)
		tmp = j * (((y3 * t_6) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	elseif (i <= 4.5e-77)
		tmp = ((i * y5) * t_5) + ((((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3))) + (t_2 * t_1));
	elseif (i <= 7.5e-44)
		tmp = i * (((y1 * t_7) + (y5 * t_5)) - (c * t_3));
	elseif (i <= 3.5e+22)
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	elseif (i <= 9.2e+46)
		tmp = y3 * (((j * t_6) + (z * ((a * y1) - (c * y0)))) - (y * t_1));
	elseif (i <= 3.1e+101)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (i <= 8.5e+242)
		tmp = y1 * (i * t_7);
	else
		tmp = c * ((x * (y0 * y2)) - (i * t_3));
	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[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.8e+235], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1e-83], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$4), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e-263], N[(a * N[(N[(b * t$95$3), $MachinePrecision] + N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e-192], N[(j * N[(N[(N[(y3 * t$95$6), $MachinePrecision] + N[(t * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.5e-77], N[(N[(N[(i * y5), $MachinePrecision] * t$95$5), $MachinePrecision] + N[(N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.5e-44], N[(i * N[(N[(N[(y1 * t$95$7), $MachinePrecision] + N[(y5 * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.5e+22], N[(y * N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.2e+46], N[(y3 * N[(N[(N[(j * t$95$6), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e+101], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.5e+242], N[(y1 * N[(i * t$95$7), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if i < -1.79999999999999993e235

   1. Initial program 20.0%

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

      1. +-commutative 20.0%

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

      2. fma-def 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in y1 around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. mul-1-neg 40.3%

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

      3. sub-neg 40.3%

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

   6. Simplified 40.3%

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

   7. Taylor expanded in j around inf 70.2%

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

      1. associate-*r* 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

      4. *-commutative 70.2%

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

      5. *-commutative 70.2%

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

   9. Simplified 70.2%

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

   if -1.79999999999999993e235 < i < -1e-83

   1. Initial program 40.1%

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

      1. associate-+l- 40.1%

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

   3. Simplified 40.1%

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

   4. Taylor expanded in t around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. mul-1-neg 64.9%

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

   6. Simplified 64.9%

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

   if -1e-83 < i < 1.6e-263

   1. Initial program 36.2%

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

      1. associate-+l- 36.2%

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

   3. Simplified 36.2%

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

   4. Taylor expanded in a around inf 50.1%

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

      1. associate--l+ 50.1%

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

      2. mul-1-neg 50.1%

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

      3. mul-1-neg 50.1%

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

   6. Simplified 50.1%

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

   if 1.6e-263 < i < 1.15000000000000009e-192

   1. Initial program 23.8%

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

      1. +-commutative 23.8%

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

      2. fma-def 29.7%

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

      3. *-commutative 29.7%

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

      4. *-commutative 29.7%

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

   3. Simplified 29.7%

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

   4. Taylor expanded in j around inf 76.8%

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

   if 1.15000000000000009e-192 < i < 4.5000000000000001e-77

   1. Initial program 35.0%

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

      1. associate-+l- 35.0%

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

   3. Simplified 35.0%

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

   4. Taylor expanded in y5 around inf 60.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot \left(i \cdot y5\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 60.5%

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

   6. Simplified 60.5%

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

   if 4.5000000000000001e-77 < i < 7.50000000000000008e-44

   1. Initial program 37.5%

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

      1. associate-+l- 37.5%

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

   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 i around -inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. associate--l+ 87.5%

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

   6. Simplified 87.5%

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

   if 7.50000000000000008e-44 < i < 3.5e22

   1. Initial program 26.7%

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

      1. associate-+l- 26.7%

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

   3. Simplified 26.7%

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

   4. Taylor expanded in y around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. mul-1-neg 73.5%

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

      3. mul-1-neg 73.5%

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

   6. Simplified 73.5%

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

   if 3.5e22 < i < 9.2000000000000002e46

   1. Initial program 28.6%

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

      1. associate-+l- 28.6%

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

   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 y3 around -inf 85.7%

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

   if 9.2000000000000002e46 < i < 3.09999999999999999e101

   1. Initial program 11.1%

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

      1. associate-+l- 11.1%

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

   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 c around inf 44.5%

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

      1. associate--l+ 44.5%

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

      2. mul-1-neg 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in i around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. *-commutative 77.9%

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

   9. Simplified 77.9%

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

   if 3.09999999999999999e101 < i < 8.5000000000000003e242

   1. Initial program 18.1%

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

      1. +-commutative 18.1%

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

      2. fma-def 21.2%

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

   3. Simplified 30.3%

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

   4. Taylor expanded in y1 around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. mul-1-neg 60.7%

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

      3. sub-neg 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in i around inf 67.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \cdot y1 \]
   8. Step-by-step derivation

      1. *-commutative 67.3%

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

      2. *-commutative 67.3%

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

   9. Simplified 67.3%

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

   if 8.5000000000000003e242 < i

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

   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 c around inf 56.4%

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

      1. associate--l+ 56.4%

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

      2. mul-1-neg 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in y4 around 0 68.9%

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

   8. Taylor expanded in y3 around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

   10. Simplified 69.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x - i \cdot \left(x \cdot y - z \cdot t\right)\right)} \]
3. Recombined 11 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{+235}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-83}:\\ \;\;\;\;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}\;i \leq 1.6 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-77}:\\ \;\;\;\;\left(i \cdot y5\right) \cdot \left(y \cdot k - t \cdot j\right) + \left(\left(y1 \cdot y4 - y0 \cdot y5\right) \cdot \left(k \cdot y2 - j \cdot y3\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-44}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;y3 \cdot \left(\left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right) - y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+242}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 2: 53.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := i \cdot y1 - b \cdot y0\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := \left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - z \cdot t\right)\\ t_7 := a \cdot y5 - c \cdot y4\\ t_8 := \left(t \cdot y2 - y \cdot y3\right) \cdot t_7\\ t_9 := b \cdot y4 - i \cdot y5\\ t_10 := y1 \cdot y4 - y0 \cdot y5\\ \mathbf{if}\;\left(\left(\left(\left(t_6 + \left(x \cdot j - z \cdot k\right) \cdot t_4\right) + t_2 \cdot t_3\right) + t_9 \cdot t_1\right) + t_8\right) + t_10 \cdot t_5 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t_5, t_10, \mathsf{fma}\left(t_1, t_9, \mathsf{fma}\left(t_3, t_2, t_6 + \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot t_4\right)\right) + t_8\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(\left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right) - y \cdot t_7\right)\\ \end{array} \end{array} \]

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 (- (* c y0) (* a y1)))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (- (* i y1) (* b y0)))
        (t_5 (- (* k y2) (* j y3)))
        (t_6 (* (- (* a b) (* c i)) (- (* x y) (* z t))))
        (t_7 (- (* a y5) (* c y4)))
        (t_8 (* (- (* t y2) (* y y3)) t_7))
        (t_9 (- (* b y4) (* i y5)))
        (t_10 (- (* y1 y4) (* y0 y5))))
   (if (<=
        (+
         (+
          (+ (+ (+ t_6 (* (- (* x j) (* z k)) t_4)) (* t_2 t_3)) (* t_9 t_1))
          t_8)
         (* t_10 t_5))
        INFINITY)
     (fma
      t_5
      t_10
      (+
       (fma t_1 t_9 (fma t_3 t_2 (+ t_6 (* (fma x j (* z (- k))) t_4))))
       t_8))
     (*
      y3
      (-
       (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))
       (* y t_7))))))

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 = (c * y0) - (a * y1);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (i * y1) - (b * y0);
	double t_5 = (k * y2) - (j * y3);
	double t_6 = ((a * b) - (c * i)) * ((x * y) - (z * t));
	double t_7 = (a * y5) - (c * y4);
	double t_8 = ((t * y2) - (y * y3)) * t_7;
	double t_9 = (b * y4) - (i * y5);
	double t_10 = (y1 * y4) - (y0 * y5);
	double tmp;
	if ((((((t_6 + (((x * j) - (z * k)) * t_4)) + (t_2 * t_3)) + (t_9 * t_1)) + t_8) + (t_10 * t_5)) <= ((double) INFINITY)) {
		tmp = fma(t_5, t_10, (fma(t_1, t_9, fma(t_3, t_2, (t_6 + (fma(x, j, (z * -k)) * t_4)))) + t_8));
	} else {
		tmp = y3 * (((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))) - (y * t_7));
	}
	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(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(Float64(i * y1) - Float64(b * y0))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t)))
	t_7 = Float64(Float64(a * y5) - Float64(c * y4))
	t_8 = Float64(Float64(Float64(t * y2) - Float64(y * y3)) * t_7)
	t_9 = Float64(Float64(b * y4) - Float64(i * y5))
	t_10 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(t_6 + Float64(Float64(Float64(x * j) - Float64(z * k)) * t_4)) + Float64(t_2 * t_3)) + Float64(t_9 * t_1)) + t_8) + Float64(t_10 * t_5)) <= Inf)
		tmp = fma(t_5, t_10, Float64(fma(t_1, t_9, fma(t_3, t_2, Float64(t_6 + Float64(fma(x, j, Float64(z * Float64(-k))) * t_4)))) + t_8));
	else
		tmp = Float64(y3 * Float64(Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))) - Float64(y * t_7)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]}, Block[{t$95$9 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(t$95$6 + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(t$95$9 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision] + N[(t$95$10 * t$95$5), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$5 * t$95$10 + N[(N[(t$95$1 * t$95$9 + N[(t$95$3 * t$95$2 + N[(t$95$6 + N[(N[(x * j + N[(z * (-k)), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$8), $MachinePrecision]), $MachinePrecision], N[(y3 * N[(N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$7), $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 92.9%

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

      1. +-commutative 92.9%

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

      2. fma-def 92.9%

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

      3. *-commutative 92.9%

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

      4. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   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%

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

      1. associate-+l- 0.0%

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

   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 y3 around -inf 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(j \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot z\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.7%

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

Alternative 3: 53.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((c * y0) - (a * y1)) * ((x * y2) - (z * y3)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = y3 * (((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))) - (y * 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[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(y3 * N[(N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$1), $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 92.9%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

   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 y3 around -inf 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(j \cdot \left(y4 \cdot y1 - y0 \cdot y5\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot z\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.6%

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

Alternative 4: 38.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ t_2 := b \cdot \left(z \cdot k - x \cdot j\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := y0 \cdot \left(c \cdot t_3 + \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + t_2\right)\right)\\ t_5 := \left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \mathbf{if}\;y0 \leq -1.8 \cdot 10^{+79}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y0 \leq -2.7 \cdot 10^{-51}:\\ \;\;\;\;\left(y1 \cdot y3 - t \cdot b\right) \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{-137}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{-272}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 3.2 \cdot 10^{-235}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{-234}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq 2.25 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 1.85 \cdot 10^{-106}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 8.7 \cdot 10^{+80}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(y0 \cdot t_3 - \left(y4 \cdot \left(t \cdot y2\right) - \left(z \cdot t\right) \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+170}:\\ \;\;\;\;y0 \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          t
          (+
           (* z (- (* c i) (* a b)))
           (+ (* j (- (* b y4) (* i y5))) (* y2 (- (* a y5) (* c y4)))))))
        (t_2 (* b (- (* z k) (* x j))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (* y0 (+ (* c t_3) (+ (* y5 (- (* j y3) (* k y2))) t_2))))
        (t_5 (* (* y a) (- (* x b) (* y3 y5)))))
   (if (<= y0 -1.8e+79)
     t_4
     (if (<= y0 -2.7e-51)
       (* (- (* y1 y3) (* t b)) (* z a))
       (if (<= y0 -1.7e-137)
         (* c (- (* y0 (* x y2)) (* t (- (* y2 y4) (* z i)))))
         (if (<= y0 1.7e-272)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j (- (* i y1) (* b y0)))))
           (if (<= y0 3.2e-235)
             (* y0 (* c (* x y2)))
             (if (<= y0 7e-234)
               t_5
               (if (<= y0 2.25e-145)
                 t_1
                 (if (<= y0 1.85e-106)
                   (* y4 (* y3 (- (* y c) (* j y1))))
                   (if (<= y0 5.2e+66)
                     t_1
                     (if (<= y0 8.7e+80)
                       t_5
                       (if (<= y0 1.4e+120)
                         (* c (- (* y0 t_3) (- (* y4 (* t y2)) (* (* z t) i))))
                         (if (<= y0 5e+170) (* y0 t_2) t_4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))));
	double t_2 = b * ((z * k) - (x * j));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y0 * ((c * t_3) + ((y5 * ((j * y3) - (k * y2))) + t_2));
	double t_5 = (y * a) * ((x * b) - (y3 * y5));
	double tmp;
	if (y0 <= -1.8e+79) {
		tmp = t_4;
	} else if (y0 <= -2.7e-51) {
		tmp = ((y1 * y3) - (t * b)) * (z * a);
	} else if (y0 <= -1.7e-137) {
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	} else if (y0 <= 1.7e-272) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= 3.2e-235) {
		tmp = y0 * (c * (x * y2));
	} else if (y0 <= 7e-234) {
		tmp = t_5;
	} else if (y0 <= 2.25e-145) {
		tmp = t_1;
	} else if (y0 <= 1.85e-106) {
		tmp = y4 * (y3 * ((y * c) - (j * y1)));
	} else if (y0 <= 5.2e+66) {
		tmp = t_1;
	} else if (y0 <= 8.7e+80) {
		tmp = t_5;
	} else if (y0 <= 1.4e+120) {
		tmp = c * ((y0 * t_3) - ((y4 * (t * y2)) - ((z * t) * i)));
	} else if (y0 <= 5e+170) {
		tmp = y0 * t_2;
	} else {
		tmp = t_4;
	}
	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) :: t_5
    real(8) :: tmp
    t_1 = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))))
    t_2 = b * ((z * k) - (x * j))
    t_3 = (x * y2) - (z * y3)
    t_4 = y0 * ((c * t_3) + ((y5 * ((j * y3) - (k * y2))) + t_2))
    t_5 = (y * a) * ((x * b) - (y3 * y5))
    if (y0 <= (-1.8d+79)) then
        tmp = t_4
    else if (y0 <= (-2.7d-51)) then
        tmp = ((y1 * y3) - (t * b)) * (z * a)
    else if (y0 <= (-1.7d-137)) then
        tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))))
    else if (y0 <= 1.7d-272) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (y0 <= 3.2d-235) then
        tmp = y0 * (c * (x * y2))
    else if (y0 <= 7d-234) then
        tmp = t_5
    else if (y0 <= 2.25d-145) then
        tmp = t_1
    else if (y0 <= 1.85d-106) then
        tmp = y4 * (y3 * ((y * c) - (j * y1)))
    else if (y0 <= 5.2d+66) then
        tmp = t_1
    else if (y0 <= 8.7d+80) then
        tmp = t_5
    else if (y0 <= 1.4d+120) then
        tmp = c * ((y0 * t_3) - ((y4 * (t * y2)) - ((z * t) * i)))
    else if (y0 <= 5d+170) then
        tmp = y0 * t_2
    else
        tmp = t_4
    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 = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))));
	double t_2 = b * ((z * k) - (x * j));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y0 * ((c * t_3) + ((y5 * ((j * y3) - (k * y2))) + t_2));
	double t_5 = (y * a) * ((x * b) - (y3 * y5));
	double tmp;
	if (y0 <= -1.8e+79) {
		tmp = t_4;
	} else if (y0 <= -2.7e-51) {
		tmp = ((y1 * y3) - (t * b)) * (z * a);
	} else if (y0 <= -1.7e-137) {
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	} else if (y0 <= 1.7e-272) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= 3.2e-235) {
		tmp = y0 * (c * (x * y2));
	} else if (y0 <= 7e-234) {
		tmp = t_5;
	} else if (y0 <= 2.25e-145) {
		tmp = t_1;
	} else if (y0 <= 1.85e-106) {
		tmp = y4 * (y3 * ((y * c) - (j * y1)));
	} else if (y0 <= 5.2e+66) {
		tmp = t_1;
	} else if (y0 <= 8.7e+80) {
		tmp = t_5;
	} else if (y0 <= 1.4e+120) {
		tmp = c * ((y0 * t_3) - ((y4 * (t * y2)) - ((z * t) * i)));
	} else if (y0 <= 5e+170) {
		tmp = y0 * t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))))
	t_2 = b * ((z * k) - (x * j))
	t_3 = (x * y2) - (z * y3)
	t_4 = y0 * ((c * t_3) + ((y5 * ((j * y3) - (k * y2))) + t_2))
	t_5 = (y * a) * ((x * b) - (y3 * y5))
	tmp = 0
	if y0 <= -1.8e+79:
		tmp = t_4
	elif y0 <= -2.7e-51:
		tmp = ((y1 * y3) - (t * b)) * (z * a)
	elif y0 <= -1.7e-137:
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))))
	elif y0 <= 1.7e-272:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif y0 <= 3.2e-235:
		tmp = y0 * (c * (x * y2))
	elif y0 <= 7e-234:
		tmp = t_5
	elif y0 <= 2.25e-145:
		tmp = t_1
	elif y0 <= 1.85e-106:
		tmp = y4 * (y3 * ((y * c) - (j * y1)))
	elif y0 <= 5.2e+66:
		tmp = t_1
	elif y0 <= 8.7e+80:
		tmp = t_5
	elif y0 <= 1.4e+120:
		tmp = c * ((y0 * t_3) - ((y4 * (t * y2)) - ((z * t) * i)))
	elif y0 <= 5e+170:
		tmp = y0 * t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))))
	t_2 = Float64(b * Float64(Float64(z * k) - Float64(x * j)))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(y0 * Float64(Float64(c * t_3) + Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + t_2)))
	t_5 = Float64(Float64(y * a) * Float64(Float64(x * b) - Float64(y3 * y5)))
	tmp = 0.0
	if (y0 <= -1.8e+79)
		tmp = t_4;
	elseif (y0 <= -2.7e-51)
		tmp = Float64(Float64(Float64(y1 * y3) - Float64(t * b)) * Float64(z * a));
	elseif (y0 <= -1.7e-137)
		tmp = Float64(c * Float64(Float64(y0 * Float64(x * y2)) - Float64(t * Float64(Float64(y2 * y4) - Float64(z * i)))));
	elseif (y0 <= 1.7e-272)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y0 <= 3.2e-235)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (y0 <= 7e-234)
		tmp = t_5;
	elseif (y0 <= 2.25e-145)
		tmp = t_1;
	elseif (y0 <= 1.85e-106)
		tmp = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))));
	elseif (y0 <= 5.2e+66)
		tmp = t_1;
	elseif (y0 <= 8.7e+80)
		tmp = t_5;
	elseif (y0 <= 1.4e+120)
		tmp = Float64(c * Float64(Float64(y0 * t_3) - Float64(Float64(y4 * Float64(t * y2)) - Float64(Float64(z * t) * i))));
	elseif (y0 <= 5e+170)
		tmp = Float64(y0 * t_2);
	else
		tmp = t_4;
	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 * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))));
	t_2 = b * ((z * k) - (x * j));
	t_3 = (x * y2) - (z * y3);
	t_4 = y0 * ((c * t_3) + ((y5 * ((j * y3) - (k * y2))) + t_2));
	t_5 = (y * a) * ((x * b) - (y3 * y5));
	tmp = 0.0;
	if (y0 <= -1.8e+79)
		tmp = t_4;
	elseif (y0 <= -2.7e-51)
		tmp = ((y1 * y3) - (t * b)) * (z * a);
	elseif (y0 <= -1.7e-137)
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	elseif (y0 <= 1.7e-272)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (y0 <= 3.2e-235)
		tmp = y0 * (c * (x * y2));
	elseif (y0 <= 7e-234)
		tmp = t_5;
	elseif (y0 <= 2.25e-145)
		tmp = t_1;
	elseif (y0 <= 1.85e-106)
		tmp = y4 * (y3 * ((y * c) - (j * y1)));
	elseif (y0 <= 5.2e+66)
		tmp = t_1;
	elseif (y0 <= 8.7e+80)
		tmp = t_5;
	elseif (y0 <= 1.4e+120)
		tmp = c * ((y0 * t_3) - ((y4 * (t * y2)) - ((z * t) * i)));
	elseif (y0 <= 5e+170)
		tmp = y0 * t_2;
	else
		tmp = t_4;
	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[(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 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y0 * N[(N[(c * t$95$3), $MachinePrecision] + N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * a), $MachinePrecision] * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.8e+79], t$95$4, If[LessEqual[y0, -2.7e-51], N[(N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision] * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.7e-137], N[(c * N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.7e-272], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.2e-235], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7e-234], t$95$5, If[LessEqual[y0, 2.25e-145], t$95$1, If[LessEqual[y0, 1.85e-106], N[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.2e+66], t$95$1, If[LessEqual[y0, 8.7e+80], t$95$5, If[LessEqual[y0, 1.4e+120], N[(c * N[(N[(y0 * t$95$3), $MachinePrecision] - N[(N[(y4 * N[(t * y2), $MachinePrecision]), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5e+170], N[(y0 * t$95$2), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -1.8e79 or 4.99999999999999977e170 < y0

   1. Initial program 22.4%

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

      1. +-commutative 22.4%

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

      2. fma-def 23.7%

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

      3. *-commutative 23.7%

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

      4. *-commutative 23.7%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in y0 around inf 66.3%

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

      1. mul-1-neg 66.3%

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

   6. Simplified 66.3%

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

   if -1.8e79 < y0 < -2.6999999999999997e-51

   1. Initial program 29.4%

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

      1. associate-+l- 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in a around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. mul-1-neg 55.0%

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

      3. mul-1-neg 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in z around inf 51.1%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) - -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 51.2%

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

      2. distribute-lft-out-- 51.2%

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

      3. mul-1-neg 51.2%

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

      4. distribute-rgt-neg-in 51.2%

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

      5. *-commutative 51.2%

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

      6. mul-1-neg 51.2%

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

      7. associate-*r* 51.2%

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

      8. distribute-lft-out-- 51.2%

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

      9. sub-neg 51.2%

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

      10. mul-1-neg 51.2%

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

      11. remove-double-neg 51.2%

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

      12. +-commutative 51.2%

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

      13. mul-1-neg 51.2%

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

      14. unsub-neg 51.2%

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

      15. *-commutative 51.2%

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

      16. *-commutative 51.2%

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

   9. Simplified 51.2%

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

   if -2.6999999999999997e-51 < y0 < -1.70000000000000007e-137

   1. Initial program 35.6%

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

      1. associate-+l- 35.6%

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

   3. Simplified 35.6%

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

   4. Taylor expanded in c around inf 64.5%

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

      1. associate--l+ 64.5%

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

      2. mul-1-neg 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y2 around inf 64.5%

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

   8. Taylor expanded in y around 0 65.2%

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

      1. associate-*r* 65.2%

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

      2. *-commutative 65.2%

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

      3. associate-*r* 71.9%

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

      4. associate-*r* 71.9%

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

      5. *-commutative 71.9%

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

      6. associate-*r* 71.9%

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

      7. distribute-rgt-in 71.9%

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

      8. +-commutative 71.9%

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

      9. mul-1-neg 71.9%

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

      10. unsub-neg 71.9%

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

      11. *-commutative 71.9%

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

   10. Simplified 71.9%

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

   if -1.70000000000000007e-137 < y0 < 1.7000000000000002e-272

   1. Initial program 21.7%

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

      1. associate-+l- 21.7%

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

   3. Simplified 21.7%

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

   4. Taylor expanded in x around inf 62.9%

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

   if 1.7000000000000002e-272 < y0 < 3.2000000000000001e-235

   1. Initial program 49.9%

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

      1. associate-+l- 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in c around inf 25.5%

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

      1. associate--l+ 25.5%

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

      2. mul-1-neg 25.5%

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

   6. Simplified 25.5%

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

   7. Taylor expanded in y2 around inf 25.5%

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

   8. Taylor expanded in y0 around inf 24.7%

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

      1. *-commutative 24.7%

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

      2. associate-*l* 56.3%

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

      3. *-commutative 56.3%

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

   10. Simplified 56.3%

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

   if 3.2000000000000001e-235 < y0 < 7.0000000000000003e-234 or 5.20000000000000024e66 < y0 < 8.70000000000000009e80

   1. Initial program 22.2%

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

      1. associate-+l- 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in a around inf 56.0%

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

      1. associate--l+ 56.0%

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

      2. mul-1-neg 56.0%

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

      3. mul-1-neg 56.0%

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

   6. Simplified 56.0%

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

   7. Taylor expanded in y around inf 78.4%

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

      1. associate-*r* 78.4%

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

      2. +-commutative 78.4%

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

      3. mul-1-neg 78.4%

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

      4. unsub-neg 78.4%

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

      5. *-commutative 78.4%

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

   9. Simplified 78.4%

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

   if 7.0000000000000003e-234 < y0 < 2.25e-145 or 1.8499999999999999e-106 < y0 < 5.20000000000000024e66

   1. Initial program 40.9%

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

      1. associate-+l- 40.9%

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

   3. Simplified 40.9%

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

   4. Taylor expanded in t around inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. mul-1-neg 60.8%

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

   6. Simplified 60.8%

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

   if 2.25e-145 < y0 < 1.8499999999999999e-106

   1. Initial program 45.0%

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

      1. associate-+l- 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in y4 around inf 55.7%

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

   5. Taylor expanded in y3 around -inf 77.9%

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

   if 8.70000000000000009e80 < y0 < 1.4e120

   1. Initial program 20.0%

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

      1. associate-+l- 20.0%

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

   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 c around inf 60.5%

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

      1. associate--l+ 60.5%

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

      2. mul-1-neg 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in y around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

      4. *-commutative 60.9%

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

      5. *-commutative 60.9%

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

   9. Simplified 60.9%

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

   if 1.4e120 < y0 < 4.99999999999999977e170

   1. Initial program 18.2%

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

      1. +-commutative 18.2%

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

      2. fma-def 18.2%

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

      3. *-commutative 18.2%

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

      4. *-commutative 18.2%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in y0 around inf 54.5%

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

      1. mul-1-neg 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in b around inf 82.6%

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

      1. *-commutative 82.6%

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

      2. *-commutative 82.6%

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

   9. Simplified 82.6%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.8 \cdot 10^{+79}:\\ \;\;\;\;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}\;y0 \leq -2.7 \cdot 10^{-51}:\\ \;\;\;\;\left(y1 \cdot y3 - t \cdot b\right) \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{-137}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 1.7 \cdot 10^{-272}:\\ \;\;\;\;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}\;y0 \leq 3.2 \cdot 10^{-235}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 7 \cdot 10^{-234}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \mathbf{elif}\;y0 \leq 2.25 \cdot 10^{-145}:\\ \;\;\;\;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}\;y0 \leq 1.85 \cdot 10^{-106}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{+66}:\\ \;\;\;\;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}\;y0 \leq 8.7 \cdot 10^{+80}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b - y3 \cdot y5\right)\\ \mathbf{elif}\;y0 \leq 1.4 \cdot 10^{+120}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(y4 \cdot \left(t \cdot y2\right) - \left(z \cdot t\right) \cdot i\right)\right)\\ \mathbf{elif}\;y0 \leq 5 \cdot 10^{+170}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]

Alternative 5: 38.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := i \cdot \left(z \cdot t - x \cdot y\right)\\ t_4 := z \cdot k - x \cdot j\\ t_5 := y0 \cdot \left(b \cdot t_4\right)\\ t_6 := y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_2\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_1\right) + y0 \cdot t_4\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(t_3 + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-232}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(t_3 + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot t_2\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

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 (- (* y y3) (* t y2)))
        (t_3 (* i (- (* z t) (* x y))))
        (t_4 (- (* z k) (* x j)))
        (t_5 (* y0 (* b t_4)))
        (t_6 (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) (* c t_2)))))
   (if (<= b -1.55e+119)
     (* b (+ (+ (* a (- (* x y) (* z t))) (* y4 t_1)) (* y0 t_4)))
     (if (<= b -2.9e+47)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= b -2e+44)
         t_5
         (if (<= b -1.75e-134)
           (* c (+ t_3 (* y2 (- (* x y0) (* t y4)))))
           (if (<= b 2.1e-299)
             t_6
             (if (<= b 4.4e-281)
               (* y (* y3 (* a (- y5))))
               (if (<= b 1.05e-232)
                 t_6
                 (if (<= b 2.2e+104)
                   (* c (+ t_3 (+ (* y0 (* x y2)) (* y4 t_2))))
                   (if (<= b 2.9e+238)
                     (* y4 (* t (- (* b j) (* c y2))))
                     t_5)))))))))))

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 = (y * y3) - (t * y2);
	double t_3 = i * ((z * t) - (x * y));
	double t_4 = (z * k) - (x * j);
	double t_5 = y0 * (b * t_4);
	double t_6 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double tmp;
	if (b <= -1.55e+119) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_4));
	} else if (b <= -2.9e+47) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (b <= -2e+44) {
		tmp = t_5;
	} else if (b <= -1.75e-134) {
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 2.1e-299) {
		tmp = t_6;
	} else if (b <= 4.4e-281) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1.05e-232) {
		tmp = t_6;
	} else if (b <= 2.2e+104) {
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_2)));
	} else if (b <= 2.9e+238) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_5;
	}
	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) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (y * y3) - (t * y2)
    t_3 = i * ((z * t) - (x * y))
    t_4 = (z * k) - (x * j)
    t_5 = y0 * (b * t_4)
    t_6 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
    if (b <= (-1.55d+119)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_4))
    else if (b <= (-2.9d+47)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (b <= (-2d+44)) then
        tmp = t_5
    else if (b <= (-1.75d-134)) then
        tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))))
    else if (b <= 2.1d-299) then
        tmp = t_6
    else if (b <= 4.4d-281) then
        tmp = y * (y3 * (a * -y5))
    else if (b <= 1.05d-232) then
        tmp = t_6
    else if (b <= 2.2d+104) then
        tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_2)))
    else if (b <= 2.9d+238) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = t_5
    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 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = i * ((z * t) - (x * y));
	double t_4 = (z * k) - (x * j);
	double t_5 = y0 * (b * t_4);
	double t_6 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	double tmp;
	if (b <= -1.55e+119) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_4));
	} else if (b <= -2.9e+47) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (b <= -2e+44) {
		tmp = t_5;
	} else if (b <= -1.75e-134) {
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 2.1e-299) {
		tmp = t_6;
	} else if (b <= 4.4e-281) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1.05e-232) {
		tmp = t_6;
	} else if (b <= 2.2e+104) {
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_2)));
	} else if (b <= 2.9e+238) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = t_5;
	}
	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 = (y * y3) - (t * y2)
	t_3 = i * ((z * t) - (x * y))
	t_4 = (z * k) - (x * j)
	t_5 = y0 * (b * t_4)
	t_6 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
	tmp = 0
	if b <= -1.55e+119:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_4))
	elif b <= -2.9e+47:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif b <= -2e+44:
		tmp = t_5
	elif b <= -1.75e-134:
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))))
	elif b <= 2.1e-299:
		tmp = t_6
	elif b <= 4.4e-281:
		tmp = y * (y3 * (a * -y5))
	elif b <= 1.05e-232:
		tmp = t_6
	elif b <= 2.2e+104:
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_2)))
	elif b <= 2.9e+238:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_5
	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(y * y3) - Float64(t * y2))
	t_3 = Float64(i * Float64(Float64(z * t) - Float64(x * y)))
	t_4 = Float64(Float64(z * k) - Float64(x * j))
	t_5 = Float64(y0 * Float64(b * t_4))
	t_6 = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_2)))
	tmp = 0.0
	if (b <= -1.55e+119)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * t_4)));
	elseif (b <= -2.9e+47)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (b <= -2e+44)
		tmp = t_5;
	elseif (b <= -1.75e-134)
		tmp = Float64(c * Float64(t_3 + Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4)))));
	elseif (b <= 2.1e-299)
		tmp = t_6;
	elseif (b <= 4.4e-281)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (b <= 1.05e-232)
		tmp = t_6;
	elseif (b <= 2.2e+104)
		tmp = Float64(c * Float64(t_3 + Float64(Float64(y0 * Float64(x * y2)) + Float64(y4 * t_2))));
	elseif (b <= 2.9e+238)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = t_5;
	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 = (y * y3) - (t * y2);
	t_3 = i * ((z * t) - (x * y));
	t_4 = (z * k) - (x * j);
	t_5 = y0 * (b * t_4);
	t_6 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	tmp = 0.0;
	if (b <= -1.55e+119)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_4));
	elseif (b <= -2.9e+47)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (b <= -2e+44)
		tmp = t_5;
	elseif (b <= -1.75e-134)
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))));
	elseif (b <= 2.1e-299)
		tmp = t_6;
	elseif (b <= 4.4e-281)
		tmp = y * (y3 * (a * -y5));
	elseif (b <= 1.05e-232)
		tmp = t_6;
	elseif (b <= 2.2e+104)
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_2)));
	elseif (b <= 2.9e+238)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = t_5;
	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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y0 * N[(b * t$95$4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+119], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9e+47], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e+44], t$95$5, If[LessEqual[b, -1.75e-134], N[(c * N[(t$95$3 + N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-299], t$95$6, If[LessEqual[b, 4.4e-281], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-232], t$95$6, If[LessEqual[b, 2.2e+104], N[(c * N[(t$95$3 + N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+238], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -1.54999999999999998e119

   1. Initial program 20.9%

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

      1. associate-+l- 20.9%

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

   3. Simplified 20.9%

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

   4. Taylor expanded in b around inf 54.4%

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

   if -1.54999999999999998e119 < b < -2.8999999999999998e47

   1. Initial program 25.0%

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

      1. associate-+l- 25.0%

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

   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 i around -inf 28.9%

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

      1. mul-1-neg 28.9%

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

      2. associate--l+ 28.9%

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

   6. Simplified 28.9%

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

   7. Taylor expanded in y5 around inf 47.9%

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

      1. *-commutative 47.9%

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

   9. Simplified 47.9%

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

   if -2.8999999999999998e47 < b < -2.0000000000000002e44 or 2.9000000000000002e238 < b

   1. Initial program 21.3%

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

      1. +-commutative 21.3%

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

      2. fma-def 28.6%

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

      3. *-commutative 28.6%

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

      4. *-commutative 28.6%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in y0 around inf 50.5%

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

      1. mul-1-neg 50.5%

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

   6. Simplified 50.5%

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

   7. Taylor expanded in b around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   9. Simplified 72.3%

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

   if -2.0000000000000002e44 < b < -1.7499999999999999e-134

   1. Initial program 42.4%

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

      1. associate-+l- 42.4%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in c around inf 43.0%

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

      1. associate--l+ 43.0%

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

      2. mul-1-neg 43.0%

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

   6. Simplified 43.0%

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

   7. Taylor expanded in y2 around inf 40.1%

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

   8. Taylor expanded in y3 around 0 43.4%

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

      1. +-commutative 43.4%

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

      2. associate--r+ 43.4%

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

      3. associate-*r* 46.4%

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

      4. *-commutative 46.4%

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

      5. cancel-sign-sub-inv 46.4%

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

      6. associate-*r* 46.4%

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

      7. neg-mul-1 46.4%

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

      8. *-commutative 46.4%

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

      9. distribute-rgt-in 46.4%

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

      10. mul-1-neg 46.4%

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

      11. sub-neg 46.4%

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

      12. *-commutative 46.4%

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

      13. *-commutative 46.4%

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

   10. Simplified 46.4%

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

   if -1.7499999999999999e-134 < b < 2.1000000000000001e-299 or 4.40000000000000008e-281 < b < 1.05e-232

   1. Initial program 33.6%

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

      1. associate-+l- 33.6%

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

   3. Simplified 33.6%

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

   4. Taylor expanded in y4 around inf 50.9%

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

   if 2.1000000000000001e-299 < b < 4.40000000000000008e-281

   1. Initial program 33.3%

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

      1. associate-+l- 33.3%

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

   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 a around inf 83.3%

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

      1. associate--l+ 83.3%

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

      2. mul-1-neg 83.3%

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

      3. mul-1-neg 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around inf 67.5%

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

      1. associate-*r* 67.5%

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

      2. +-commutative 67.5%

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

      3. mul-1-neg 67.5%

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

      4. unsub-neg 67.5%

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

      5. *-commutative 67.5%

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

   9. Simplified 67.5%

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

   10. Taylor expanded in x around 0 67.5%

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

       1. mul-1-neg 67.5%

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

       2. *-commutative 67.5%

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

   12. Simplified 67.5%

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

   13. Taylor expanded in a around 0 83.3%

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

       1. *-commutative 83.3%

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

       2. associate-*l* 83.5%

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

   15. Simplified 83.5%

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

   if 1.05e-232 < b < 2.2e104

   1. Initial program 29.4%

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

      1. associate-+l- 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. associate--l+ 60.3%

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

      2. mul-1-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y2 around inf 55.7%

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

   if 2.2e104 < b < 2.9000000000000002e238

   1. Initial program 28.1%

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

      1. associate-+l- 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in y4 around inf 35.1%

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

   5. Taylor expanded in t around inf 59.9%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-232}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 6: 38.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := z \cdot k - x \cdot j\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_4 := y \cdot y3 - t \cdot y2\\ t_5 := y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_4\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+193}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_1\right) + y0 \cdot t_2\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{+97}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 10^{-232}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot t_4\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* z k) (* x j)))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_4 (- (* y y3) (* t y2)))
        (t_5 (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) (* c t_4)))))
   (if (<= b -7.2e+193)
     (* b (+ (+ (* a (- (* x y) (* z t))) (* y4 t_1)) (* y0 t_2)))
     (if (<= b -1.45e+148)
       t_3
       (if (<= b -1.42e+97)
         t_5
         (if (<= b -2.3e-132)
           t_3
           (if (<= b 2.1e-299)
             t_5
             (if (<= b 5.8e-282)
               (* y (* y3 (* a (- y5))))
               (if (<= b 1e-232)
                 t_5
                 (if (<= b 8.4e+105)
                   (*
                    c
                    (+
                     (* i (- (* z t) (* x y)))
                     (+ (* y0 (* x y2)) (* y4 t_4))))
                   (if (<= b 1.12e+237)
                     (* y4 (* t (- (* b j) (* c y2))))
                     (* y0 (* b 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 = (t * j) - (y * k);
	double t_2 = (z * k) - (x * j);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = (y * y3) - (t * y2);
	double t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	double tmp;
	if (b <= -7.2e+193) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_2));
	} else if (b <= -1.45e+148) {
		tmp = t_3;
	} else if (b <= -1.42e+97) {
		tmp = t_5;
	} else if (b <= -2.3e-132) {
		tmp = t_3;
	} else if (b <= 2.1e-299) {
		tmp = t_5;
	} else if (b <= 5.8e-282) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1e-232) {
		tmp = t_5;
	} else if (b <= 8.4e+105) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_4)));
	} else if (b <= 1.12e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y0 * (b * 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) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (z * k) - (x * j)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_4 = (y * y3) - (t * y2)
    t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4))
    if (b <= (-7.2d+193)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_2))
    else if (b <= (-1.45d+148)) then
        tmp = t_3
    else if (b <= (-1.42d+97)) then
        tmp = t_5
    else if (b <= (-2.3d-132)) then
        tmp = t_3
    else if (b <= 2.1d-299) then
        tmp = t_5
    else if (b <= 5.8d-282) then
        tmp = y * (y3 * (a * -y5))
    else if (b <= 1d-232) then
        tmp = t_5
    else if (b <= 8.4d+105) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_4)))
    else if (b <= 1.12d+237) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = y0 * (b * 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 = (t * j) - (y * k);
	double t_2 = (z * k) - (x * j);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = (y * y3) - (t * y2);
	double t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	double tmp;
	if (b <= -7.2e+193) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_2));
	} else if (b <= -1.45e+148) {
		tmp = t_3;
	} else if (b <= -1.42e+97) {
		tmp = t_5;
	} else if (b <= -2.3e-132) {
		tmp = t_3;
	} else if (b <= 2.1e-299) {
		tmp = t_5;
	} else if (b <= 5.8e-282) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1e-232) {
		tmp = t_5;
	} else if (b <= 8.4e+105) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_4)));
	} else if (b <= 1.12e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y0 * (b * 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 = (t * j) - (y * k)
	t_2 = (z * k) - (x * j)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_4 = (y * y3) - (t * y2)
	t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4))
	tmp = 0
	if b <= -7.2e+193:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_2))
	elif b <= -1.45e+148:
		tmp = t_3
	elif b <= -1.42e+97:
		tmp = t_5
	elif b <= -2.3e-132:
		tmp = t_3
	elif b <= 2.1e-299:
		tmp = t_5
	elif b <= 5.8e-282:
		tmp = y * (y3 * (a * -y5))
	elif b <= 1e-232:
		tmp = t_5
	elif b <= 8.4e+105:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_4)))
	elif b <= 1.12e+237:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = y0 * (b * 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(t * j) - Float64(y * k))
	t_2 = Float64(Float64(z * k) - Float64(x * j))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_4 = Float64(Float64(y * y3) - Float64(t * y2))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_4)))
	tmp = 0.0
	if (b <= -7.2e+193)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * t_2)));
	elseif (b <= -1.45e+148)
		tmp = t_3;
	elseif (b <= -1.42e+97)
		tmp = t_5;
	elseif (b <= -2.3e-132)
		tmp = t_3;
	elseif (b <= 2.1e-299)
		tmp = t_5;
	elseif (b <= 5.8e-282)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (b <= 1e-232)
		tmp = t_5;
	elseif (b <= 8.4e+105)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(x * y2)) + Float64(y4 * t_4))));
	elseif (b <= 1.12e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = Float64(y0 * Float64(b * 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 = (t * j) - (y * k);
	t_2 = (z * k) - (x * j);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_4 = (y * y3) - (t * y2);
	t_5 = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_4));
	tmp = 0.0;
	if (b <= -7.2e+193)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * t_2));
	elseif (b <= -1.45e+148)
		tmp = t_3;
	elseif (b <= -1.42e+97)
		tmp = t_5;
	elseif (b <= -2.3e-132)
		tmp = t_3;
	elseif (b <= 2.1e-299)
		tmp = t_5;
	elseif (b <= 5.8e-282)
		tmp = y * (y3 * (a * -y5));
	elseif (b <= 1e-232)
		tmp = t_5;
	elseif (b <= 8.4e+105)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_4)));
	elseif (b <= 1.12e+237)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = y0 * (b * 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[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+193], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e+148], t$95$3, If[LessEqual[b, -1.42e+97], t$95$5, If[LessEqual[b, -2.3e-132], t$95$3, If[LessEqual[b, 2.1e-299], t$95$5, If[LessEqual[b, 5.8e-282], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-232], t$95$5, If[LessEqual[b, 8.4e+105], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -7.2e193

   1. Initial program 13.5%

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

      1. associate-+l- 13.5%

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

   3. Simplified 13.5%

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

   4. Taylor expanded in b around inf 59.9%

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

   if -7.2e193 < b < -1.45e148 or -1.41999999999999991e97 < b < -2.30000000000000003e-132

   1. Initial program 41.1%

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

      1. associate-+l- 41.1%

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

   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 x around inf 53.4%

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

   if -1.45e148 < b < -1.41999999999999991e97 or -2.30000000000000003e-132 < b < 2.1000000000000001e-299 or 5.79999999999999995e-282 < b < 1.00000000000000002e-232

   1. Initial program 29.3%

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

      1. associate-+l- 29.3%

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

   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 y4 around inf 53.4%

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

   if 2.1000000000000001e-299 < b < 5.79999999999999995e-282

   1. Initial program 33.3%

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

      1. associate-+l- 33.3%

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

   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 a around inf 83.3%

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

      1. associate--l+ 83.3%

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

      2. mul-1-neg 83.3%

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

      3. mul-1-neg 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around inf 67.5%

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

      1. associate-*r* 67.5%

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

      2. +-commutative 67.5%

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

      3. mul-1-neg 67.5%

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

      4. unsub-neg 67.5%

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

      5. *-commutative 67.5%

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

   9. Simplified 67.5%

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

   10. Taylor expanded in x around 0 67.5%

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

       1. mul-1-neg 67.5%

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

       2. *-commutative 67.5%

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

   12. Simplified 67.5%

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

   13. Taylor expanded in a around 0 83.3%

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

       1. *-commutative 83.3%

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

       2. associate-*l* 83.5%

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

   15. Simplified 83.5%

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

   if 1.00000000000000002e-232 < b < 8.4000000000000004e105

   1. Initial program 29.4%

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

      1. associate-+l- 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. associate--l+ 60.3%

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

      2. mul-1-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y2 around inf 55.7%

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

   if 8.4000000000000004e105 < b < 1.11999999999999997e237

   1. Initial program 28.1%

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

      1. associate-+l- 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in y4 around inf 35.1%

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

   5. Taylor expanded in t around inf 59.9%

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

   if 1.11999999999999997e237 < b

   1. Initial program 16.5%

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

      1. +-commutative 16.5%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y0 around inf 42.3%

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

      1. mul-1-neg 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   9. Simplified 67.7%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+193}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -1.42 \cdot 10^{+97}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 10^{-232}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 7: 39.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := x \cdot y - z \cdot t\\ t_3 := z \cdot k - x \cdot j\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_5 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_2 + y4 \cdot t_1\right) + y0 \cdot t_3\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+98}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_5\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-234}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot t_2\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_5\right) - i \cdot t_2\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot t_3\right)\\ \end{array} \end{array} \]

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 (- (* x y) (* z t)))
        (t_3 (- (* z k) (* x j)))
        (t_4
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_5 (- (* y y3) (* t y2))))
   (if (<= b -3.5e+200)
     (* b (+ (+ (* a t_2) (* y4 t_1)) (* y0 t_3)))
     (if (<= b -6.6e+148)
       t_4
       (if (<= b -5e+98)
         (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) (* c t_5)))
         (if (<= b -3.6e+61)
           t_4
           (if (<= b 1.7e-234)
             (*
              i
              (-
               (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))
               (* c t_2)))
             (if (<= b 3.8e+104)
               (* c (- (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_5)) (* i t_2)))
               (if (<= b 2.55e+237)
                 (* y4 (* t (- (* b j) (* c y2))))
                 (* y0 (* b t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (x * y) - (z * t);
	double t_3 = (z * k) - (x * j);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = (y * y3) - (t * y2);
	double tmp;
	if (b <= -3.5e+200) {
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3));
	} else if (b <= -6.6e+148) {
		tmp = t_4;
	} else if (b <= -5e+98) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	} else if (b <= -3.6e+61) {
		tmp = t_4;
	} else if (b <= 1.7e-234) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2));
	} else if (b <= 3.8e+104) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (y4 * t_5)) - (i * t_2));
	} else if (b <= 2.55e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y0 * (b * t_3);
	}
	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) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (x * y) - (z * t)
    t_3 = (z * k) - (x * j)
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_5 = (y * y3) - (t * y2)
    if (b <= (-3.5d+200)) then
        tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3))
    else if (b <= (-6.6d+148)) then
        tmp = t_4
    else if (b <= (-5d+98)) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5))
    else if (b <= (-3.6d+61)) then
        tmp = t_4
    else if (b <= 1.7d-234) then
        tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2))
    else if (b <= 3.8d+104) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) + (y4 * t_5)) - (i * t_2))
    else if (b <= 2.55d+237) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = y0 * (b * t_3)
    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 = (t * j) - (y * k);
	double t_2 = (x * y) - (z * t);
	double t_3 = (z * k) - (x * j);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = (y * y3) - (t * y2);
	double tmp;
	if (b <= -3.5e+200) {
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3));
	} else if (b <= -6.6e+148) {
		tmp = t_4;
	} else if (b <= -5e+98) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	} else if (b <= -3.6e+61) {
		tmp = t_4;
	} else if (b <= 1.7e-234) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2));
	} else if (b <= 3.8e+104) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (y4 * t_5)) - (i * t_2));
	} else if (b <= 2.55e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y0 * (b * t_3);
	}
	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 = (x * y) - (z * t)
	t_3 = (z * k) - (x * j)
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_5 = (y * y3) - (t * y2)
	tmp = 0
	if b <= -3.5e+200:
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3))
	elif b <= -6.6e+148:
		tmp = t_4
	elif b <= -5e+98:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5))
	elif b <= -3.6e+61:
		tmp = t_4
	elif b <= 1.7e-234:
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2))
	elif b <= 3.8e+104:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (y4 * t_5)) - (i * t_2))
	elif b <= 2.55e+237:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = y0 * (b * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(z * k) - Float64(x * j))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_5 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (b <= -3.5e+200)
		tmp = Float64(b * Float64(Float64(Float64(a * t_2) + Float64(y4 * t_1)) + Float64(y0 * t_3)));
	elseif (b <= -6.6e+148)
		tmp = t_4;
	elseif (b <= -5e+98)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_5)));
	elseif (b <= -3.6e+61)
		tmp = t_4;
	elseif (b <= 1.7e-234)
		tmp = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))) - Float64(c * t_2)));
	elseif (b <= 3.8e+104)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_5)) - Float64(i * t_2)));
	elseif (b <= 2.55e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = Float64(y0 * Float64(b * t_3));
	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 = (x * y) - (z * t);
	t_3 = (z * k) - (x * j);
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_5 = (y * y3) - (t * y2);
	tmp = 0.0;
	if (b <= -3.5e+200)
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3));
	elseif (b <= -6.6e+148)
		tmp = t_4;
	elseif (b <= -5e+98)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	elseif (b <= -3.6e+61)
		tmp = t_4;
	elseif (b <= 1.7e-234)
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2));
	elseif (b <= 3.8e+104)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) + (y4 * t_5)) - (i * t_2));
	elseif (b <= 2.55e+237)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = y0 * (b * t_3);
	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[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+200], N[(b * N[(N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.6e+148], t$95$4, If[LessEqual[b, -5e+98], N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e+61], t$95$4, If[LessEqual[b, 1.7e-234], N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+104], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -3.50000000000000006e200

   1. Initial program 13.5%

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

      1. associate-+l- 13.5%

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

   3. Simplified 13.5%

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

   4. Taylor expanded in b around inf 59.9%

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

   if -3.50000000000000006e200 < b < -6.60000000000000021e148 or -4.9999999999999998e98 < b < -3.6000000000000001e61

   1. Initial program 40.0%

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

      1. associate-+l- 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in x around inf 75.1%

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

   if -6.60000000000000021e148 < b < -4.9999999999999998e98

   1. Initial program 15.4%

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

      1. associate-+l- 15.4%

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

   3. Simplified 15.4%

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

   4. Taylor expanded in y4 around inf 61.7%

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

   if -3.6000000000000001e61 < b < 1.69999999999999993e-234

   1. Initial program 37.0%

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

      1. associate-+l- 37.0%

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

   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 i around -inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. associate--l+ 44.9%

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

   6. Simplified 44.9%

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

   if 1.69999999999999993e-234 < b < 3.79999999999999969e104

   1. Initial program 29.4%

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

      1. associate-+l- 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. associate--l+ 60.3%

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

      2. mul-1-neg 60.3%

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

   6. Simplified 60.3%

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

   if 3.79999999999999969e104 < b < 2.54999999999999989e237

   1. Initial program 28.1%

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

      1. associate-+l- 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in y4 around inf 35.1%

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

   5. Taylor expanded in t around inf 59.9%

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

   if 2.54999999999999989e237 < b

   1. Initial program 16.5%

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

      1. +-commutative 16.5%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y0 around inf 42.3%

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

      1. mul-1-neg 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   9. Simplified 67.7%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+98}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-234}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 8: 39.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ t_2 := c \cdot i - a \cdot b\\ t_3 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(z \cdot t_2 + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot t_1\right)\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-193}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-97}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_3 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_1\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+151}:\\ \;\;\;\;z \cdot \left(\left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot t_2\right) - y3 \cdot t_3\right)\\ \mathbf{elif}\;t \leq 10^{+194}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+261}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2 (- (* c i) (* a b)))
        (t_3 (- (* c y0) (* a y1))))
   (if (<= t -2.5e+151)
     (* t (+ (* z t_2) (+ (* j (- (* b y4) (* i y5))) (* y2 t_1))))
     (if (<= t -1.5e-50)
       (*
        c
        (+
         (* i (- (* z t) (* x y)))
         (+ (* y0 (* x y2)) (* y4 (- (* y y3) (* t y2))))))
       (if (<= t -1.35e-193)
         (*
          y1
          (+
           (* a (- (* z y3) (* x y2)))
           (+ (* i (- (* x j) (* z k))) (* y4 (- (* k y2) (* j y3))))))
         (if (<= t 6.8e-97)
           (*
            y5
            (+
             (* i (- (* y k) (* t j)))
             (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
           (if (<= t 5.8e+67)
             (* y2 (+ (+ (* x t_3) (* k (- (* y1 y4) (* y0 y5)))) (* t t_1)))
             (if (<= t 6.4e+151)
               (* z (- (+ (* k (- (* b y0) (* i y1))) (* t t_2)) (* y3 t_3)))
               (if (<= t 1e+194)
                 (*
                  c
                  (- (* y0 (- (* x y2) (* z y3))) (* i (- (* x y) (* z t)))))
                 (if (<= t 1.35e+261)
                   (* a (* (* z t) (- b)))
                   (* i (* (* z t) c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (c * i) - (a * b);
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (t <= -2.5e+151) {
		tmp = t * ((z * t_2) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)));
	} else if (t <= -1.5e-50) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	} else if (t <= -1.35e-193) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	} else if (t <= 6.8e-97) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (t <= 5.8e+67) {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	} else if (t <= 6.4e+151) {
		tmp = z * (((k * ((b * y0) - (i * y1))) + (t * t_2)) - (y3 * t_3));
	} else if (t <= 1e+194) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))));
	} else if (t <= 1.35e+261) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = i * ((z * t) * c);
	}
	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 = (a * y5) - (c * y4)
    t_2 = (c * i) - (a * b)
    t_3 = (c * y0) - (a * y1)
    if (t <= (-2.5d+151)) then
        tmp = t * ((z * t_2) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)))
    else if (t <= (-1.5d-50)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))))
    else if (t <= (-1.35d-193)) then
        tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))))
    else if (t <= 6.8d-97) then
        tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (t <= 5.8d+67) then
        tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1))
    else if (t <= 6.4d+151) then
        tmp = z * (((k * ((b * y0) - (i * y1))) + (t * t_2)) - (y3 * t_3))
    else if (t <= 1d+194) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))))
    else if (t <= 1.35d+261) then
        tmp = a * ((z * t) * -b)
    else
        tmp = i * ((z * t) * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y5) - (c * y4);
	double t_2 = (c * i) - (a * b);
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (t <= -2.5e+151) {
		tmp = t * ((z * t_2) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)));
	} else if (t <= -1.5e-50) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	} else if (t <= -1.35e-193) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	} else if (t <= 6.8e-97) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (t <= 5.8e+67) {
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	} else if (t <= 6.4e+151) {
		tmp = z * (((k * ((b * y0) - (i * y1))) + (t * t_2)) - (y3 * t_3));
	} else if (t <= 1e+194) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))));
	} else if (t <= 1.35e+261) {
		tmp = a * ((z * t) * -b);
	} else {
		tmp = i * ((z * t) * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	t_2 = (c * i) - (a * b)
	t_3 = (c * y0) - (a * y1)
	tmp = 0
	if t <= -2.5e+151:
		tmp = t * ((z * t_2) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)))
	elif t <= -1.5e-50:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))))
	elif t <= -1.35e-193:
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))))
	elif t <= 6.8e-97:
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif t <= 5.8e+67:
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1))
	elif t <= 6.4e+151:
		tmp = z * (((k * ((b * y0) - (i * y1))) + (t * t_2)) - (y3 * t_3))
	elif t <= 1e+194:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))))
	elif t <= 1.35e+261:
		tmp = a * ((z * t) * -b)
	else:
		tmp = i * ((z * t) * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y5) - Float64(c * y4))
	t_2 = Float64(Float64(c * i) - Float64(a * b))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (t <= -2.5e+151)
		tmp = Float64(t * Float64(Float64(z * t_2) + Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * t_1))));
	elseif (t <= -1.5e-50)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(x * y2)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (t <= -1.35e-193)
		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 * Float64(Float64(k * y2) - Float64(j * y3))))));
	elseif (t <= 6.8e-97)
		tmp = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (t <= 5.8e+67)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_3) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_1)));
	elseif (t <= 6.4e+151)
		tmp = Float64(z * Float64(Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * t_2)) - Float64(y3 * t_3)));
	elseif (t <= 1e+194)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(i * Float64(Float64(x * y) - Float64(z * t)))));
	elseif (t <= 1.35e+261)
		tmp = Float64(a * Float64(Float64(z * t) * Float64(-b)));
	else
		tmp = Float64(i * Float64(Float64(z * t) * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y5) - (c * y4);
	t_2 = (c * i) - (a * b);
	t_3 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (t <= -2.5e+151)
		tmp = t * ((z * t_2) + ((j * ((b * y4) - (i * y5))) + (y2 * t_1)));
	elseif (t <= -1.5e-50)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	elseif (t <= -1.35e-193)
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	elseif (t <= 6.8e-97)
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (t <= 5.8e+67)
		tmp = y2 * (((x * t_3) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_1));
	elseif (t <= 6.4e+151)
		tmp = z * (((k * ((b * y0) - (i * y1))) + (t * t_2)) - (y3 * t_3));
	elseif (t <= 1e+194)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))));
	elseif (t <= 1.35e+261)
		tmp = a * ((z * t) * -b);
	else
		tmp = i * ((z * t) * c);
	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[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+151], N[(t * N[(N[(z * t$95$2), $MachinePrecision] + N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-50], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-193], 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 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-97], N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+67], N[(y2 * N[(N[(N[(x * t$95$3), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e+151], N[(z * N[(N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y3 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+194], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+261], N[(a * N[(N[(z * t), $MachinePrecision] * (-b)), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if t < -2.5000000000000001e151

   1. Initial program 18.8%

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

      1. associate-+l- 18.8%

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

   3. Simplified 18.8%

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

   4. Taylor expanded in t around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. mul-1-neg 62.8%

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

   6. Simplified 62.8%

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

   if -2.5000000000000001e151 < t < -1.49999999999999995e-50

   1. Initial program 23.9%

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

      1. associate-+l- 23.9%

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

   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 59.0%

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

      1. associate--l+ 59.0%

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

      2. mul-1-neg 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in y2 around inf 63.4%

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

   if -1.49999999999999995e-50 < t < -1.35e-193

   1. Initial program 39.9%

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

      1. +-commutative 39.9%

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

      2. fma-def 39.9%

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

   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 y1 around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. mul-1-neg 57.4%

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

      3. sub-neg 57.4%

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

   6. Simplified 57.4%

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

   if -1.35e-193 < t < 6.7999999999999998e-97

   1. Initial program 30.1%

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

      1. +-commutative 30.1%

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

      2. fma-def 31.9%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in y5 around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. mul-1-neg 55.0%

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

      3. mul-1-neg 55.0%

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

      4. sub-neg 55.0%

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

      5. sub-neg 55.0%

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

   6. Simplified 55.0%

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

   if 6.7999999999999998e-97 < t < 5.80000000000000047e67

   1. Initial program 33.6%

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

      1. associate-+l- 33.6%

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

   3. Simplified 33.6%

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

   4. Taylor expanded in y2 around inf 57.6%

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

   if 5.80000000000000047e67 < t < 6.39999999999999988e151

   1. Initial program 52.9%

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

      1. associate-+l- 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in z around -inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate--l+ 58.9%

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

   6. Simplified 58.9%

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

   if 6.39999999999999988e151 < t < 9.99999999999999945e193

   1. Initial program 9.1%

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

      1. associate-+l- 9.1%

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

   3. Simplified 9.1%

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

   4. Taylor expanded in c around inf 63.9%

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

      1. associate--l+ 63.9%

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

      2. mul-1-neg 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in y4 around 0 82.0%

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

   if 9.99999999999999945e193 < t < 1.35000000000000001e261

   1. Initial program 35.3%

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

      1. associate-+l- 35.3%

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

   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 a around inf 41.6%

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

      1. associate--l+ 41.6%

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

      2. mul-1-neg 41.6%

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

      3. mul-1-neg 41.6%

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

   6. Simplified 41.6%

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

   7. Taylor expanded in b around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. *-commutative 42.3%

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

      3. *-commutative 42.3%

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

   9. Simplified 42.3%

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

   10. Taylor expanded in x around 0 48.2%

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

       1. mul-1-neg 48.2%

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

       2. distribute-lft-neg-out 48.2%

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

       3. *-commutative 48.2%

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

   12. Simplified 48.2%

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

   if 1.35000000000000001e261 < t

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

   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 c around inf 14.8%

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

      1. associate--l+ 14.8%

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

      2. mul-1-neg 14.8%

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

   6. Simplified 14.8%

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

   7. Taylor expanded in y2 around inf 14.8%

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

   8. Taylor expanded in z around inf 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*l* 86.2%

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

   10. Simplified 86.2%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-50}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-193}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-97}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+67}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+151}:\\ \;\;\;\;z \cdot \left(\left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right) - y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 10^{+194}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+261}:\\ \;\;\;\;a \cdot \left(\left(z \cdot t\right) \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \end{array} \]

Alternative 9: 39.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;t \leq -7 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot t_2\right)\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-193}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-98}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+105}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_1 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_2\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+216}:\\ \;\;\;\;y3 \cdot \left(\left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right) - y \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \end{array} \]

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))))
   (if (<= t -7e+153)
     (*
      t
      (+ (* z (- (* c i) (* a b))) (+ (* j (- (* b y4) (* i y5))) (* y2 t_2))))
     (if (<= t -4e-55)
       (*
        c
        (+
         (* i (- (* z t) (* x y)))
         (+ (* y0 (* x y2)) (* y4 (- (* y y3) (* t y2))))))
       (if (<= t -1.9e-193)
         (*
          y1
          (+
           (* a (- (* z y3) (* x y2)))
           (+ (* i (- (* x j) (* z k))) (* y4 (- (* k y2) (* j y3))))))
         (if (<= t 3.6e-98)
           (*
            y5
            (+
             (* i (- (* y k) (* t j)))
             (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))
           (if (<= t 6.6e+105)
             (* y2 (+ (+ (* x t_1) (* k (- (* y1 y4) (* y0 y5)))) (* t t_2)))
             (if (<= t 9.5e+216)
               (*
                y3
                (-
                 (+ (* j (- (* y0 y5) (* y1 y4))) (* z (- (* a y1) (* c y0))))
                 (* y t_2)))
               (*
                x
                (+
                 (+ (* y (- (* a b) (* c i))) (* y2 t_1))
                 (* j (- (* i y1) (* b y0)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (a * y5) - (c * y4);
	double tmp;
	if (t <= -7e+153) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)));
	} else if (t <= -4e-55) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	} else if (t <= -1.9e-193) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	} else if (t <= 3.6e-98) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (t <= 6.6e+105) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	} else if (t <= 9.5e+216) {
		tmp = y3 * (((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))) - (y * t_2));
	} else {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	}
	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 * y0) - (a * y1)
    t_2 = (a * y5) - (c * y4)
    if (t <= (-7d+153)) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)))
    else if (t <= (-4d-55)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))))
    else if (t <= (-1.9d-193)) then
        tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))))
    else if (t <= 3.6d-98) then
        tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else if (t <= 6.6d+105) then
        tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
    else if (t <= 9.5d+216) then
        tmp = y3 * (((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))) - (y * t_2))
    else
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    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 tmp;
	if (t <= -7e+153) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)));
	} else if (t <= -4e-55) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	} else if (t <= -1.9e-193) {
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	} else if (t <= 3.6e-98) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else if (t <= 6.6e+105) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	} else if (t <= 9.5e+216) {
		tmp = y3 * (((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))) - (y * t_2));
	} else {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	}
	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)
	tmp = 0
	if t <= -7e+153:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)))
	elif t <= -4e-55:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))))
	elif t <= -1.9e-193:
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))))
	elif t <= 3.6e-98:
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	elif t <= 6.6e+105:
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
	elif t <= 9.5e+216:
		tmp = y3 * (((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))) - (y * t_2))
	else:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	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))
	tmp = 0.0
	if (t <= -7e+153)
		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 (t <= -4e-55)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(x * y2)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (t <= -1.9e-193)
		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 * Float64(Float64(k * y2) - Float64(j * y3))))));
	elseif (t <= 3.6e-98)
		tmp = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	elseif (t <= 6.6e+105)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_1) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_2)));
	elseif (t <= 9.5e+216)
		tmp = Float64(y3 * Float64(Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))) - Float64(y * t_2)));
	else
		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)))));
	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);
	tmp = 0.0;
	if (t <= -7e+153)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * t_2)));
	elseif (t <= -4e-55)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	elseif (t <= -1.9e-193)
		tmp = y1 * ((a * ((z * y3) - (x * y2))) + ((i * ((x * j) - (z * k))) + (y4 * ((k * y2) - (j * y3)))));
	elseif (t <= 3.6e-98)
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	elseif (t <= 6.6e+105)
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	elseif (t <= 9.5e+216)
		tmp = y3 * (((j * ((y0 * y5) - (y1 * y4))) + (z * ((a * y1) - (c * y0)))) - (y * t_2));
	else
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	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]}, If[LessEqual[t, -7e+153], 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[t, -4e-55], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-193], 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 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-98], N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+105], 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[t, 9.5e+216], N[(y3 * N[(N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -6.9999999999999998e153

   1. Initial program 18.8%

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

      1. associate-+l- 18.8%

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

   3. Simplified 18.8%

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

   4. Taylor expanded in t around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. mul-1-neg 62.8%

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

   6. Simplified 62.8%

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

   if -6.9999999999999998e153 < t < -3.99999999999999998e-55

   1. Initial program 23.9%

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

      1. associate-+l- 23.9%

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

   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 59.0%

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

      1. associate--l+ 59.0%

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

      2. mul-1-neg 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in y2 around inf 63.4%

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

   if -3.99999999999999998e-55 < t < -1.90000000000000002e-193

   1. Initial program 39.9%

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

      1. +-commutative 39.9%

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

      2. fma-def 39.9%

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

   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 y1 around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. mul-1-neg 57.4%

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

      3. sub-neg 57.4%

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

   6. Simplified 57.4%

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

   if -1.90000000000000002e-193 < t < 3.6000000000000002e-98

   1. Initial program 30.1%

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

      1. +-commutative 30.1%

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

      2. fma-def 31.9%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in y5 around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. mul-1-neg 55.0%

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

      3. mul-1-neg 55.0%

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

      4. sub-neg 55.0%

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

      5. sub-neg 55.0%

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

   6. Simplified 55.0%

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

   if 3.6000000000000002e-98 < t < 6.59999999999999995e105

   1. Initial program 40.2%

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

      1. associate-+l- 40.2%

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

   3. Simplified 40.2%

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

   4. Taylor expanded in y2 around inf 54.5%

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

   if 6.59999999999999995e105 < t < 9.50000000000000005e216

   1. Initial program 28.6%

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

      1. associate-+l- 28.6%

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

   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 y3 around -inf 64.7%

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

   if 9.50000000000000005e216 < t

   1. Initial program 16.7%

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

      1. associate-+l- 16.7%

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

   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 x around inf 55.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-193}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + \left(i \cdot \left(x \cdot j - z \cdot k\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-98}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+105}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+216}:\\ \;\;\;\;y3 \cdot \left(\left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right) - y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 10: 38.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := x \cdot y - z \cdot t\\ t_4 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+234}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot t_4 + y2 \cdot t_2\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot t_3 + \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot t_1 + t \cdot t_4\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+48}:\\ \;\;\;\;y3 \cdot \left(\left(j \cdot t_1 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right) - y \cdot t_2\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+242}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - i \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (- (* x y) (* z t)))
        (t_4 (- (* b y4) (* i y5))))
   (if (<= i -1.4e+234)
     (* (* j y1) (- (* x i) (* y3 y4)))
     (if (<= i -1.12e-83)
       (* t (+ (* z (- (* c i) (* a b))) (+ (* j t_4) (* y2 t_2))))
       (if (<= i 5e-265)
         (*
          a
          (+
           (* b t_3)
           (+ (* y1 (- (* z y3) (* x y2))) (* y5 (- (* t y2) (* y y3))))))
         (if (<= i 3.9e-185)
           (* j (+ (+ (* y3 t_1) (* t t_4)) (* x (- (* i y1) (* b y0)))))
           (if (<= i 1.8e+22)
             (*
              y
              (+
               (* k (- (* i y5) (* b y4)))
               (+ (* x (- (* a b) (* c i))) (* y3 (- (* c y4) (* a y5))))))
             (if (<= i 5.8e+48)
               (* y3 (- (+ (* j t_1) (* z (- (* a y1) (* c y0)))) (* y t_2)))
               (if (<= i 3.2e+100)
                 (* c (* i (- (* z t) (* x y))))
                 (if (<= i 7.2e+242)
                   (* y1 (* i (- (* x j) (* z k))))
                   (* c (- (* x (* y0 y2)) (* i t_3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (x * y) - (z * t);
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (i <= -1.4e+234) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (i <= -1.12e-83) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_2)));
	} else if (i <= 5e-265) {
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))));
	} else if (i <= 3.9e-185) {
		tmp = j * (((y3 * t_1) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	} else if (i <= 1.8e+22) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	} else if (i <= 5.8e+48) {
		tmp = y3 * (((j * t_1) + (z * ((a * y1) - (c * y0)))) - (y * t_2));
	} else if (i <= 3.2e+100) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (i <= 7.2e+242) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else {
		tmp = c * ((x * (y0 * y2)) - (i * t_3));
	}
	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 = (y0 * y5) - (y1 * y4)
    t_2 = (a * y5) - (c * y4)
    t_3 = (x * y) - (z * t)
    t_4 = (b * y4) - (i * y5)
    if (i <= (-1.4d+234)) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (i <= (-1.12d-83)) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_2)))
    else if (i <= 5d-265) then
        tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))))
    else if (i <= 3.9d-185) then
        tmp = j * (((y3 * t_1) + (t * t_4)) + (x * ((i * y1) - (b * y0))))
    else if (i <= 1.8d+22) then
        tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
    else if (i <= 5.8d+48) then
        tmp = y3 * (((j * t_1) + (z * ((a * y1) - (c * y0)))) - (y * t_2))
    else if (i <= 3.2d+100) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (i <= 7.2d+242) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else
        tmp = c * ((x * (y0 * y2)) - (i * t_3))
    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 = (y0 * y5) - (y1 * y4);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (x * y) - (z * t);
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (i <= -1.4e+234) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (i <= -1.12e-83) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_2)));
	} else if (i <= 5e-265) {
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))));
	} else if (i <= 3.9e-185) {
		tmp = j * (((y3 * t_1) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	} else if (i <= 1.8e+22) {
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	} else if (i <= 5.8e+48) {
		tmp = y3 * (((j * t_1) + (z * ((a * y1) - (c * y0)))) - (y * t_2));
	} else if (i <= 3.2e+100) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (i <= 7.2e+242) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else {
		tmp = c * ((x * (y0 * y2)) - (i * t_3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y5) - (y1 * y4)
	t_2 = (a * y5) - (c * y4)
	t_3 = (x * y) - (z * t)
	t_4 = (b * y4) - (i * y5)
	tmp = 0
	if i <= -1.4e+234:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif i <= -1.12e-83:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_2)))
	elif i <= 5e-265:
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))))
	elif i <= 3.9e-185:
		tmp = j * (((y3 * t_1) + (t * t_4)) + (x * ((i * y1) - (b * y0))))
	elif i <= 1.8e+22:
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))))
	elif i <= 5.8e+48:
		tmp = y3 * (((j * t_1) + (z * ((a * y1) - (c * y0)))) - (y * t_2))
	elif i <= 3.2e+100:
		tmp = c * (i * ((z * t) - (x * y)))
	elif i <= 7.2e+242:
		tmp = y1 * (i * ((x * j) - (z * k)))
	else:
		tmp = c * ((x * (y0 * y2)) - (i * t_3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(Float64(x * y) - Float64(z * t))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (i <= -1.4e+234)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (i <= -1.12e-83)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * t_4) + Float64(y2 * t_2))));
	elseif (i <= 5e-265)
		tmp = Float64(a * Float64(Float64(b * t_3) + Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))))));
	elseif (i <= 3.9e-185)
		tmp = Float64(j * Float64(Float64(Float64(y3 * t_1) + Float64(t * t_4)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (i <= 1.8e+22)
		tmp = Float64(y * Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(Float64(x * Float64(Float64(a * b) - Float64(c * i))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5))))));
	elseif (i <= 5.8e+48)
		tmp = Float64(y3 * Float64(Float64(Float64(j * t_1) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))) - Float64(y * t_2)));
	elseif (i <= 3.2e+100)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (i <= 7.2e+242)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	else
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(i * t_3)));
	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 = (y0 * y5) - (y1 * y4);
	t_2 = (a * y5) - (c * y4);
	t_3 = (x * y) - (z * t);
	t_4 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (i <= -1.4e+234)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (i <= -1.12e-83)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * t_4) + (y2 * t_2)));
	elseif (i <= 5e-265)
		tmp = a * ((b * t_3) + ((y1 * ((z * y3) - (x * y2))) + (y5 * ((t * y2) - (y * y3)))));
	elseif (i <= 3.9e-185)
		tmp = j * (((y3 * t_1) + (t * t_4)) + (x * ((i * y1) - (b * y0))));
	elseif (i <= 1.8e+22)
		tmp = y * ((k * ((i * y5) - (b * y4))) + ((x * ((a * b) - (c * i))) + (y3 * ((c * y4) - (a * y5)))));
	elseif (i <= 5.8e+48)
		tmp = y3 * (((j * t_1) + (z * ((a * y1) - (c * y0)))) - (y * t_2));
	elseif (i <= 3.2e+100)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (i <= 7.2e+242)
		tmp = y1 * (i * ((x * j) - (z * k)));
	else
		tmp = c * ((x * (y0 * y2)) - (i * t_3));
	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[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+234], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.12e-83], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$4), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-265], N[(a * N[(N[(b * t$95$3), $MachinePrecision] + N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.9e-185], N[(j * N[(N[(N[(y3 * t$95$1), $MachinePrecision] + N[(t * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e+22], N[(y * N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e+48], N[(y3 * N[(N[(N[(j * t$95$1), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+100], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.2e+242], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -1.3999999999999999e234

   1. Initial program 20.0%

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

      1. +-commutative 20.0%

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

      2. fma-def 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in y1 around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. mul-1-neg 40.3%

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

      3. sub-neg 40.3%

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

   6. Simplified 40.3%

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

   7. Taylor expanded in j around inf 70.2%

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

      1. associate-*r* 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

      4. *-commutative 70.2%

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

      5. *-commutative 70.2%

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

   9. Simplified 70.2%

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

   if -1.3999999999999999e234 < i < -1.11999999999999993e-83

   1. Initial program 40.1%

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

      1. associate-+l- 40.1%

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

   3. Simplified 40.1%

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

   4. Taylor expanded in t around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. mul-1-neg 64.9%

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

   6. Simplified 64.9%

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

   if -1.11999999999999993e-83 < i < 5.0000000000000001e-265

   1. Initial program 36.2%

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

      1. associate-+l- 36.2%

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

   3. Simplified 36.2%

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

   4. Taylor expanded in a around inf 50.1%

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

      1. associate--l+ 50.1%

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

      2. mul-1-neg 50.1%

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

      3. mul-1-neg 50.1%

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

   6. Simplified 50.1%

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

   if 5.0000000000000001e-265 < i < 3.8999999999999999e-185

   1. Initial program 23.8%

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

      1. +-commutative 23.8%

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

      2. fma-def 29.7%

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

      3. *-commutative 29.7%

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

      4. *-commutative 29.7%

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

   3. Simplified 29.7%

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

   4. Taylor expanded in j around inf 76.8%

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

   if 3.8999999999999999e-185 < i < 1.8e22

   1. Initial program 32.6%

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

      1. associate-+l- 32.6%

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

   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 y around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. mul-1-neg 58.4%

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

      3. mul-1-neg 58.4%

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

   6. Simplified 58.4%

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

   if 1.8e22 < i < 5.7999999999999998e48

   1. Initial program 28.6%

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

      1. associate-+l- 28.6%

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

   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 y3 around -inf 85.7%

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

   if 5.7999999999999998e48 < i < 3.1999999999999999e100

   1. Initial program 11.1%

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

      1. associate-+l- 11.1%

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

   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 c around inf 44.5%

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

      1. associate--l+ 44.5%

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

      2. mul-1-neg 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in i around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. *-commutative 77.9%

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

   9. Simplified 77.9%

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

   if 3.1999999999999999e100 < i < 7.19999999999999989e242

   1. Initial program 18.1%

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

      1. +-commutative 18.1%

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

      2. fma-def 21.2%

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

   3. Simplified 30.3%

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

   4. Taylor expanded in y1 around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. mul-1-neg 60.7%

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

      3. sub-neg 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in i around inf 67.3%

      \[\leadsto \color{blue}{\left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \cdot y1 \]
   8. Step-by-step derivation

      1. *-commutative 67.3%

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

      2. *-commutative 67.3%

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

   9. Simplified 67.3%

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

   if 7.19999999999999989e242 < i

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

   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 c around inf 56.4%

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

      1. associate--l+ 56.4%

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

      2. mul-1-neg 56.4%

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

   6. Simplified 56.4%

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

   7. Taylor expanded in y4 around 0 68.9%

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

   8. Taylor expanded in y3 around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

   10. Simplified 69.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x - i \cdot \left(x \cdot y - z \cdot t\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+234}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(x \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+48}:\\ \;\;\;\;y3 \cdot \left(\left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right) - y \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+242}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 36.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := i \cdot \left(z \cdot t - x \cdot y\right)\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_1\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(t_3 + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 10^{-236}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(t_3 + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot t_1\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2 (* y0 (* b (- (* z k) (* x j)))))
        (t_3 (* i (- (* z t) (* x y))))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c t_1)))))
   (if (<= b -4e+44)
     t_2
     (if (<= b -1.9e-132)
       (* c (+ t_3 (* y2 (- (* x y0) (* t y4)))))
       (if (<= b 2.1e-299)
         t_4
         (if (<= b 6.4e-282)
           (* y (* y3 (* a (- y5))))
           (if (<= b 1e-236)
             t_4
             (if (<= b 4e+105)
               (* c (+ t_3 (+ (* y0 (* x y2)) (* y4 t_1))))
               (if (<= b 2.2e+237)
                 (* y4 (* t (- (* b j) (* c y2))))
                 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = i * ((z * t) - (x * y));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	double tmp;
	if (b <= -4e+44) {
		tmp = t_2;
	} else if (b <= -1.9e-132) {
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 2.1e-299) {
		tmp = t_4;
	} else if (b <= 6.4e-282) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1e-236) {
		tmp = t_4;
	} else if (b <= 4e+105) {
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_1)));
	} else if (b <= 2.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = y0 * (b * ((z * k) - (x * j)))
    t_3 = i * ((z * t) - (x * y))
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
    if (b <= (-4d+44)) then
        tmp = t_2
    else if (b <= (-1.9d-132)) then
        tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))))
    else if (b <= 2.1d-299) then
        tmp = t_4
    else if (b <= 6.4d-282) then
        tmp = y * (y3 * (a * -y5))
    else if (b <= 1d-236) then
        tmp = t_4
    else if (b <= 4d+105) then
        tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_1)))
    else if (b <= 2.2d+237) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    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 * y3) - (t * y2);
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = i * ((z * t) - (x * y));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	double tmp;
	if (b <= -4e+44) {
		tmp = t_2;
	} else if (b <= -1.9e-132) {
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 2.1e-299) {
		tmp = t_4;
	} else if (b <= 6.4e-282) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1e-236) {
		tmp = t_4;
	} else if (b <= 4e+105) {
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_1)));
	} else if (b <= 2.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * y3) - (t * y2)
	t_2 = y0 * (b * ((z * k) - (x * j)))
	t_3 = i * ((z * t) - (x * y))
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
	tmp = 0
	if b <= -4e+44:
		tmp = t_2
	elif b <= -1.9e-132:
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))))
	elif b <= 2.1e-299:
		tmp = t_4
	elif b <= 6.4e-282:
		tmp = y * (y3 * (a * -y5))
	elif b <= 1e-236:
		tmp = t_4
	elif b <= 4e+105:
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_1)))
	elif b <= 2.2e+237:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * y3) - Float64(t * y2))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_3 = Float64(i * Float64(Float64(z * t) - Float64(x * y)))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_1)))
	tmp = 0.0
	if (b <= -4e+44)
		tmp = t_2;
	elseif (b <= -1.9e-132)
		tmp = Float64(c * Float64(t_3 + Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4)))));
	elseif (b <= 2.1e-299)
		tmp = t_4;
	elseif (b <= 6.4e-282)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (b <= 1e-236)
		tmp = t_4;
	elseif (b <= 4e+105)
		tmp = Float64(c * Float64(t_3 + Float64(Float64(y0 * Float64(x * y2)) + Float64(y4 * t_1))));
	elseif (b <= 2.2e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	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 * y3) - (t * y2);
	t_2 = y0 * (b * ((z * k) - (x * j)));
	t_3 = i * ((z * t) - (x * y));
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	tmp = 0.0;
	if (b <= -4e+44)
		tmp = t_2;
	elseif (b <= -1.9e-132)
		tmp = c * (t_3 + (y2 * ((x * y0) - (t * y4))));
	elseif (b <= 2.1e-299)
		tmp = t_4;
	elseif (b <= 6.4e-282)
		tmp = y * (y3 * (a * -y5));
	elseif (b <= 1e-236)
		tmp = t_4;
	elseif (b <= 4e+105)
		tmp = c * (t_3 + ((y0 * (x * y2)) + (y4 * t_1)));
	elseif (b <= 2.2e+237)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	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[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $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 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+44], t$95$2, If[LessEqual[b, -1.9e-132], N[(c * N[(t$95$3 + N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-299], t$95$4, If[LessEqual[b, 6.4e-282], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-236], t$95$4, If[LessEqual[b, 4e+105], N[(c * N[(t$95$3 + N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.0000000000000004e44 or 2.2e237 < b

   1. Initial program 21.8%

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

      1. +-commutative 21.8%

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

      2. fma-def 24.4%

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

      3. *-commutative 24.4%

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

      4. *-commutative 24.4%

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

   3. Simplified 28.3%

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

   4. Taylor expanded in y0 around inf 40.3%

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

      1. mul-1-neg 40.3%

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

   6. Simplified 40.3%

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

   7. Taylor expanded in b around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   9. Simplified 50.9%

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

   if -4.0000000000000004e44 < b < -1.8999999999999998e-132

   1. Initial program 42.4%

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

      1. associate-+l- 42.4%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in c around inf 43.0%

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

      1. associate--l+ 43.0%

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

      2. mul-1-neg 43.0%

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

   6. Simplified 43.0%

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

   7. Taylor expanded in y2 around inf 40.1%

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

   8. Taylor expanded in y3 around 0 43.4%

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

      1. +-commutative 43.4%

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

      2. associate--r+ 43.4%

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

      3. associate-*r* 46.4%

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

      4. *-commutative 46.4%

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

      5. cancel-sign-sub-inv 46.4%

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

      6. associate-*r* 46.4%

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

      7. neg-mul-1 46.4%

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

      8. *-commutative 46.4%

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

      9. distribute-rgt-in 46.4%

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

      10. mul-1-neg 46.4%

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

      11. sub-neg 46.4%

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

      12. *-commutative 46.4%

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

      13. *-commutative 46.4%

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

   10. Simplified 46.4%

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

   if -1.8999999999999998e-132 < b < 2.1000000000000001e-299 or 6.39999999999999966e-282 < b < 1e-236

   1. Initial program 33.6%

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

      1. associate-+l- 33.6%

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

   3. Simplified 33.6%

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

   4. Taylor expanded in y4 around inf 50.9%

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

   if 2.1000000000000001e-299 < b < 6.39999999999999966e-282

   1. Initial program 33.3%

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

      1. associate-+l- 33.3%

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

   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 a around inf 83.3%

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

      1. associate--l+ 83.3%

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

      2. mul-1-neg 83.3%

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

      3. mul-1-neg 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around inf 67.5%

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

      1. associate-*r* 67.5%

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

      2. +-commutative 67.5%

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

      3. mul-1-neg 67.5%

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

      4. unsub-neg 67.5%

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

      5. *-commutative 67.5%

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

   9. Simplified 67.5%

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

   10. Taylor expanded in x around 0 67.5%

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

       1. mul-1-neg 67.5%

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

       2. *-commutative 67.5%

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

   12. Simplified 67.5%

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

   13. Taylor expanded in a around 0 83.3%

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

       1. *-commutative 83.3%

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

       2. associate-*l* 83.5%

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

   15. Simplified 83.5%

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

   if 1e-236 < b < 3.9999999999999998e105

   1. Initial program 29.4%

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

      1. associate-+l- 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. associate--l+ 60.3%

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

      2. mul-1-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y2 around inf 55.7%

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

   if 3.9999999999999998e105 < b < 2.2e237

   1. Initial program 28.1%

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

      1. associate-+l- 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in y4 around inf 35.1%

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

   5. Taylor expanded in t around inf 59.9%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 10^{-236}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 12: 39.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := x \cdot y - z \cdot t\\ t_3 := z \cdot k - x \cdot j\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_5 := y \cdot y3 - t \cdot y2\\ \mathbf{if}\;b \leq -2 \cdot 10^{+198}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_2 + y4 \cdot t_1\right) + y0 \cdot t_3\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -6.7 \cdot 10^{+97}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t_5\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+53}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot t_2\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot t_5\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+239}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot t_3\right)\\ \end{array} \end{array} \]

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 (- (* x y) (* z t)))
        (t_3 (- (* z k) (* x j)))
        (t_4
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_5 (- (* y y3) (* t y2))))
   (if (<= b -2e+198)
     (* b (+ (+ (* a t_2) (* y4 t_1)) (* y0 t_3)))
     (if (<= b -1.25e+148)
       t_4
       (if (<= b -6.7e+97)
         (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) (* c t_5)))
         (if (<= b -2e+53)
           t_4
           (if (<= b 1.2e-231)
             (*
              i
              (-
               (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))
               (* c t_2)))
             (if (<= b 6e+104)
               (*
                c
                (+ (* i (- (* z t) (* x y))) (+ (* y0 (* x y2)) (* y4 t_5))))
               (if (<= b 2.55e+239)
                 (* y4 (* t (- (* b j) (* c y2))))
                 (* y0 (* b t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (x * y) - (z * t);
	double t_3 = (z * k) - (x * j);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = (y * y3) - (t * y2);
	double tmp;
	if (b <= -2e+198) {
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3));
	} else if (b <= -1.25e+148) {
		tmp = t_4;
	} else if (b <= -6.7e+97) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	} else if (b <= -2e+53) {
		tmp = t_4;
	} else if (b <= 1.2e-231) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2));
	} else if (b <= 6e+104) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_5)));
	} else if (b <= 2.55e+239) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y0 * (b * t_3);
	}
	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) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (x * y) - (z * t)
    t_3 = (z * k) - (x * j)
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_5 = (y * y3) - (t * y2)
    if (b <= (-2d+198)) then
        tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3))
    else if (b <= (-1.25d+148)) then
        tmp = t_4
    else if (b <= (-6.7d+97)) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5))
    else if (b <= (-2d+53)) then
        tmp = t_4
    else if (b <= 1.2d-231) then
        tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2))
    else if (b <= 6d+104) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_5)))
    else if (b <= 2.55d+239) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else
        tmp = y0 * (b * t_3)
    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 = (t * j) - (y * k);
	double t_2 = (x * y) - (z * t);
	double t_3 = (z * k) - (x * j);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_5 = (y * y3) - (t * y2);
	double tmp;
	if (b <= -2e+198) {
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3));
	} else if (b <= -1.25e+148) {
		tmp = t_4;
	} else if (b <= -6.7e+97) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	} else if (b <= -2e+53) {
		tmp = t_4;
	} else if (b <= 1.2e-231) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2));
	} else if (b <= 6e+104) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_5)));
	} else if (b <= 2.55e+239) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else {
		tmp = y0 * (b * t_3);
	}
	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 = (x * y) - (z * t)
	t_3 = (z * k) - (x * j)
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_5 = (y * y3) - (t * y2)
	tmp = 0
	if b <= -2e+198:
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3))
	elif b <= -1.25e+148:
		tmp = t_4
	elif b <= -6.7e+97:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5))
	elif b <= -2e+53:
		tmp = t_4
	elif b <= 1.2e-231:
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2))
	elif b <= 6e+104:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_5)))
	elif b <= 2.55e+239:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = y0 * (b * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(z * k) - Float64(x * j))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_5 = Float64(Float64(y * y3) - Float64(t * y2))
	tmp = 0.0
	if (b <= -2e+198)
		tmp = Float64(b * Float64(Float64(Float64(a * t_2) + Float64(y4 * t_1)) + Float64(y0 * t_3)));
	elseif (b <= -1.25e+148)
		tmp = t_4;
	elseif (b <= -6.7e+97)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_5)));
	elseif (b <= -2e+53)
		tmp = t_4;
	elseif (b <= 1.2e-231)
		tmp = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))) - Float64(c * t_2)));
	elseif (b <= 6e+104)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(x * y2)) + Float64(y4 * t_5))));
	elseif (b <= 2.55e+239)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	else
		tmp = Float64(y0 * Float64(b * t_3));
	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 = (x * y) - (z * t);
	t_3 = (z * k) - (x * j);
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_5 = (y * y3) - (t * y2);
	tmp = 0.0;
	if (b <= -2e+198)
		tmp = b * (((a * t_2) + (y4 * t_1)) + (y0 * t_3));
	elseif (b <= -1.25e+148)
		tmp = t_4;
	elseif (b <= -6.7e+97)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + (c * t_5));
	elseif (b <= -2e+53)
		tmp = t_4;
	elseif (b <= 1.2e-231)
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_2));
	elseif (b <= 6e+104)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * (x * y2)) + (y4 * t_5)));
	elseif (b <= 2.55e+239)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	else
		tmp = y0 * (b * t_3);
	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[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+198], N[(b * N[(N[(N[(a * t$95$2), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e+148], t$95$4, If[LessEqual[b, -6.7e+97], N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e+53], t$95$4, If[LessEqual[b, 1.2e-231], N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+104], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e+239], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(b * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.00000000000000004e198

   1. Initial program 13.5%

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

      1. associate-+l- 13.5%

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

   3. Simplified 13.5%

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

   4. Taylor expanded in b around inf 59.9%

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

   if -2.00000000000000004e198 < b < -1.25000000000000006e148 or -6.69999999999999985e97 < b < -2e53

   1. Initial program 40.0%

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

      1. associate-+l- 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in x around inf 75.1%

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

   if -1.25000000000000006e148 < b < -6.69999999999999985e97

   1. Initial program 15.4%

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

      1. associate-+l- 15.4%

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

   3. Simplified 15.4%

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

   4. Taylor expanded in y4 around inf 61.7%

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

   if -2e53 < b < 1.19999999999999996e-231

   1. Initial program 37.0%

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

      1. associate-+l- 37.0%

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

   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 i around -inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. associate--l+ 44.9%

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

   6. Simplified 44.9%

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

   if 1.19999999999999996e-231 < b < 5.99999999999999937e104

   1. Initial program 29.4%

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

      1. associate-+l- 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in c around inf 60.3%

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

      1. associate--l+ 60.3%

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

      2. mul-1-neg 60.3%

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

   6. Simplified 60.3%

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

   7. Taylor expanded in y2 around inf 55.7%

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

   if 5.99999999999999937e104 < b < 2.5499999999999999e239

   1. Initial program 28.1%

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

      1. associate-+l- 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in y4 around inf 35.1%

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

   5. Taylor expanded in t around inf 59.9%

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

   if 2.5499999999999999e239 < b

   1. Initial program 16.5%

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

      1. +-commutative 16.5%

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

      2. fma-def 25.0%

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

      3. *-commutative 25.0%

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

      4. *-commutative 25.0%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y0 around inf 42.3%

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

      1. mul-1-neg 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   9. Simplified 67.7%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+198}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -6.7 \cdot 10^{+97}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+239}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 13: 35.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := i \cdot \left(z \cdot t - x \cdot y\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(t_2 + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-272}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(t_2 + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j))))) (t_2 (* i (- (* z t) (* x y)))))
   (if (<= b -4e+44)
     t_1
     (if (<= b -1.15e-132)
       (* c (+ t_2 (* y2 (- (* x y0) (* t y4)))))
       (if (<= b 1.65e-272)
         (* y4 (* y3 (- (* y c) (* j y1))))
         (if (<= b 8.2e+105)
           (* c (+ t_2 (+ (* y0 (* x y2)) (* y4 (- (* y y3) (* t y2))))))
           (if (<= b 1.1e+237) (* y4 (* t (- (* b j) (* c 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = i * ((z * t) - (x * y));
	double tmp;
	if (b <= -4e+44) {
		tmp = t_1;
	} else if (b <= -1.15e-132) {
		tmp = c * (t_2 + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 1.65e-272) {
		tmp = y4 * (y3 * ((y * c) - (j * y1)));
	} else if (b <= 8.2e+105) {
		tmp = c * (t_2 + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	} else if (b <= 1.1e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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) :: t_2
    real(8) :: tmp
    t_1 = y0 * (b * ((z * k) - (x * j)))
    t_2 = i * ((z * t) - (x * y))
    if (b <= (-4d+44)) then
        tmp = t_1
    else if (b <= (-1.15d-132)) then
        tmp = c * (t_2 + (y2 * ((x * y0) - (t * y4))))
    else if (b <= 1.65d-272) then
        tmp = y4 * (y3 * ((y * c) - (j * y1)))
    else if (b <= 8.2d+105) then
        tmp = c * (t_2 + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))))
    else if (b <= 1.1d+237) then
        tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = i * ((z * t) - (x * y));
	double tmp;
	if (b <= -4e+44) {
		tmp = t_1;
	} else if (b <= -1.15e-132) {
		tmp = c * (t_2 + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 1.65e-272) {
		tmp = y4 * (y3 * ((y * c) - (j * y1)));
	} else if (b <= 8.2e+105) {
		tmp = c * (t_2 + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	} else if (b <= 1.1e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
	t_2 = i * ((z * t) - (x * y))
	tmp = 0
	if b <= -4e+44:
		tmp = t_1
	elif b <= -1.15e-132:
		tmp = c * (t_2 + (y2 * ((x * y0) - (t * y4))))
	elif b <= 1.65e-272:
		tmp = y4 * (y3 * ((y * c) - (j * y1)))
	elif b <= 8.2e+105:
		tmp = c * (t_2 + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))))
	elif b <= 1.1e+237:
		tmp = y4 * (t * ((b * j) - (c * 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(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_2 = Float64(i * Float64(Float64(z * t) - Float64(x * y)))
	tmp = 0.0
	if (b <= -4e+44)
		tmp = t_1;
	elseif (b <= -1.15e-132)
		tmp = Float64(c * Float64(t_2 + Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4)))));
	elseif (b <= 1.65e-272)
		tmp = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))));
	elseif (b <= 8.2e+105)
		tmp = Float64(c * Float64(t_2 + Float64(Float64(y0 * Float64(x * y2)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))));
	elseif (b <= 1.1e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 = y0 * (b * ((z * k) - (x * j)));
	t_2 = i * ((z * t) - (x * y));
	tmp = 0.0;
	if (b <= -4e+44)
		tmp = t_1;
	elseif (b <= -1.15e-132)
		tmp = c * (t_2 + (y2 * ((x * y0) - (t * y4))));
	elseif (b <= 1.65e-272)
		tmp = y4 * (y3 * ((y * c) - (j * y1)));
	elseif (b <= 8.2e+105)
		tmp = c * (t_2 + ((y0 * (x * y2)) + (y4 * ((y * y3) - (t * y2)))));
	elseif (b <= 1.1e+237)
		tmp = y4 * (t * ((b * j) - (c * 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[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+44], t$95$1, If[LessEqual[b, -1.15e-132], N[(c * N[(t$95$2 + N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-272], N[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+105], N[(c * N[(t$95$2 + N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.0000000000000004e44 or 1.1e237 < b

   1. Initial program 21.8%

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

      1. +-commutative 21.8%

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

      2. fma-def 24.4%

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

      3. *-commutative 24.4%

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

      4. *-commutative 24.4%

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

   3. Simplified 28.3%

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

   4. Taylor expanded in y0 around inf 40.3%

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

      1. mul-1-neg 40.3%

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

   6. Simplified 40.3%

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

   7. Taylor expanded in b around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   9. Simplified 50.9%

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

   if -4.0000000000000004e44 < b < -1.15000000000000002e-132

   1. Initial program 42.4%

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

      1. associate-+l- 42.4%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in c around inf 43.0%

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

      1. associate--l+ 43.0%

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

      2. mul-1-neg 43.0%

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

   6. Simplified 43.0%

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

   7. Taylor expanded in y2 around inf 40.1%

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

   8. Taylor expanded in y3 around 0 43.4%

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

      1. +-commutative 43.4%

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

      2. associate--r+ 43.4%

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

      3. associate-*r* 46.4%

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

      4. *-commutative 46.4%

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

      5. cancel-sign-sub-inv 46.4%

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

      6. associate-*r* 46.4%

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

      7. neg-mul-1 46.4%

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

      8. *-commutative 46.4%

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

      9. distribute-rgt-in 46.4%

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

      10. mul-1-neg 46.4%

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

      11. sub-neg 46.4%

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

      12. *-commutative 46.4%

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

      13. *-commutative 46.4%

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

   10. Simplified 46.4%

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

   if -1.15000000000000002e-132 < b < 1.65000000000000016e-272

   1. Initial program 35.8%

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

      1. associate-+l- 35.8%

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

   3. Simplified 35.8%

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

   4. Taylor expanded in y4 around inf 45.9%

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

   5. Taylor expanded in y3 around -inf 43.9%

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

   if 1.65000000000000016e-272 < b < 8.2000000000000005e105

   1. Initial program 28.4%

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

      1. associate-+l- 28.4%

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

   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 c around inf 58.0%

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

      1. associate--l+ 58.0%

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

      2. mul-1-neg 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in y2 around inf 53.9%

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

   if 8.2000000000000005e105 < b < 1.1e237

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 35.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 59.9%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-272}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 14: 34.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(y4 \cdot \left(t \cdot y2\right) - \left(z \cdot t\right) \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j)))))
        (t_2 (* y4 (* y3 (- (* y c) (* j y1))))))
   (if (<= b -9.8e+43)
     t_1
     (if (<= b -7e-134)
       (* c (+ (* i (- (* z t) (* x y))) (* y2 (- (* x y0) (* t y4)))))
       (if (<= b 1.02e-269)
         t_2
         (if (<= b 9e+40)
           (*
            c
            (- (* y0 (- (* x y2) (* z y3))) (- (* y4 (* t y2)) (* (* z t) i))))
           (if (<= b 3.2e+118)
             t_2
             (if (<= b 9.2e+237) (* y4 (* t (- (* b j) (* c 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -9.8e+43) {
		tmp = t_1;
	} else if (b <= -7e-134) {
		tmp = c * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 1.02e-269) {
		tmp = t_2;
	} else if (b <= 9e+40) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - ((y4 * (t * y2)) - ((z * t) * i)));
	} else if (b <= 3.2e+118) {
		tmp = t_2;
	} else if (b <= 9.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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) :: t_2
    real(8) :: tmp
    t_1 = y0 * (b * ((z * k) - (x * j)))
    t_2 = y4 * (y3 * ((y * c) - (j * y1)))
    if (b <= (-9.8d+43)) then
        tmp = t_1
    else if (b <= (-7d-134)) then
        tmp = c * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))))
    else if (b <= 1.02d-269) then
        tmp = t_2
    else if (b <= 9d+40) then
        tmp = c * ((y0 * ((x * y2) - (z * y3))) - ((y4 * (t * y2)) - ((z * t) * i)))
    else if (b <= 3.2d+118) then
        tmp = t_2
    else if (b <= 9.2d+237) then
        tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -9.8e+43) {
		tmp = t_1;
	} else if (b <= -7e-134) {
		tmp = c * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))));
	} else if (b <= 1.02e-269) {
		tmp = t_2;
	} else if (b <= 9e+40) {
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - ((y4 * (t * y2)) - ((z * t) * i)));
	} else if (b <= 3.2e+118) {
		tmp = t_2;
	} else if (b <= 9.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
	t_2 = y4 * (y3 * ((y * c) - (j * y1)))
	tmp = 0
	if b <= -9.8e+43:
		tmp = t_1
	elif b <= -7e-134:
		tmp = c * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))))
	elif b <= 1.02e-269:
		tmp = t_2
	elif b <= 9e+40:
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - ((y4 * (t * y2)) - ((z * t) * i)))
	elif b <= 3.2e+118:
		tmp = t_2
	elif b <= 9.2e+237:
		tmp = y4 * (t * ((b * j) - (c * 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(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_2 = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))))
	tmp = 0.0
	if (b <= -9.8e+43)
		tmp = t_1;
	elseif (b <= -7e-134)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4)))));
	elseif (b <= 1.02e-269)
		tmp = t_2;
	elseif (b <= 9e+40)
		tmp = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(Float64(y4 * Float64(t * y2)) - Float64(Float64(z * t) * i))));
	elseif (b <= 3.2e+118)
		tmp = t_2;
	elseif (b <= 9.2e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 = y0 * (b * ((z * k) - (x * j)));
	t_2 = y4 * (y3 * ((y * c) - (j * y1)));
	tmp = 0.0;
	if (b <= -9.8e+43)
		tmp = t_1;
	elseif (b <= -7e-134)
		tmp = c * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))));
	elseif (b <= 1.02e-269)
		tmp = t_2;
	elseif (b <= 9e+40)
		tmp = c * ((y0 * ((x * y2) - (z * y3))) - ((y4 * (t * y2)) - ((z * t) * i)));
	elseif (b <= 3.2e+118)
		tmp = t_2;
	elseif (b <= 9.2e+237)
		tmp = y4 * (t * ((b * j) - (c * 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[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+43], t$95$1, If[LessEqual[b, -7e-134], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-269], t$95$2, If[LessEqual[b, 9e+40], N[(c * N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y4 * N[(t * y2), $MachinePrecision]), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+118], t$95$2, If[LessEqual[b, 9.2e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -9.7999999999999999e43 or 9.19999999999999981e237 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -9.7999999999999999e43 < b < -6.9999999999999997e-134

   1. Initial program 42.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 40.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around 0 43.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(i \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{\left(y4 \cdot \left(t \cdot y2\right) + i \cdot \left(y \cdot x - t \cdot z\right)\right)}\right) \]

      2. associate--r+ 43.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot \left(x \cdot y2\right) - y4 \cdot \left(t \cdot y2\right)\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

      3. associate-*r* 46.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{\left(y4 \cdot t\right) \cdot y2}\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      4. *-commutative 46.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{\left(t \cdot y4\right)} \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 46.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2\right) + \left(-t \cdot y4\right) \cdot y2\right)} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      6. associate-*r* 46.4%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(y0 \cdot x\right) \cdot y2} + \left(-t \cdot y4\right) \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      7. neg-mul-1 46.4%

         \[\leadsto c \cdot \left(\left(\left(y0 \cdot x\right) \cdot y2 + \color{blue}{\left(-1 \cdot \left(t \cdot y4\right)\right)} \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      8. *-commutative 46.4%

         \[\leadsto c \cdot \left(\left(\left(y0 \cdot x\right) \cdot y2 + \left(-1 \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      9. distribute-rgt-in 46.4%

         \[\leadsto c \cdot \left(\color{blue}{y2 \cdot \left(y0 \cdot x + -1 \cdot \left(y4 \cdot t\right)\right)} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      10. mul-1-neg 46.4%

          \[\leadsto c \cdot \left(y2 \cdot \left(y0 \cdot x + \color{blue}{\left(-y4 \cdot t\right)}\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      11. sub-neg 46.4%

          \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\left(y0 \cdot x - y4 \cdot t\right)} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      12. *-commutative 46.4%

          \[\leadsto c \cdot \left(y2 \cdot \left(y0 \cdot x - \color{blue}{t \cdot y4}\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      13. *-commutative 46.4%

          \[\leadsto c \cdot \left(y2 \cdot \left(y0 \cdot x - t \cdot y4\right) - i \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

   10. Simplified 46.4%

       \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(y0 \cdot x - t \cdot y4\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -6.9999999999999997e-134 < b < 1.02000000000000002e-269 or 9.00000000000000064e40 < b < 3.20000000000000016e118

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 45.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf 49.3%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(\left(y1 \cdot j - c \cdot y\right) \cdot y3\right)\right)} \]

   if 1.02000000000000002e-269 < b < 9.00000000000000064e40

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 58.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 58.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 58.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 58.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around 0 51.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(-1 \cdot \left(i \cdot \left(t \cdot z\right)\right) + y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{\left(y4 \cdot \left(t \cdot y2\right) + -1 \cdot \left(i \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      2. mul-1-neg 51.4%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y4 \cdot \left(t \cdot y2\right) + \color{blue}{\left(-i \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      3. unsub-neg 51.4%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - \color{blue}{\left(y4 \cdot \left(t \cdot y2\right) - i \cdot \left(t \cdot z\right)\right)}\right) \]

      4. *-commutative 51.4%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y4 \cdot \color{blue}{\left(y2 \cdot t\right)} - i \cdot \left(t \cdot z\right)\right)\right) \]

      5. *-commutative 51.4%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y4 \cdot \left(y2 \cdot t\right) - i \cdot \color{blue}{\left(z \cdot t\right)}\right)\right) \]

   9. Simplified 51.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right) - \left(y4 \cdot \left(y2 \cdot t\right) - i \cdot \left(z \cdot t\right)\right)\right)} \]

   if 3.20000000000000016e118 < b < 9.19999999999999981e237

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 40.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-269}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(y4 \cdot \left(t \cdot y2\right) - \left(z \cdot t\right) \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 15: 31.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\\ t_2 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq -8.2 \cdot 10^{-125}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq -2.6 \cdot 10^{-295}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y1 \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 6.8 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{+121}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* i y1) (- (* x j) (* z k))))
        (t_2 (* y4 (* c (- (* y y3) (* t y2))))))
   (if (<= y1 -6.8e+74)
     t_1
     (if (<= y1 -8.2e-125)
       (* y4 (* t (- (* b j) (* c y2))))
       (if (<= y1 -3.5e-238)
         t_2
         (if (<= y1 -2.6e-295)
           (* y4 (* b (- (* t j) (* y k))))
           (if (<= y1 1.8e-260)
             t_2
             (if (<= y1 2.6e-219)
               (* c (* i (- (* z t) (* x y))))
               (if (<= y1 1.3e-57)
                 t_2
                 (if (<= y1 6.8e+93)
                   (* y4 (* j (- (* t b) (* y1 y3))))
                   (if (<= y1 5.8e+121)
                     (* y2 (* a (- (* t y5) (* x y1))))
                     t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (i * y1) * ((x * j) - (z * k));
	double t_2 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (y1 <= -6.8e+74) {
		tmp = t_1;
	} else if (y1 <= -8.2e-125) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y1 <= -3.5e-238) {
		tmp = t_2;
	} else if (y1 <= -2.6e-295) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y1 <= 1.8e-260) {
		tmp = t_2;
	} else if (y1 <= 2.6e-219) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y1 <= 1.3e-57) {
		tmp = t_2;
	} else if (y1 <= 6.8e+93) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (y1 <= 5.8e+121) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} 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 = (i * y1) * ((x * j) - (z * k))
    t_2 = y4 * (c * ((y * y3) - (t * y2)))
    if (y1 <= (-6.8d+74)) then
        tmp = t_1
    else if (y1 <= (-8.2d-125)) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (y1 <= (-3.5d-238)) then
        tmp = t_2
    else if (y1 <= (-2.6d-295)) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (y1 <= 1.8d-260) then
        tmp = t_2
    else if (y1 <= 2.6d-219) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y1 <= 1.3d-57) then
        tmp = t_2
    else if (y1 <= 6.8d+93) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else if (y1 <= 5.8d+121) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    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 = (i * y1) * ((x * j) - (z * k));
	double t_2 = y4 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (y1 <= -6.8e+74) {
		tmp = t_1;
	} else if (y1 <= -8.2e-125) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (y1 <= -3.5e-238) {
		tmp = t_2;
	} else if (y1 <= -2.6e-295) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (y1 <= 1.8e-260) {
		tmp = t_2;
	} else if (y1 <= 2.6e-219) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y1 <= 1.3e-57) {
		tmp = t_2;
	} else if (y1 <= 6.8e+93) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (y1 <= 5.8e+121) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} 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 = (i * y1) * ((x * j) - (z * k))
	t_2 = y4 * (c * ((y * y3) - (t * y2)))
	tmp = 0
	if y1 <= -6.8e+74:
		tmp = t_1
	elif y1 <= -8.2e-125:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif y1 <= -3.5e-238:
		tmp = t_2
	elif y1 <= -2.6e-295:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif y1 <= 1.8e-260:
		tmp = t_2
	elif y1 <= 2.6e-219:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y1 <= 1.3e-57:
		tmp = t_2
	elif y1 <= 6.8e+93:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	elif y1 <= 5.8e+121:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(i * y1) * Float64(Float64(x * j) - Float64(z * k)))
	t_2 = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (y1 <= -6.8e+74)
		tmp = t_1;
	elseif (y1 <= -8.2e-125)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (y1 <= -3.5e-238)
		tmp = t_2;
	elseif (y1 <= -2.6e-295)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y1 <= 1.8e-260)
		tmp = t_2;
	elseif (y1 <= 2.6e-219)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y1 <= 1.3e-57)
		tmp = t_2;
	elseif (y1 <= 6.8e+93)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y1 <= 5.8e+121)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	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 = (i * y1) * ((x * j) - (z * k));
	t_2 = y4 * (c * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (y1 <= -6.8e+74)
		tmp = t_1;
	elseif (y1 <= -8.2e-125)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (y1 <= -3.5e-238)
		tmp = t_2;
	elseif (y1 <= -2.6e-295)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (y1 <= 1.8e-260)
		tmp = t_2;
	elseif (y1 <= 2.6e-219)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y1 <= 1.3e-57)
		tmp = t_2;
	elseif (y1 <= 6.8e+93)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	elseif (y1 <= 5.8e+121)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	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[(N[(i * y1), $MachinePrecision] * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -6.8e+74], t$95$1, If[LessEqual[y1, -8.2e-125], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.5e-238], t$95$2, If[LessEqual[y1, -2.6e-295], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.8e-260], t$95$2, If[LessEqual[y1, 2.6e-219], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.3e-57], t$95$2, If[LessEqual[y1, 6.8e+93], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.8e+121], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -6.7999999999999998e74 or 5.7999999999999998e121 < y1

   1. Initial program 21.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 21.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 50.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 50.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 50.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around inf 42.1%

      \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto \color{blue}{\left(y1 \cdot i\right) \cdot \left(j \cdot x - k \cdot z\right)} \]

      2. *-commutative 44.4%

         \[\leadsto \color{blue}{\left(i \cdot y1\right)} \cdot \left(j \cdot x - k \cdot z\right) \]

      3. *-commutative 44.4%

         \[\leadsto \left(i \cdot y1\right) \cdot \left(\color{blue}{x \cdot j} - k \cdot z\right) \]

      4. *-commutative 44.4%

         \[\leadsto \left(i \cdot y1\right) \cdot \left(x \cdot j - \color{blue}{z \cdot k}\right) \]

   9. Simplified 44.4%

      \[\leadsto \color{blue}{\left(i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)} \]

   if -6.7999999999999998e74 < y1 < -8.1999999999999995e-125

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 43.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 46.3%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]

   if -8.1999999999999995e-125 < y1 < -3.49999999999999997e-238 or -2.59999999999999985e-295 < y1 < 1.8e-260 or 2.60000000000000002e-219 < y1 < 1.29999999999999993e-57

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 49.5%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.5%

         \[\leadsto y4 \cdot \left(c \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 49.5%

         \[\leadsto y4 \cdot \left(c \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 49.5%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if -3.49999999999999997e-238 < y1 < -2.59999999999999985e-295

   1. Initial program 14.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 28.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around inf 72.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(t \cdot j - k \cdot y\right) \cdot b\right)} \]

   if 1.8e-260 < y1 < 2.60000000000000002e-219

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 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. Step-by-step derivation

      1. associate--l+ 45.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 56.0%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 56.0%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 56.0%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 56.0%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if 1.29999999999999993e-57 < y1 < 6.8000000000000001e93

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 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 inf 46.1%

      \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.1%

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.1%

         \[\leadsto y4 \cdot \left(j \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \]

      3. sub-neg 46.1%

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)}\right) \]

      4. *-commutative 46.1%

         \[\leadsto y4 \cdot \left(j \cdot \left(t \cdot b - \color{blue}{y3 \cdot y1}\right)\right) \]

   7. Simplified 46.1%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(t \cdot b - y3 \cdot y1\right)\right)} \]

   if 6.8000000000000001e93 < y1 < 5.7999999999999998e121

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 55.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 55.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 55.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 55.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 55.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 89.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 89.0%

         \[\leadsto \color{blue}{\left(a \cdot \left(t \cdot y5 - y1 \cdot x\right)\right) \cdot y2} \]

      2. *-commutative 89.0%

         \[\leadsto \left(a \cdot \left(t \cdot y5 - \color{blue}{x \cdot y1}\right)\right) \cdot y2 \]

   9. Simplified 89.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right) \cdot y2} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6.8 \cdot 10^{+74}:\\ \;\;\;\;\left(i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\\ \mathbf{elif}\;y1 \leq -8.2 \cdot 10^{-125}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-238}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.6 \cdot 10^{-295}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq 1.8 \cdot 10^{-260}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-219}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y1 \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 6.8 \cdot 10^{+93}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 5.8 \cdot 10^{+121}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot y1\right) \cdot \left(x \cdot j - z \cdot k\right)\\ \end{array} \]

Alternative 16: 32.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ t_3 := y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+116}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j)))))
        (t_2 (* c (- (* y0 (* x y2)) (* t (- (* y2 y4) (* z i))))))
        (t_3 (* y4 (* y3 (- (* y c) (* j y1))))))
   (if (<= b -6.8e+43)
     t_1
     (if (<= b -3.1e-97)
       t_2
       (if (<= b 2.6e-272)
         t_3
         (if (<= b 1.9e-177)
           t_2
           (if (<= b 1.55e-116)
             (* a (* z (- (* y1 y3) (* t b))))
             (if (<= b 6.4e+32)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= b 1.55e+98)
                 t_3
                 (if (<= b 3e+116)
                   (* (* j y1) (- (* x i) (* y3 y4)))
                   (if (<= b 4.6e+237)
                     (* y4 (* t (- (* b j) (* c 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	double t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -6.8e+43) {
		tmp = t_1;
	} else if (b <= -3.1e-97) {
		tmp = t_2;
	} else if (b <= 2.6e-272) {
		tmp = t_3;
	} else if (b <= 1.9e-177) {
		tmp = t_2;
	} else if (b <= 1.55e-116) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= 6.4e+32) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.55e+98) {
		tmp = t_3;
	} else if (b <= 3e+116) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= 4.6e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y0 * (b * ((z * k) - (x * j)))
    t_2 = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))))
    t_3 = y4 * (y3 * ((y * c) - (j * y1)))
    if (b <= (-6.8d+43)) then
        tmp = t_1
    else if (b <= (-3.1d-97)) then
        tmp = t_2
    else if (b <= 2.6d-272) then
        tmp = t_3
    else if (b <= 1.9d-177) then
        tmp = t_2
    else if (b <= 1.55d-116) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (b <= 6.4d+32) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 1.55d+98) then
        tmp = t_3
    else if (b <= 3d+116) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (b <= 4.6d+237) then
        tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	double t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -6.8e+43) {
		tmp = t_1;
	} else if (b <= -3.1e-97) {
		tmp = t_2;
	} else if (b <= 2.6e-272) {
		tmp = t_3;
	} else if (b <= 1.9e-177) {
		tmp = t_2;
	} else if (b <= 1.55e-116) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= 6.4e+32) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.55e+98) {
		tmp = t_3;
	} else if (b <= 3e+116) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= 4.6e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
	t_2 = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))))
	t_3 = y4 * (y3 * ((y * c) - (j * y1)))
	tmp = 0
	if b <= -6.8e+43:
		tmp = t_1
	elif b <= -3.1e-97:
		tmp = t_2
	elif b <= 2.6e-272:
		tmp = t_3
	elif b <= 1.9e-177:
		tmp = t_2
	elif b <= 1.55e-116:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif b <= 6.4e+32:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 1.55e+98:
		tmp = t_3
	elif b <= 3e+116:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif b <= 4.6e+237:
		tmp = y4 * (t * ((b * j) - (c * 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(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_2 = Float64(c * Float64(Float64(y0 * Float64(x * y2)) - Float64(t * Float64(Float64(y2 * y4) - Float64(z * i)))))
	t_3 = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))))
	tmp = 0.0
	if (b <= -6.8e+43)
		tmp = t_1;
	elseif (b <= -3.1e-97)
		tmp = t_2;
	elseif (b <= 2.6e-272)
		tmp = t_3;
	elseif (b <= 1.9e-177)
		tmp = t_2;
	elseif (b <= 1.55e-116)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (b <= 6.4e+32)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 1.55e+98)
		tmp = t_3;
	elseif (b <= 3e+116)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (b <= 4.6e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 = y0 * (b * ((z * k) - (x * j)));
	t_2 = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	tmp = 0.0;
	if (b <= -6.8e+43)
		tmp = t_1;
	elseif (b <= -3.1e-97)
		tmp = t_2;
	elseif (b <= 2.6e-272)
		tmp = t_3;
	elseif (b <= 1.9e-177)
		tmp = t_2;
	elseif (b <= 1.55e-116)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (b <= 6.4e+32)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 1.55e+98)
		tmp = t_3;
	elseif (b <= 3e+116)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (b <= 4.6e+237)
		tmp = y4 * (t * ((b * j) - (c * 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[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+43], t$95$1, If[LessEqual[b, -3.1e-97], t$95$2, If[LessEqual[b, 2.6e-272], t$95$3, If[LessEqual[b, 1.9e-177], t$95$2, If[LessEqual[b, 1.55e-116], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+32], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+98], t$95$3, If[LessEqual[b, 3e+116], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -6.80000000000000024e43 or 4.59999999999999991e237 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -6.80000000000000024e43 < b < -3.10000000000000002e-97 or 2.59999999999999992e-272 < b < 1.90000000000000002e-177

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 47.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 47.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 47.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 48.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y around 0 43.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(-1 \cdot \left(i \cdot \left(t \cdot z\right)\right) + y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot z\right)} + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      2. *-commutative 43.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\left(-1 \cdot i\right) \cdot \color{blue}{\left(z \cdot t\right)} + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      3. associate-*r* 43.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\color{blue}{\left(\left(-1 \cdot i\right) \cdot z\right) \cdot t} + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      4. associate-*r* 43.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\color{blue}{\left(-1 \cdot \left(i \cdot z\right)\right)} \cdot t + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      5. *-commutative 43.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\left(-1 \cdot \left(i \cdot z\right)\right) \cdot t + y4 \cdot \color{blue}{\left(y2 \cdot t\right)}\right)\right) \]

      6. associate-*r* 46.1%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\left(-1 \cdot \left(i \cdot z\right)\right) \cdot t + \color{blue}{\left(y4 \cdot y2\right) \cdot t}\right)\right) \]

      7. distribute-rgt-in 48.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{t \cdot \left(-1 \cdot \left(i \cdot z\right) + y4 \cdot y2\right)}\right) \]

      8. +-commutative 48.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \color{blue}{\left(y4 \cdot y2 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      9. mul-1-neg 48.6%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y4 \cdot y2 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      10. unsub-neg 48.6%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \color{blue}{\left(y4 \cdot y2 - i \cdot z\right)}\right) \]

      11. *-commutative 48.6%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(\color{blue}{y2 \cdot y4} - i \cdot z\right)\right) \]

   10. Simplified 48.6%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if -3.10000000000000002e-97 < b < 2.59999999999999992e-272 or 6.3999999999999998e32 < b < 1.5500000000000001e98

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 46.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf 48.5%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(\left(y1 \cdot j - c \cdot y\right) \cdot y3\right)\right)} \]

   if 1.90000000000000002e-177 < b < 1.55000000000000009e-116

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 38.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 38.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 38.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 38.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 38.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in z around inf 45.2%

      \[\leadsto \color{blue}{\left(z \cdot \left(-1 \cdot \left(t \cdot b\right) - -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot a \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 45.2%

         \[\leadsto \left(z \cdot \color{blue}{\left(-1 \cdot \left(t \cdot b\right) + \left(--1\right) \cdot \left(y1 \cdot y3\right)\right)}\right) \cdot a \]

      2. metadata-eval 45.2%

         \[\leadsto \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{1} \cdot \left(y1 \cdot y3\right)\right)\right) \cdot a \]

      3. *-lft-identity 45.2%

         \[\leadsto \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{y1 \cdot y3}\right)\right) \cdot a \]

      4. +-commutative 45.2%

         \[\leadsto \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(t \cdot b\right)\right)}\right) \cdot a \]

      5. mul-1-neg 45.2%

         \[\leadsto \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-t \cdot b\right)}\right)\right) \cdot a \]

      6. unsub-neg 45.2%

         \[\leadsto \left(z \cdot \color{blue}{\left(y1 \cdot y3 - t \cdot b\right)}\right) \cdot a \]

      7. *-commutative 45.2%

         \[\leadsto \left(z \cdot \left(\color{blue}{y3 \cdot y1} - t \cdot b\right)\right) \cdot a \]

   9. Simplified 45.2%

      \[\leadsto \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \cdot a \]

   if 1.55000000000000009e-116 < b < 6.3999999999999998e32

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 62.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 62.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 62.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 62.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 54.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 1.5500000000000001e98 < b < 2.9999999999999999e116

   1. Initial program 39.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 39.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 39.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 44.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 44.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 44.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 62.4%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 80.3%

         \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)} \]

      2. mul-1-neg 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \]

      3. unsub-neg 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \]

      4. *-commutative 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(\color{blue}{x \cdot i} - y4 \cdot y3\right) \]

      5. *-commutative 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(x \cdot i - \color{blue}{y3 \cdot y4}\right) \]

   9. Simplified 80.3%

      \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(x \cdot i - y3 \cdot y4\right)} \]

   if 2.9999999999999999e116 < b < 4.59999999999999991e237

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 40.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-272}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-177}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+32}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+98}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+116}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 17: 32.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-178}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+117}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* y3 (- (* y c) (* j y1)))))
        (t_2 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -2e+44)
     t_2
     (if (<= b -2.8e-132)
       (* c (- (* x (* y0 y2)) (* i (- (* x y) (* z t)))))
       (if (<= b 1.7e-271)
         t_1
         (if (<= b 7e-178)
           (* c (- (* y0 (* x y2)) (* t (- (* y2 y4) (* z i)))))
           (if (<= b 2.3e-116)
             (* a (* z (- (* y1 y3) (* t b))))
             (if (<= b 1.1e+34)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= b 1.5e+100)
                 t_1
                 (if (<= b 6.5e+117)
                   (* (* j y1) (- (* x i) (* y3 y4)))
                   (if (<= b 2.4e+237)
                     (* y4 (* t (- (* b j) (* c y2))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (y3 * ((y * c) - (j * y1)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -2e+44) {
		tmp = t_2;
	} else if (b <= -2.8e-132) {
		tmp = c * ((x * (y0 * y2)) - (i * ((x * y) - (z * t))));
	} else if (b <= 1.7e-271) {
		tmp = t_1;
	} else if (b <= 7e-178) {
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	} else if (b <= 2.3e-116) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= 1.1e+34) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.5e+100) {
		tmp = t_1;
	} else if (b <= 6.5e+117) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= 2.4e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 = y4 * (y3 * ((y * c) - (j * y1)))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-2d+44)) then
        tmp = t_2
    else if (b <= (-2.8d-132)) then
        tmp = c * ((x * (y0 * y2)) - (i * ((x * y) - (z * t))))
    else if (b <= 1.7d-271) then
        tmp = t_1
    else if (b <= 7d-178) then
        tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))))
    else if (b <= 2.3d-116) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (b <= 1.1d+34) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 1.5d+100) then
        tmp = t_1
    else if (b <= 6.5d+117) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (b <= 2.4d+237) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    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 = y4 * (y3 * ((y * c) - (j * y1)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -2e+44) {
		tmp = t_2;
	} else if (b <= -2.8e-132) {
		tmp = c * ((x * (y0 * y2)) - (i * ((x * y) - (z * t))));
	} else if (b <= 1.7e-271) {
		tmp = t_1;
	} else if (b <= 7e-178) {
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	} else if (b <= 2.3e-116) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= 1.1e+34) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.5e+100) {
		tmp = t_1;
	} else if (b <= 6.5e+117) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= 2.4e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 = y4 * (y3 * ((y * c) - (j * y1)))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -2e+44:
		tmp = t_2
	elif b <= -2.8e-132:
		tmp = c * ((x * (y0 * y2)) - (i * ((x * y) - (z * t))))
	elif b <= 1.7e-271:
		tmp = t_1
	elif b <= 7e-178:
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))))
	elif b <= 2.3e-116:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif b <= 1.1e+34:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 1.5e+100:
		tmp = t_1
	elif b <= 6.5e+117:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif b <= 2.4e+237:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -2e+44)
		tmp = t_2;
	elseif (b <= -2.8e-132)
		tmp = Float64(c * Float64(Float64(x * Float64(y0 * y2)) - Float64(i * Float64(Float64(x * y) - Float64(z * t)))));
	elseif (b <= 1.7e-271)
		tmp = t_1;
	elseif (b <= 7e-178)
		tmp = Float64(c * Float64(Float64(y0 * Float64(x * y2)) - Float64(t * Float64(Float64(y2 * y4) - Float64(z * i)))));
	elseif (b <= 2.3e-116)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (b <= 1.1e+34)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 1.5e+100)
		tmp = t_1;
	elseif (b <= 6.5e+117)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (b <= 2.4e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	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 = y4 * (y3 * ((y * c) - (j * y1)));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -2e+44)
		tmp = t_2;
	elseif (b <= -2.8e-132)
		tmp = c * ((x * (y0 * y2)) - (i * ((x * y) - (z * t))));
	elseif (b <= 1.7e-271)
		tmp = t_1;
	elseif (b <= 7e-178)
		tmp = c * ((y0 * (x * y2)) - (t * ((y2 * y4) - (z * i))));
	elseif (b <= 2.3e-116)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (b <= 1.1e+34)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 1.5e+100)
		tmp = t_1;
	elseif (b <= 6.5e+117)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (b <= 2.4e+237)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	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[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+44], t$95$2, If[LessEqual[b, -2.8e-132], N[(c * N[(N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-271], t$95$1, If[LessEqual[b, 7e-178], N[(c * N[(N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-116], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+34], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+100], t$95$1, If[LessEqual[b, 6.5e+117], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -2.0000000000000002e44 or 2.3999999999999999e237 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -2.0000000000000002e44 < b < -2.80000000000000002e-132

   1. Initial program 42.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y4 around 0 46.0%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y3 around 0 43.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(y2 \cdot x\right)} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      2. associate-*r* 43.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot y2\right) \cdot x} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      3. *-commutative 43.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot y2\right) \cdot x - i \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

      4. *-commutative 43.5%

         \[\leadsto c \cdot \left(\left(y0 \cdot y2\right) \cdot x - i \cdot \left(x \cdot y - \color{blue}{z \cdot t}\right)\right) \]

   10. Simplified 43.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x - i \cdot \left(x \cdot y - z \cdot t\right)\right)} \]

   if -2.80000000000000002e-132 < b < 1.7e-271 or 1.1000000000000001e34 < b < 1.49999999999999993e100

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 38.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 38.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 48.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf 50.9%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(\left(y1 \cdot j - c \cdot y\right) \cdot y3\right)\right)} \]

   if 1.7e-271 < b < 6.99999999999999966e-178

   1. Initial program 14.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 14.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 14.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 50.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 50.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 57.5%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y around 0 58.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(-1 \cdot \left(i \cdot \left(t \cdot z\right)\right) + y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 58.0%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot z\right)} + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      2. *-commutative 58.0%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\left(-1 \cdot i\right) \cdot \color{blue}{\left(z \cdot t\right)} + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      3. associate-*r* 57.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\color{blue}{\left(\left(-1 \cdot i\right) \cdot z\right) \cdot t} + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      4. associate-*r* 57.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\color{blue}{\left(-1 \cdot \left(i \cdot z\right)\right)} \cdot t + y4 \cdot \left(t \cdot y2\right)\right)\right) \]

      5. *-commutative 57.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\left(-1 \cdot \left(i \cdot z\right)\right) \cdot t + y4 \cdot \color{blue}{\left(y2 \cdot t\right)}\right)\right) \]

      6. associate-*r* 57.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(\left(-1 \cdot \left(i \cdot z\right)\right) \cdot t + \color{blue}{\left(y4 \cdot y2\right) \cdot t}\right)\right) \]

      7. distribute-rgt-in 57.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{t \cdot \left(-1 \cdot \left(i \cdot z\right) + y4 \cdot y2\right)}\right) \]

      8. +-commutative 57.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \color{blue}{\left(y4 \cdot y2 + -1 \cdot \left(i \cdot z\right)\right)}\right) \]

      9. mul-1-neg 57.9%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y4 \cdot y2 + \color{blue}{\left(-i \cdot z\right)}\right)\right) \]

      10. unsub-neg 57.9%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \color{blue}{\left(y4 \cdot y2 - i \cdot z\right)}\right) \]

      11. *-commutative 57.9%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(\color{blue}{y2 \cdot y4} - i \cdot z\right)\right) \]

   10. Simplified 57.9%

       \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]

   if 6.99999999999999966e-178 < b < 2.30000000000000002e-116

   1. Initial program 18.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 38.2%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 38.2%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 38.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 38.2%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 38.2%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in z around inf 45.2%

      \[\leadsto \color{blue}{\left(z \cdot \left(-1 \cdot \left(t \cdot b\right) - -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot a \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 45.2%

         \[\leadsto \left(z \cdot \color{blue}{\left(-1 \cdot \left(t \cdot b\right) + \left(--1\right) \cdot \left(y1 \cdot y3\right)\right)}\right) \cdot a \]

      2. metadata-eval 45.2%

         \[\leadsto \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{1} \cdot \left(y1 \cdot y3\right)\right)\right) \cdot a \]

      3. *-lft-identity 45.2%

         \[\leadsto \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{y1 \cdot y3}\right)\right) \cdot a \]

      4. +-commutative 45.2%

         \[\leadsto \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(t \cdot b\right)\right)}\right) \cdot a \]

      5. mul-1-neg 45.2%

         \[\leadsto \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-t \cdot b\right)}\right)\right) \cdot a \]

      6. unsub-neg 45.2%

         \[\leadsto \left(z \cdot \color{blue}{\left(y1 \cdot y3 - t \cdot b\right)}\right) \cdot a \]

      7. *-commutative 45.2%

         \[\leadsto \left(z \cdot \left(\color{blue}{y3 \cdot y1} - t \cdot b\right)\right) \cdot a \]

   9. Simplified 45.2%

      \[\leadsto \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \cdot a \]

   if 2.30000000000000002e-116 < b < 1.1000000000000001e34

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 62.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 62.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 62.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 62.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 54.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 1.49999999999999993e100 < b < 6.5000000000000004e117

   1. Initial program 39.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 39.7%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 39.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 44.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 44.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 44.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 62.4%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 80.3%

         \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)} \]

      2. mul-1-neg 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \]

      3. unsub-neg 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \]

      4. *-commutative 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(\color{blue}{x \cdot i} - y4 \cdot y3\right) \]

      5. *-commutative 80.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(x \cdot i - \color{blue}{y3 \cdot y4}\right) \]

   9. Simplified 80.3%

      \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(x \cdot i - y3 \cdot y4\right)} \]

   if 6.5000000000000004e117 < b < 2.3999999999999999e237

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 40.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-271}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-178}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right) - t \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-116}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+100}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+117}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 18: 34.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -2.55 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (- (* y0 (- (* x y2) (* z y3))) (* i (- (* x y) (* z t))))))
        (t_2 (* y0 (* b (- (* z k) (* x j)))))
        (t_3 (* y4 (* y3 (- (* y c) (* j y1))))))
   (if (<= b -2.55e+44)
     t_2
     (if (<= b -1.15e-135)
       t_1
       (if (<= b 1.4e-269)
         t_3
         (if (<= b 1.05e-26)
           t_1
           (if (<= b 1.02e+50)
             (* c (* y3 (- (* y y4) (* z y0))))
             (if (<= b 6e+117)
               t_3
               (if (<= b 5.3e+237)
                 (* y4 (* t (- (* b j) (* c y2))))
                 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -2.55e+44) {
		tmp = t_2;
	} else if (b <= -1.15e-135) {
		tmp = t_1;
	} else if (b <= 1.4e-269) {
		tmp = t_3;
	} else if (b <= 1.05e-26) {
		tmp = t_1;
	} else if (b <= 1.02e+50) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (b <= 6e+117) {
		tmp = t_3;
	} else if (b <= 5.3e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    t_3 = y4 * (y3 * ((y * c) - (j * y1)))
    if (b <= (-2.55d+44)) then
        tmp = t_2
    else if (b <= (-1.15d-135)) then
        tmp = t_1
    else if (b <= 1.4d-269) then
        tmp = t_3
    else if (b <= 1.05d-26) then
        tmp = t_1
    else if (b <= 1.02d+50) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (b <= 6d+117) then
        tmp = t_3
    else if (b <= 5.3d+237) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    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 * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -2.55e+44) {
		tmp = t_2;
	} else if (b <= -1.15e-135) {
		tmp = t_1;
	} else if (b <= 1.4e-269) {
		tmp = t_3;
	} else if (b <= 1.05e-26) {
		tmp = t_1;
	} else if (b <= 1.02e+50) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (b <= 6e+117) {
		tmp = t_3;
	} else if (b <= 5.3e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	t_3 = y4 * (y3 * ((y * c) - (j * y1)))
	tmp = 0
	if b <= -2.55e+44:
		tmp = t_2
	elif b <= -1.15e-135:
		tmp = t_1
	elif b <= 1.4e-269:
		tmp = t_3
	elif b <= 1.05e-26:
		tmp = t_1
	elif b <= 1.02e+50:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif b <= 6e+117:
		tmp = t_3
	elif b <= 5.3e+237:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(i * Float64(Float64(x * y) - Float64(z * t)))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_3 = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))))
	tmp = 0.0
	if (b <= -2.55e+44)
		tmp = t_2;
	elseif (b <= -1.15e-135)
		tmp = t_1;
	elseif (b <= 1.4e-269)
		tmp = t_3;
	elseif (b <= 1.05e-26)
		tmp = t_1;
	elseif (b <= 1.02e+50)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (b <= 6e+117)
		tmp = t_3;
	elseif (b <= 5.3e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	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 * ((y0 * ((x * y2) - (z * y3))) - (i * ((x * y) - (z * t))));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	tmp = 0.0;
	if (b <= -2.55e+44)
		tmp = t_2;
	elseif (b <= -1.15e-135)
		tmp = t_1;
	elseif (b <= 1.4e-269)
		tmp = t_3;
	elseif (b <= 1.05e-26)
		tmp = t_1;
	elseif (b <= 1.02e+50)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (b <= 6e+117)
		tmp = t_3;
	elseif (b <= 5.3e+237)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	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[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.55e+44], t$95$2, If[LessEqual[b, -1.15e-135], t$95$1, If[LessEqual[b, 1.4e-269], t$95$3, If[LessEqual[b, 1.05e-26], t$95$1, If[LessEqual[b, 1.02e+50], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+117], t$95$3, If[LessEqual[b, 5.3e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.55e44 or 5.30000000000000032e237 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -2.55e44 < b < -1.15e-135 or 1.39999999999999997e-269 < b < 1.05000000000000004e-26

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 51.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 51.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y4 around 0 44.7%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -1.15e-135 < b < 1.39999999999999997e-269 or 1.01999999999999991e50 < b < 6e117

   1. Initial program 37.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf 46.7%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(\left(y1 \cdot j - c \cdot y\right) \cdot y3\right)\right)} \]

   if 1.05000000000000004e-26 < b < 1.01999999999999991e50

   1. Initial program 44.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 44.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 44.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 61.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 61.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 61.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 61.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 67.4%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y4 \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 67.4%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y4 \cdot y\right)\right)}\right) \]

      2. mul-1-neg 67.4%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-\left(y0 \cdot z - y4 \cdot y\right)\right)}\right) \]

      3. distribute-rgt-neg-in 67.4%

         \[\leadsto c \cdot \color{blue}{\left(-y3 \cdot \left(y0 \cdot z - y4 \cdot y\right)\right)} \]

      4. *-commutative 67.4%

         \[\leadsto c \cdot \left(-y3 \cdot \left(y0 \cdot z - \color{blue}{y \cdot y4}\right)\right) \]

   9. Simplified 67.4%

      \[\leadsto \color{blue}{c \cdot \left(-y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if 6e117 < b < 5.30000000000000032e237

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 40.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - i \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+117}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 19: 34.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-278}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+239}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (+ (* i (- (* z t) (* x y))) (* y2 (- (* x y0) (* t y4))))))
        (t_2 (* y0 (* b (- (* z k) (* x j)))))
        (t_3 (* y4 (* y3 (- (* y c) (* j y1))))))
   (if (<= b -2.3e+44)
     t_2
     (if (<= b -2.5e-135)
       t_1
       (if (<= b 4e-278)
         t_3
         (if (<= b 4.2e+41)
           t_1
           (if (<= b 2.5e+117)
             t_3
             (if (<= b 1.2e+239) (* y4 (* t (- (* b j) (* c y2)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -2.3e+44) {
		tmp = t_2;
	} else if (b <= -2.5e-135) {
		tmp = t_1;
	} else if (b <= 4e-278) {
		tmp = t_3;
	} else if (b <= 4.2e+41) {
		tmp = t_1;
	} else if (b <= 2.5e+117) {
		tmp = t_3;
	} else if (b <= 1.2e+239) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    t_3 = y4 * (y3 * ((y * c) - (j * y1)))
    if (b <= (-2.3d+44)) then
        tmp = t_2
    else if (b <= (-2.5d-135)) then
        tmp = t_1
    else if (b <= 4d-278) then
        tmp = t_3
    else if (b <= 4.2d+41) then
        tmp = t_1
    else if (b <= 2.5d+117) then
        tmp = t_3
    else if (b <= 1.2d+239) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    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 * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -2.3e+44) {
		tmp = t_2;
	} else if (b <= -2.5e-135) {
		tmp = t_1;
	} else if (b <= 4e-278) {
		tmp = t_3;
	} else if (b <= 4.2e+41) {
		tmp = t_1;
	} else if (b <= 2.5e+117) {
		tmp = t_3;
	} else if (b <= 1.2e+239) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	t_3 = y4 * (y3 * ((y * c) - (j * y1)))
	tmp = 0
	if b <= -2.3e+44:
		tmp = t_2
	elif b <= -2.5e-135:
		tmp = t_1
	elif b <= 4e-278:
		tmp = t_3
	elif b <= 4.2e+41:
		tmp = t_1
	elif b <= 2.5e+117:
		tmp = t_3
	elif b <= 1.2e+239:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4)))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_3 = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))))
	tmp = 0.0
	if (b <= -2.3e+44)
		tmp = t_2;
	elseif (b <= -2.5e-135)
		tmp = t_1;
	elseif (b <= 4e-278)
		tmp = t_3;
	elseif (b <= 4.2e+41)
		tmp = t_1;
	elseif (b <= 2.5e+117)
		tmp = t_3;
	elseif (b <= 1.2e+239)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	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 * ((i * ((z * t) - (x * y))) + (y2 * ((x * y0) - (t * y4))));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	t_3 = y4 * (y3 * ((y * c) - (j * y1)));
	tmp = 0.0;
	if (b <= -2.3e+44)
		tmp = t_2;
	elseif (b <= -2.5e-135)
		tmp = t_1;
	elseif (b <= 4e-278)
		tmp = t_3;
	elseif (b <= 4.2e+41)
		tmp = t_1;
	elseif (b <= 2.5e+117)
		tmp = t_3;
	elseif (b <= 1.2e+239)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	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[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+44], t$95$2, If[LessEqual[b, -2.5e-135], t$95$1, If[LessEqual[b, 4e-278], t$95$3, If[LessEqual[b, 4.2e+41], t$95$1, If[LessEqual[b, 2.5e+117], t$95$3, If[LessEqual[b, 1.2e+239], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.30000000000000004e44 or 1.2e239 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -2.30000000000000004e44 < b < -2.5000000000000001e-135 or 3.99999999999999975e-278 < b < 4.1999999999999999e41

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 32.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 32.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 51.5%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 51.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 47.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around 0 46.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \left(i \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. +-commutative 46.4%

         \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{\left(y4 \cdot \left(t \cdot y2\right) + i \cdot \left(y \cdot x - t \cdot z\right)\right)}\right) \]

      2. associate--r+ 46.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot \left(x \cdot y2\right) - y4 \cdot \left(t \cdot y2\right)\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

      3. associate-*r* 46.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{\left(y4 \cdot t\right) \cdot y2}\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      4. *-commutative 46.4%

         \[\leadsto c \cdot \left(\left(y0 \cdot \left(x \cdot y2\right) - \color{blue}{\left(t \cdot y4\right)} \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 46.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot \left(x \cdot y2\right) + \left(-t \cdot y4\right) \cdot y2\right)} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      6. associate-*r* 48.6%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(y0 \cdot x\right) \cdot y2} + \left(-t \cdot y4\right) \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      7. neg-mul-1 48.6%

         \[\leadsto c \cdot \left(\left(\left(y0 \cdot x\right) \cdot y2 + \color{blue}{\left(-1 \cdot \left(t \cdot y4\right)\right)} \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      8. *-commutative 48.6%

         \[\leadsto c \cdot \left(\left(\left(y0 \cdot x\right) \cdot y2 + \left(-1 \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \cdot y2\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      9. distribute-rgt-in 48.6%

         \[\leadsto c \cdot \left(\color{blue}{y2 \cdot \left(y0 \cdot x + -1 \cdot \left(y4 \cdot t\right)\right)} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      10. mul-1-neg 48.6%

          \[\leadsto c \cdot \left(y2 \cdot \left(y0 \cdot x + \color{blue}{\left(-y4 \cdot t\right)}\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      11. sub-neg 48.6%

          \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\left(y0 \cdot x - y4 \cdot t\right)} - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      12. *-commutative 48.6%

          \[\leadsto c \cdot \left(y2 \cdot \left(y0 \cdot x - \color{blue}{t \cdot y4}\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right) \]

      13. *-commutative 48.6%

          \[\leadsto c \cdot \left(y2 \cdot \left(y0 \cdot x - t \cdot y4\right) - i \cdot \left(\color{blue}{x \cdot y} - t \cdot z\right)\right) \]

   10. Simplified 48.6%

       \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(y0 \cdot x - t \cdot y4\right) - i \cdot \left(x \cdot y - t \cdot z\right)\right)} \]

   if -2.5000000000000001e-135 < b < 3.99999999999999975e-278 or 4.1999999999999999e41 < b < 2.49999999999999992e117

   1. Initial program 37.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 37.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 37.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y3 around -inf 49.3%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(\left(y1 \cdot j - c \cdot y\right) \cdot y3\right)\right)} \]

   if 2.49999999999999992e117 < b < 1.2e239

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 40.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-278}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+117}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+239}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 20: 31.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-289}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-179}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i)))))
        (t_2 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -4.2e+44)
     t_2
     (if (<= b -1.02e-192)
       t_1
       (if (<= b -1.85e-281)
         (* a (* z (- (* y1 y3) (* t b))))
         (if (<= b 3.1e-289)
           (* y4 (* c (- (* y y3) (* t y2))))
           (if (<= b 1.45e-179)
             (* y2 (* y1 (- (* k y4) (* x a))))
             (if (<= b 1.26e-23)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= b 6.4e+98)
                 t_1
                 (if (<= b 4.6e+237)
                   (* y4 (* t (- (* b j) (* c y2))))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -4.2e+44) {
		tmp = t_2;
	} else if (b <= -1.02e-192) {
		tmp = t_1;
	} else if (b <= -1.85e-281) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= 3.1e-289) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 1.45e-179) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.26e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 6.4e+98) {
		tmp = t_1;
	} else if (b <= 4.6e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * (y * ((y3 * y4) - (x * i)))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-4.2d+44)) then
        tmp = t_2
    else if (b <= (-1.02d-192)) then
        tmp = t_1
    else if (b <= (-1.85d-281)) then
        tmp = a * (z * ((y1 * y3) - (t * b)))
    else if (b <= 3.1d-289) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (b <= 1.45d-179) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (b <= 1.26d-23) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 6.4d+98) then
        tmp = t_1
    else if (b <= 4.6d+237) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    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 * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -4.2e+44) {
		tmp = t_2;
	} else if (b <= -1.02e-192) {
		tmp = t_1;
	} else if (b <= -1.85e-281) {
		tmp = a * (z * ((y1 * y3) - (t * b)));
	} else if (b <= 3.1e-289) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 1.45e-179) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.26e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 6.4e+98) {
		tmp = t_1;
	} else if (b <= 4.6e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * (y * ((y3 * y4) - (x * i)))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -4.2e+44:
		tmp = t_2
	elif b <= -1.02e-192:
		tmp = t_1
	elif b <= -1.85e-281:
		tmp = a * (z * ((y1 * y3) - (t * b)))
	elif b <= 3.1e-289:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif b <= 1.45e-179:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif b <= 1.26e-23:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 6.4e+98:
		tmp = t_1
	elif b <= 4.6e+237:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -4.2e+44)
		tmp = t_2;
	elseif (b <= -1.02e-192)
		tmp = t_1;
	elseif (b <= -1.85e-281)
		tmp = Float64(a * Float64(z * Float64(Float64(y1 * y3) - Float64(t * b))));
	elseif (b <= 3.1e-289)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 1.45e-179)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (b <= 1.26e-23)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 6.4e+98)
		tmp = t_1;
	elseif (b <= 4.6e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	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 * (y * ((y3 * y4) - (x * i)));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -4.2e+44)
		tmp = t_2;
	elseif (b <= -1.02e-192)
		tmp = t_1;
	elseif (b <= -1.85e-281)
		tmp = a * (z * ((y1 * y3) - (t * b)));
	elseif (b <= 3.1e-289)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (b <= 1.45e-179)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (b <= 1.26e-23)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 6.4e+98)
		tmp = t_1;
	elseif (b <= 4.6e+237)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	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[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+44], t$95$2, If[LessEqual[b, -1.02e-192], t$95$1, If[LessEqual[b, -1.85e-281], N[(a * N[(z * N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-289], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-179], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.26e-23], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+98], t$95$1, If[LessEqual[b, 4.6e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -4.19999999999999974e44 or 4.59999999999999991e237 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -4.19999999999999974e44 < b < -1.02e-192 or 1.25999999999999996e-23 < b < 6.4000000000000005e98

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 39.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 44.1%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 44.1%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 44.1%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 44.1%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 44.1%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if -1.02e-192 < b < -1.84999999999999996e-281

   1. Initial program 44.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 44.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 44.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 44.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 44.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 44.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 44.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 44.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in z around inf 41.1%

      \[\leadsto \color{blue}{\left(z \cdot \left(-1 \cdot \left(t \cdot b\right) - -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \cdot a \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 41.1%

         \[\leadsto \left(z \cdot \color{blue}{\left(-1 \cdot \left(t \cdot b\right) + \left(--1\right) \cdot \left(y1 \cdot y3\right)\right)}\right) \cdot a \]

      2. metadata-eval 41.1%

         \[\leadsto \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{1} \cdot \left(y1 \cdot y3\right)\right)\right) \cdot a \]

      3. *-lft-identity 41.1%

         \[\leadsto \left(z \cdot \left(-1 \cdot \left(t \cdot b\right) + \color{blue}{y1 \cdot y3}\right)\right) \cdot a \]

      4. +-commutative 41.1%

         \[\leadsto \left(z \cdot \color{blue}{\left(y1 \cdot y3 + -1 \cdot \left(t \cdot b\right)\right)}\right) \cdot a \]

      5. mul-1-neg 41.1%

         \[\leadsto \left(z \cdot \left(y1 \cdot y3 + \color{blue}{\left(-t \cdot b\right)}\right)\right) \cdot a \]

      6. unsub-neg 41.1%

         \[\leadsto \left(z \cdot \color{blue}{\left(y1 \cdot y3 - t \cdot b\right)}\right) \cdot a \]

      7. *-commutative 41.1%

         \[\leadsto \left(z \cdot \left(\color{blue}{y3 \cdot y1} - t \cdot b\right)\right) \cdot a \]

   9. Simplified 41.1%

      \[\leadsto \color{blue}{\left(z \cdot \left(y3 \cdot y1 - t \cdot b\right)\right)} \cdot a \]

   if -1.84999999999999996e-281 < b < 3.1e-289

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 56.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 56.7%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 56.7%

         \[\leadsto y4 \cdot \left(c \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 56.7%

         \[\leadsto y4 \cdot \left(c \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 56.7%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 3.1e-289 < b < 1.4499999999999999e-179

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 26.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 26.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 26.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 53.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 53.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in y2 around inf 53.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(k \cdot y4 - a \cdot x\right) \cdot y2\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 53.3%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(k \cdot y4 - a \cdot x\right)\right) \cdot y2} \]

      2. *-commutative 53.3%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \cdot y2 \]

      3. *-commutative 53.3%

         \[\leadsto \left(y1 \cdot \left(y4 \cdot k - \color{blue}{x \cdot a}\right)\right) \cdot y2 \]

   9. Simplified 53.3%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(y4 \cdot k - x \cdot a\right)\right) \cdot y2} \]

   if 1.4499999999999999e-179 < b < 1.25999999999999996e-23

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 60.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 60.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 60.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 60.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 44.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 6.4000000000000005e98 < b < 4.59999999999999991e237

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-192}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3 - t \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-289}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-179}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+98}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 21: 30.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-158}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-281}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-289}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-179}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -1.8e+66)
     t_1
     (if (<= b -3e-158)
       (* (* j y1) (- (* x i) (* y3 y4)))
       (if (<= b -1.05e-281)
         (* (* a y1) (- (* z y3) (* x y2)))
         (if (<= b 2e-289)
           (* y4 (* c (- (* y y3) (* t y2))))
           (if (<= b 3.4e-179)
             (* y2 (* y1 (- (* k y4) (* x a))))
             (if (<= b 1.3e-23)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= b 2.8e+101)
                 (* c (* y (- (* y3 y4) (* x i))))
                 (if (<= b 2.05e+238)
                   (* y4 (* t (- (* b j) (* c 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 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.8e+66) {
		tmp = t_1;
	} else if (b <= -3e-158) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= -1.05e-281) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 2e-289) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 3.4e-179) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.3e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 2.8e+101) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (b <= 2.05e+238) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-1.8d+66)) then
        tmp = t_1
    else if (b <= (-3d-158)) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (b <= (-1.05d-281)) then
        tmp = (a * y1) * ((z * y3) - (x * y2))
    else if (b <= 2d-289) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (b <= 3.4d-179) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (b <= 1.3d-23) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 2.8d+101) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (b <= 2.05d+238) then
        tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.8e+66) {
		tmp = t_1;
	} else if (b <= -3e-158) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= -1.05e-281) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 2e-289) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 3.4e-179) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.3e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 2.8e+101) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (b <= 2.05e+238) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -1.8e+66:
		tmp = t_1
	elif b <= -3e-158:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif b <= -1.05e-281:
		tmp = (a * y1) * ((z * y3) - (x * y2))
	elif b <= 2e-289:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif b <= 3.4e-179:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif b <= 1.3e-23:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 2.8e+101:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif b <= 2.05e+238:
		tmp = y4 * (t * ((b * j) - (c * 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(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -1.8e+66)
		tmp = t_1;
	elseif (b <= -3e-158)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (b <= -1.05e-281)
		tmp = Float64(Float64(a * y1) * Float64(Float64(z * y3) - Float64(x * y2)));
	elseif (b <= 2e-289)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 3.4e-179)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (b <= 1.3e-23)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 2.8e+101)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (b <= 2.05e+238)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -1.8e+66)
		tmp = t_1;
	elseif (b <= -3e-158)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (b <= -1.05e-281)
		tmp = (a * y1) * ((z * y3) - (x * y2));
	elseif (b <= 2e-289)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (b <= 3.4e-179)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (b <= 1.3e-23)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 2.8e+101)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (b <= 2.05e+238)
		tmp = y4 * (t * ((b * j) - (c * 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[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e+66], t$95$1, If[LessEqual[b, -3e-158], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e-281], N[(N[(a * y1), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-289], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-179], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e-23], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+101], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+238], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -1.8e66 or 2.0499999999999999e238 < b

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 20.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 23.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 23.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 23.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 27.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 39.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 39.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 52.3%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 52.3%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 52.3%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 52.3%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -1.8e66 < b < -3e-158

   1. Initial program 38.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 38.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 38.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 41.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 41.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 41.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 33.6%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.7%

         \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)} \]

      2. mul-1-neg 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \]

      3. unsub-neg 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \]

      4. *-commutative 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(\color{blue}{x \cdot i} - y4 \cdot y3\right) \]

      5. *-commutative 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(x \cdot i - \color{blue}{y3 \cdot y4}\right) \]

   9. Simplified 35.7%

      \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(x \cdot i - y3 \cdot y4\right)} \]

   if -3e-158 < b < -1.0499999999999999e-281

   1. Initial program 41.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 41.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 41.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in 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 a around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. *-commutative 42.1%

         \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot z - \color{blue}{y2 \cdot x}\right) \]

      3. *-commutative 42.1%

         \[\leadsto \color{blue}{\left(y3 \cdot z - y2 \cdot x\right) \cdot \left(a \cdot y1\right)} \]

      4. *-commutative 42.1%

         \[\leadsto \left(y3 \cdot z - \color{blue}{x \cdot y2}\right) \cdot \left(a \cdot y1\right) \]

      5. *-commutative 42.1%

         \[\leadsto \left(y3 \cdot z - x \cdot y2\right) \cdot \color{blue}{\left(y1 \cdot a\right)} \]

   9. Simplified 42.1%

      \[\leadsto \color{blue}{\left(y3 \cdot z - x \cdot y2\right) \cdot \left(y1 \cdot a\right)} \]

   if -1.0499999999999999e-281 < b < 2e-289

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 56.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 56.7%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 56.7%

         \[\leadsto y4 \cdot \left(c \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 56.7%

         \[\leadsto y4 \cdot \left(c \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 56.7%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 2e-289 < b < 3.3999999999999997e-179

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 26.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 26.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 26.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 53.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 53.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in y2 around inf 53.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(k \cdot y4 - a \cdot x\right) \cdot y2\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 53.3%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(k \cdot y4 - a \cdot x\right)\right) \cdot y2} \]

      2. *-commutative 53.3%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \cdot y2 \]

      3. *-commutative 53.3%

         \[\leadsto \left(y1 \cdot \left(y4 \cdot k - \color{blue}{x \cdot a}\right)\right) \cdot y2 \]

   9. Simplified 53.3%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(y4 \cdot k - x \cdot a\right)\right) \cdot y2} \]

   if 3.3999999999999997e-179 < b < 1.3e-23

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 60.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 60.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 60.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 60.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 44.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 1.3e-23 < b < 2.79999999999999981e101

   1. Initial program 40.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 40.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 40.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 59.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 59.5%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 59.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 59.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 55.9%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 55.9%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 55.9%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 55.9%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 55.9%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if 2.79999999999999981e101 < b < 2.0499999999999999e238

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+66}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-158}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-281}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-289}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-179}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 22: 31.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-208}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-115}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+37}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j)))))
        (t_2 (* y4 (* y3 (- (* y c) (* j y1))))))
   (if (<= b -3.5e+44)
     t_1
     (if (<= b -1.7e-135)
       (* c (* i (- (* z t) (* x y))))
       (if (<= b 1.5e-289)
         t_2
         (if (<= b 3.9e-208)
           (* y2 (* y1 (- (* k y4) (* x a))))
           (if (<= b 3.75e-115)
             (* c (* y3 (- (* y y4) (* z y0))))
             (if (<= b 3e+37)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= b 3.3e+117)
                 t_2
                 (if (<= b 1.4e+238)
                   (* y4 (* t (- (* b j) (* c 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -3.5e+44) {
		tmp = t_1;
	} else if (b <= -1.7e-135) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (b <= 1.5e-289) {
		tmp = t_2;
	} else if (b <= 3.9e-208) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 3.75e-115) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (b <= 3e+37) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 3.3e+117) {
		tmp = t_2;
	} else if (b <= 1.4e+238) {
		tmp = y4 * (t * ((b * j) - (c * 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) :: t_2
    real(8) :: tmp
    t_1 = y0 * (b * ((z * k) - (x * j)))
    t_2 = y4 * (y3 * ((y * c) - (j * y1)))
    if (b <= (-3.5d+44)) then
        tmp = t_1
    else if (b <= (-1.7d-135)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (b <= 1.5d-289) then
        tmp = t_2
    else if (b <= 3.9d-208) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (b <= 3.75d-115) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (b <= 3d+37) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 3.3d+117) then
        tmp = t_2
    else if (b <= 1.4d+238) then
        tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)));
	double t_2 = y4 * (y3 * ((y * c) - (j * y1)));
	double tmp;
	if (b <= -3.5e+44) {
		tmp = t_1;
	} else if (b <= -1.7e-135) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (b <= 1.5e-289) {
		tmp = t_2;
	} else if (b <= 3.9e-208) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 3.75e-115) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (b <= 3e+37) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 3.3e+117) {
		tmp = t_2;
	} else if (b <= 1.4e+238) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
	t_2 = y4 * (y3 * ((y * c) - (j * y1)))
	tmp = 0
	if b <= -3.5e+44:
		tmp = t_1
	elif b <= -1.7e-135:
		tmp = c * (i * ((z * t) - (x * y)))
	elif b <= 1.5e-289:
		tmp = t_2
	elif b <= 3.9e-208:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif b <= 3.75e-115:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif b <= 3e+37:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 3.3e+117:
		tmp = t_2
	elif b <= 1.4e+238:
		tmp = y4 * (t * ((b * j) - (c * 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(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_2 = Float64(y4 * Float64(y3 * Float64(Float64(y * c) - Float64(j * y1))))
	tmp = 0.0
	if (b <= -3.5e+44)
		tmp = t_1;
	elseif (b <= -1.7e-135)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (b <= 1.5e-289)
		tmp = t_2;
	elseif (b <= 3.9e-208)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (b <= 3.75e-115)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (b <= 3e+37)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 3.3e+117)
		tmp = t_2;
	elseif (b <= 1.4e+238)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 = y0 * (b * ((z * k) - (x * j)));
	t_2 = y4 * (y3 * ((y * c) - (j * y1)));
	tmp = 0.0;
	if (b <= -3.5e+44)
		tmp = t_1;
	elseif (b <= -1.7e-135)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (b <= 1.5e-289)
		tmp = t_2;
	elseif (b <= 3.9e-208)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (b <= 3.75e-115)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (b <= 3e+37)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 3.3e+117)
		tmp = t_2;
	elseif (b <= 1.4e+238)
		tmp = y4 * (t * ((b * j) - (c * 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[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(y3 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+44], t$95$1, If[LessEqual[b, -1.7e-135], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-289], t$95$2, If[LessEqual[b, 3.9e-208], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.75e-115], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+37], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+117], t$95$2, If[LessEqual[b, 1.4e+238], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -3.4999999999999999e44 or 1.39999999999999995e238 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -3.4999999999999999e44 < b < -1.69999999999999995e-135

   1. Initial program 42.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 42.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 34.9%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 34.9%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 34.9%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if -1.69999999999999995e-135 < b < 1.4999999999999999e-289 or 3.00000000000000022e37 < b < 3.2999999999999998e117

   1. Initial program 36.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 36.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   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 y3 around -inf 48.3%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(\left(y1 \cdot j - c \cdot y\right) \cdot y3\right)\right)} \]

   if 1.4999999999999999e-289 < b < 3.90000000000000004e-208

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 31.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 31.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 56.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 56.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 56.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 56.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in y2 around inf 57.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(k \cdot y4 - a \cdot x\right) \cdot y2\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 57.0%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(k \cdot y4 - a \cdot x\right)\right) \cdot y2} \]

      2. *-commutative 57.0%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \cdot y2 \]

      3. *-commutative 57.0%

         \[\leadsto \left(y1 \cdot \left(y4 \cdot k - \color{blue}{x \cdot a}\right)\right) \cdot y2 \]

   9. Simplified 57.0%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(y4 \cdot k - x \cdot a\right)\right) \cdot y2} \]

   if 3.90000000000000004e-208 < b < 3.75000000000000019e-115

   1. Initial program 15.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 15.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 15.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 55.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 55.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 55.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 55.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 41.4%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y4 \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 41.4%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y4 \cdot y\right)\right)}\right) \]

      2. mul-1-neg 41.4%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-\left(y0 \cdot z - y4 \cdot y\right)\right)}\right) \]

      3. distribute-rgt-neg-in 41.4%

         \[\leadsto c \cdot \color{blue}{\left(-y3 \cdot \left(y0 \cdot z - y4 \cdot y\right)\right)} \]

      4. *-commutative 41.4%

         \[\leadsto c \cdot \left(-y3 \cdot \left(y0 \cdot z - \color{blue}{y \cdot y4}\right)\right) \]

   9. Simplified 41.4%

      \[\leadsto \color{blue}{c \cdot \left(-y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if 3.75000000000000019e-115 < b < 3.00000000000000022e37

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 62.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 62.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 62.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 62.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 54.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 3.2999999999999998e117 < b < 1.39999999999999995e238

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 y4 around inf 40.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-135}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-289}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-208}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-115}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+37}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+117}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 23: 31.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.9 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+286}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i)))))
        (t_2 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -1.85e+44)
     t_2
     (if (<= b 2.05e-299)
       t_1
       (if (<= b 1.2e-259)
         (* y (* y3 (* a (- y5))))
         (if (<= b 1.26e-23)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= b 6.5e+100)
             t_1
             (if (<= b 8.9e+238)
               (* y4 (* j (- (* t b) (* y1 y3))))
               (if (<= b 1.7e+286) 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 = c * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.85e+44) {
		tmp = t_2;
	} else if (b <= 2.05e-299) {
		tmp = t_1;
	} else if (b <= 1.2e-259) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1.26e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 6.5e+100) {
		tmp = t_1;
	} else if (b <= 8.9e+238) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (b <= 1.7e+286) {
		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 = c * (y * ((y3 * y4) - (x * i)))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-1.85d+44)) then
        tmp = t_2
    else if (b <= 2.05d-299) then
        tmp = t_1
    else if (b <= 1.2d-259) then
        tmp = y * (y3 * (a * -y5))
    else if (b <= 1.26d-23) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 6.5d+100) then
        tmp = t_1
    else if (b <= 8.9d+238) then
        tmp = y4 * (j * ((t * b) - (y1 * y3)))
    else if (b <= 1.7d+286) 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 = c * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.85e+44) {
		tmp = t_2;
	} else if (b <= 2.05e-299) {
		tmp = t_1;
	} else if (b <= 1.2e-259) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1.26e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 6.5e+100) {
		tmp = t_1;
	} else if (b <= 8.9e+238) {
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	} else if (b <= 1.7e+286) {
		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 = c * (y * ((y3 * y4) - (x * i)))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -1.85e+44:
		tmp = t_2
	elif b <= 2.05e-299:
		tmp = t_1
	elif b <= 1.2e-259:
		tmp = y * (y3 * (a * -y5))
	elif b <= 1.26e-23:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 6.5e+100:
		tmp = t_1
	elif b <= 8.9e+238:
		tmp = y4 * (j * ((t * b) - (y1 * y3)))
	elif b <= 1.7e+286:
		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(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -1.85e+44)
		tmp = t_2;
	elseif (b <= 2.05e-299)
		tmp = t_1;
	elseif (b <= 1.2e-259)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (b <= 1.26e-23)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 6.5e+100)
		tmp = t_1;
	elseif (b <= 8.9e+238)
		tmp = Float64(y4 * Float64(j * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (b <= 1.7e+286)
		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 = c * (y * ((y3 * y4) - (x * i)));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -1.85e+44)
		tmp = t_2;
	elseif (b <= 2.05e-299)
		tmp = t_1;
	elseif (b <= 1.2e-259)
		tmp = y * (y3 * (a * -y5));
	elseif (b <= 1.26e-23)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 6.5e+100)
		tmp = t_1;
	elseif (b <= 8.9e+238)
		tmp = y4 * (j * ((t * b) - (y1 * y3)));
	elseif (b <= 1.7e+286)
		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[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85e+44], t$95$2, If[LessEqual[b, 2.05e-299], t$95$1, If[LessEqual[b, 1.2e-259], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.26e-23], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+100], t$95$1, If[LessEqual[b, 8.9e+238], N[(y4 * N[(j * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+286], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.85e44 or 8.8999999999999999e238 < b < 1.7e286

   1. Initial program 20.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 20.3%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 21.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 21.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 21.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 25.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 38.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.4%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 38.4%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 52.1%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 52.1%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 52.1%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -1.85e44 < b < 2.05e-299 or 1.25999999999999996e-23 < b < 6.50000000000000001e100 or 1.7e286 < b

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 39.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 39.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 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. Step-by-step derivation

      1. associate--l+ 42.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 40.7%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 40.7%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 40.7%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 40.7%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 40.7%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 40.7%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if 2.05e-299 < b < 1.2e-259

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 45.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 45.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 55.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.4%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 55.4%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around 0 55.4%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 55.4%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 55.4%

          \[\leadsto -a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   12. Simplified 55.4%

       \[\leadsto \color{blue}{-a \cdot \left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   13. Taylor expanded in a around 0 64.1%

       \[\leadsto -\color{blue}{y \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 64.1%

          \[\leadsto -y \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot a\right)} \]

       2. associate-*l* 64.2%

          \[\leadsto -y \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   15. Simplified 64.2%

       \[\leadsto -\color{blue}{y \cdot \left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   if 1.2e-259 < b < 1.25999999999999996e-23

   1. Initial program 20.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 57.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 57.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 57.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 57.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 38.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 6.50000000000000001e100 < b < 8.8999999999999999e238

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in j around inf 49.5%

      \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right) \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.5%

         \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(t \cdot b + -1 \cdot \left(y1 \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 49.5%

         \[\leadsto y4 \cdot \left(j \cdot \left(t \cdot b + \color{blue}{\left(-y1 \cdot y3\right)}\right)\right) \]

      3. sub-neg 49.5%

         \[\leadsto y4 \cdot \left(j \cdot \color{blue}{\left(t \cdot b - y1 \cdot y3\right)}\right) \]

      4. *-commutative 49.5%

         \[\leadsto y4 \cdot \left(j \cdot \left(t \cdot b - \color{blue}{y3 \cdot y1}\right)\right) \]

   7. Simplified 49.5%

      \[\leadsto y4 \cdot \color{blue}{\left(j \cdot \left(t \cdot b - y3 \cdot y1\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 8.9 \cdot 10^{+238}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+286}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \end{array} \]

Alternative 24: 30.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.92 \cdot 10^{-160}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-281}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-297}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-214}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -1.8e+66)
     t_1
     (if (<= b -1.92e-160)
       (* (* j y1) (- (* x i) (* y3 y4)))
       (if (<= b -1.9e-281)
         (* (* a y1) (- (* z y3) (* x y2)))
         (if (<= b 3.9e-297)
           (* y4 (* c (- (* y y3) (* t y2))))
           (if (<= b 2.4e-214)
             (* y2 (* y1 (- (* k y4) (* x a))))
             (if (<= b 2.7e+106)
               (* c (* y3 (- (* y y4) (* z y0))))
               (if (<= b 4.2e+237)
                 (* y4 (* t (- (* b j) (* c 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 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.8e+66) {
		tmp = t_1;
	} else if (b <= -1.92e-160) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= -1.9e-281) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 3.9e-297) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 2.4e-214) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 2.7e+106) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (b <= 4.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-1.8d+66)) then
        tmp = t_1
    else if (b <= (-1.92d-160)) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (b <= (-1.9d-281)) then
        tmp = (a * y1) * ((z * y3) - (x * y2))
    else if (b <= 3.9d-297) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (b <= 2.4d-214) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (b <= 2.7d+106) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (b <= 4.2d+237) then
        tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.8e+66) {
		tmp = t_1;
	} else if (b <= -1.92e-160) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (b <= -1.9e-281) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 3.9e-297) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (b <= 2.4e-214) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 2.7e+106) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (b <= 4.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * 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 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -1.8e+66:
		tmp = t_1
	elif b <= -1.92e-160:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif b <= -1.9e-281:
		tmp = (a * y1) * ((z * y3) - (x * y2))
	elif b <= 3.9e-297:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif b <= 2.4e-214:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif b <= 2.7e+106:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif b <= 4.2e+237:
		tmp = y4 * (t * ((b * j) - (c * 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(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -1.8e+66)
		tmp = t_1;
	elseif (b <= -1.92e-160)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (b <= -1.9e-281)
		tmp = Float64(Float64(a * y1) * Float64(Float64(z * y3) - Float64(x * y2)));
	elseif (b <= 3.9e-297)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (b <= 2.4e-214)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (b <= 2.7e+106)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (b <= 4.2e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -1.8e+66)
		tmp = t_1;
	elseif (b <= -1.92e-160)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (b <= -1.9e-281)
		tmp = (a * y1) * ((z * y3) - (x * y2));
	elseif (b <= 3.9e-297)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (b <= 2.4e-214)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (b <= 2.7e+106)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (b <= 4.2e+237)
		tmp = y4 * (t * ((b * j) - (c * 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[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.8e+66], t$95$1, If[LessEqual[b, -1.92e-160], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.9e-281], N[(N[(a * y1), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e-297], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-214], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+106], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.8e66 or 4.20000000000000029e237 < b

   1. Initial program 20.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 20.9%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 23.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 23.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 23.7%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 27.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 39.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.5%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 39.5%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 52.3%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 52.3%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 52.3%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 52.3%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -1.8e66 < b < -1.91999999999999999e-160

   1. Initial program 38.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 38.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 38.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 41.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 41.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 41.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 41.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 33.6%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 35.7%

         \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)} \]

      2. mul-1-neg 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \]

      3. unsub-neg 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \]

      4. *-commutative 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(\color{blue}{x \cdot i} - y4 \cdot y3\right) \]

      5. *-commutative 35.7%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(x \cdot i - \color{blue}{y3 \cdot y4}\right) \]

   9. Simplified 35.7%

      \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(x \cdot i - y3 \cdot y4\right)} \]

   if -1.91999999999999999e-160 < b < -1.89999999999999988e-281

   1. Initial program 41.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 41.1%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 41.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 41.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in 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 a around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. *-commutative 42.1%

         \[\leadsto \left(a \cdot y1\right) \cdot \left(y3 \cdot z - \color{blue}{y2 \cdot x}\right) \]

      3. *-commutative 42.1%

         \[\leadsto \color{blue}{\left(y3 \cdot z - y2 \cdot x\right) \cdot \left(a \cdot y1\right)} \]

      4. *-commutative 42.1%

         \[\leadsto \left(y3 \cdot z - \color{blue}{x \cdot y2}\right) \cdot \left(a \cdot y1\right) \]

      5. *-commutative 42.1%

         \[\leadsto \left(y3 \cdot z - x \cdot y2\right) \cdot \color{blue}{\left(y1 \cdot a\right)} \]

   9. Simplified 42.1%

      \[\leadsto \color{blue}{\left(y3 \cdot z - x \cdot y2\right) \cdot \left(y1 \cdot a\right)} \]

   if -1.89999999999999988e-281 < b < 3.9000000000000001e-297

   1. Initial program 22.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 56.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 56.7%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 56.7%

         \[\leadsto y4 \cdot \left(c \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 56.7%

         \[\leadsto y4 \cdot \left(c \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 56.7%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 3.9000000000000001e-297 < b < 2.4000000000000002e-214

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 31.5%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 31.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 56.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 56.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 56.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 56.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in y2 around inf 57.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(k \cdot y4 - a \cdot x\right) \cdot y2\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 57.0%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(k \cdot y4 - a \cdot x\right)\right) \cdot y2} \]

      2. *-commutative 57.0%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \cdot y2 \]

      3. *-commutative 57.0%

         \[\leadsto \left(y1 \cdot \left(y4 \cdot k - \color{blue}{x \cdot a}\right)\right) \cdot y2 \]

   9. Simplified 57.0%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(y4 \cdot k - x \cdot a\right)\right) \cdot y2} \]

   if 2.4000000000000002e-214 < b < 2.70000000000000006e106

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 58.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 58.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 58.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 58.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y3 around inf 41.5%

      \[\leadsto \color{blue}{c \cdot \left(y3 \cdot \left(-1 \cdot \left(y0 \cdot z\right) - -1 \cdot \left(y4 \cdot y\right)\right)\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 41.5%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot z - y4 \cdot y\right)\right)}\right) \]

      2. mul-1-neg 41.5%

         \[\leadsto c \cdot \left(y3 \cdot \color{blue}{\left(-\left(y0 \cdot z - y4 \cdot y\right)\right)}\right) \]

      3. distribute-rgt-neg-in 41.5%

         \[\leadsto c \cdot \color{blue}{\left(-y3 \cdot \left(y0 \cdot z - y4 \cdot y\right)\right)} \]

      4. *-commutative 41.5%

         \[\leadsto c \cdot \left(-y3 \cdot \left(y0 \cdot z - \color{blue}{y \cdot y4}\right)\right) \]

   9. Simplified 41.5%

      \[\leadsto \color{blue}{c \cdot \left(-y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]

   if 2.70000000000000006e106 < b < 4.20000000000000029e237

   1. Initial program 25.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 61.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+66}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.92 \cdot 10^{-160}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-281}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-297}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-214}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 25: 28.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y2 \leq -1.4 \cdot 10^{-291}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-308}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.05e-81)
   (* c (* y2 (- (* x y0) (* t y4))))
   (if (<= y2 -1.5e-236)
     (* c (* i (- (* z t) (* x y))))
     (if (<= y2 -1.4e-291)
       (* (* c y0) (* z (- y3)))
       (if (<= y2 4.5e-308)
         (* c (* (* z t) i))
         (if (<= y2 1.02e-196)
           (* y (* y3 (* a (- y5))))
           (if (<= y2 5.4e+72)
             (* c (* y (- (* y3 y4) (* x i))))
             (* a (* x (* 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 (y2 <= -1.05e-81) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -1.5e-236) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y2 <= -1.4e-291) {
		tmp = (c * y0) * (z * -y3);
	} else if (y2 <= 4.5e-308) {
		tmp = c * ((z * t) * i);
	} else if (y2 <= 1.02e-196) {
		tmp = y * (y3 * (a * -y5));
	} else if (y2 <= 5.4e+72) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = a * (x * (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 (y2 <= (-1.05d-81)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-1.5d-236)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y2 <= (-1.4d-291)) then
        tmp = (c * y0) * (z * -y3)
    else if (y2 <= 4.5d-308) then
        tmp = c * ((z * t) * i)
    else if (y2 <= 1.02d-196) then
        tmp = y * (y3 * (a * -y5))
    else if (y2 <= 5.4d+72) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else
        tmp = a * (x * (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 (y2 <= -1.05e-81) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -1.5e-236) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y2 <= -1.4e-291) {
		tmp = (c * y0) * (z * -y3);
	} else if (y2 <= 4.5e-308) {
		tmp = c * ((z * t) * i);
	} else if (y2 <= 1.02e-196) {
		tmp = y * (y3 * (a * -y5));
	} else if (y2 <= 5.4e+72) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = a * (x * (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 y2 <= -1.05e-81:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -1.5e-236:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y2 <= -1.4e-291:
		tmp = (c * y0) * (z * -y3)
	elif y2 <= 4.5e-308:
		tmp = c * ((z * t) * i)
	elif y2 <= 1.02e-196:
		tmp = y * (y3 * (a * -y5))
	elif y2 <= 5.4e+72:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	else:
		tmp = a * (x * (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 (y2 <= -1.05e-81)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -1.5e-236)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y2 <= -1.4e-291)
		tmp = Float64(Float64(c * y0) * Float64(z * Float64(-y3)));
	elseif (y2 <= 4.5e-308)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (y2 <= 1.02e-196)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (y2 <= 5.4e+72)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	else
		tmp = Float64(a * Float64(x * Float64(y1 * 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)
	tmp = 0.0;
	if (y2 <= -1.05e-81)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -1.5e-236)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y2 <= -1.4e-291)
		tmp = (c * y0) * (z * -y3);
	elseif (y2 <= 4.5e-308)
		tmp = c * ((z * t) * i);
	elseif (y2 <= 1.02e-196)
		tmp = y * (y3 * (a * -y5));
	elseif (y2 <= 5.4e+72)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	else
		tmp = a * (x * (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[LessEqual[y2, -1.05e-81], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.5e-236], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.4e-291], N[(N[(c * y0), $MachinePrecision] * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.5e-308], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.02e-196], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 5.4e+72], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y1 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -1.05e-81

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 55.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 55.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 55.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 55.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 50.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -1.05e-81 < y2 < -1.50000000000000007e-236

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 38.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 38.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 36.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.4%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 36.4%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 36.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if -1.50000000000000007e-236 < y2 < -1.4e-291

   1. Initial program 58.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 58.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 58.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 59.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y4 around 0 43.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y3 around inf 51.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.5%

         \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. associate-*r* 59.3%

         \[\leadsto -\color{blue}{\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

   10. Simplified 59.3%

       \[\leadsto \color{blue}{-\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

   if -1.4e-291 < y2 < 4.50000000000000009e-308

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 80.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 80.2%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 80.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 60.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 60.4%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 60.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   10. Taylor expanded in z around inf 60.7%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 60.7%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 60.7%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if 4.50000000000000009e-308 < y2 < 1.0200000000000001e-196

   1. Initial program 36.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 28.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 28.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 28.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 28.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 28.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 29.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 33.0%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 33.0%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around 0 33.5%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 33.5%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 33.5%

          \[\leadsto -a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   12. Simplified 33.5%

       \[\leadsto \color{blue}{-a \cdot \left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   13. Taylor expanded in a around 0 37.2%

       \[\leadsto -\color{blue}{y \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 37.2%

          \[\leadsto -y \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot a\right)} \]

       2. associate-*l* 37.2%

          \[\leadsto -y \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   15. Simplified 37.2%

       \[\leadsto -\color{blue}{y \cdot \left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   if 1.0200000000000001e-196 < y2 < 5.4000000000000001e72

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 33.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.5%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 33.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 33.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 33.9%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 33.9%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 33.9%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 33.9%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 33.9%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if 5.4000000000000001e72 < y2

   1. Initial program 11.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 11.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 11.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 36.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in x around inf 44.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot b - y1 \cdot y2\right) \cdot x\right)} \cdot a \]

   8. Taylor expanded in y around 0 41.8%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(y1 \cdot y2\right)\right)} \cdot x\right) \cdot a \]
   9. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto \left(\color{blue}{\left(-y1 \cdot y2\right)} \cdot x\right) \cdot a \]

      2. distribute-lft-neg-out 41.8%

         \[\leadsto \left(\color{blue}{\left(\left(-y1\right) \cdot y2\right)} \cdot x\right) \cdot a \]

      3. *-commutative 41.8%

         \[\leadsto \left(\color{blue}{\left(y2 \cdot \left(-y1\right)\right)} \cdot x\right) \cdot a \]

   10. Simplified 41.8%

       \[\leadsto \left(\color{blue}{\left(y2 \cdot \left(-y1\right)\right)} \cdot x\right) \cdot a \]
3. Recombined 7 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.05 \cdot 10^{-81}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.5 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y2 \leq -1.4 \cdot 10^{-291}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-308}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y2 \leq 1.02 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y1 \cdot \left(-y2\right)\right)\right)\\ \end{array} \]

Alternative 26: 29.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2.5 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.95 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y2 \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y2 \leq -2 \cdot 10^{-309}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.25 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -2.5e-82)
   (* c (* y2 (- (* x y0) (* t y4))))
   (if (<= y2 -1.95e-236)
     (* c (* i (- (* z t) (* x y))))
     (if (<= y2 -5.5e-290)
       (* (* c y0) (* z (- y3)))
       (if (<= y2 -2e-309)
         (* c (* (* z t) i))
         (if (<= y2 4.1e-196)
           (* y (* y3 (* a (- y5))))
           (if (<= y2 2.25e-27)
             (* c (* y (- (* y3 y4) (* x i))))
             (* y0 (* y5 (- (* j y3) (* k 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 <= -2.5e-82) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -1.95e-236) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y2 <= -5.5e-290) {
		tmp = (c * y0) * (z * -y3);
	} else if (y2 <= -2e-309) {
		tmp = c * ((z * t) * i);
	} else if (y2 <= 4.1e-196) {
		tmp = y * (y3 * (a * -y5));
	} else if (y2 <= 2.25e-27) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * 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 <= (-2.5d-82)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= (-1.95d-236)) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (y2 <= (-5.5d-290)) then
        tmp = (c * y0) * (z * -y3)
    else if (y2 <= (-2d-309)) then
        tmp = c * ((z * t) * i)
    else if (y2 <= 4.1d-196) then
        tmp = y * (y3 * (a * -y5))
    else if (y2 <= 2.25d-27) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else
        tmp = y0 * (y5 * ((j * y3) - (k * 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 <= -2.5e-82) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= -1.95e-236) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (y2 <= -5.5e-290) {
		tmp = (c * y0) * (z * -y3);
	} else if (y2 <= -2e-309) {
		tmp = c * ((z * t) * i);
	} else if (y2 <= 4.1e-196) {
		tmp = y * (y3 * (a * -y5));
	} else if (y2 <= 2.25e-27) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * 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 <= -2.5e-82:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= -1.95e-236:
		tmp = c * (i * ((z * t) - (x * y)))
	elif y2 <= -5.5e-290:
		tmp = (c * y0) * (z * -y3)
	elif y2 <= -2e-309:
		tmp = c * ((z * t) * i)
	elif y2 <= 4.1e-196:
		tmp = y * (y3 * (a * -y5))
	elif y2 <= 2.25e-27:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * 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 <= -2.5e-82)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= -1.95e-236)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (y2 <= -5.5e-290)
		tmp = Float64(Float64(c * y0) * Float64(z * Float64(-y3)));
	elseif (y2 <= -2e-309)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	elseif (y2 <= 4.1e-196)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (y2 <= 2.25e-27)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * 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 <= -2.5e-82)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= -1.95e-236)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (y2 <= -5.5e-290)
		tmp = (c * y0) * (z * -y3);
	elseif (y2 <= -2e-309)
		tmp = c * ((z * t) * i);
	elseif (y2 <= 4.1e-196)
		tmp = y * (y3 * (a * -y5));
	elseif (y2 <= 2.25e-27)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	else
		tmp = y0 * (y5 * ((j * y3) - (k * 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, -2.5e-82], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.95e-236], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.5e-290], N[(N[(c * y0), $MachinePrecision] * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2e-309], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.1e-196], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.25e-27], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -2.4999999999999999e-82

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 55.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 55.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 55.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 55.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 50.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   if -2.4999999999999999e-82 < y2 < -1.95e-236

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 38.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 38.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 36.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.4%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 36.4%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 36.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if -1.95e-236 < y2 < -5.5e-290

   1. Initial program 58.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 58.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 58.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 59.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 59.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y4 around 0 43.4%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y3 around inf 51.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.5%

         \[\leadsto \color{blue}{-c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

      2. associate-*r* 59.3%

         \[\leadsto -\color{blue}{\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

   10. Simplified 59.3%

       \[\leadsto \color{blue}{-\left(c \cdot y0\right) \cdot \left(y3 \cdot z\right)} \]

   if -5.5e-290 < y2 < -1.9999999999999988e-309

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 80.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 80.2%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 80.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 60.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 60.4%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 60.4%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   10. Taylor expanded in z around inf 60.7%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 60.7%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 60.7%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if -1.9999999999999988e-309 < y2 < 4.10000000000000021e-196

   1. Initial program 36.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 28.9%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 28.9%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 28.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 28.9%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 28.9%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 29.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 33.0%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 33.0%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 33.0%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around 0 33.5%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 33.5%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 33.5%

          \[\leadsto -a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   12. Simplified 33.5%

       \[\leadsto \color{blue}{-a \cdot \left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   13. Taylor expanded in a around 0 37.2%

       \[\leadsto -\color{blue}{y \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 37.2%

          \[\leadsto -y \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot a\right)} \]

       2. associate-*l* 37.2%

          \[\leadsto -y \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   15. Simplified 37.2%

       \[\leadsto -\color{blue}{y \cdot \left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   if 4.10000000000000021e-196 < y2 < 2.2500000000000001e-27

   1. Initial program 45.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 45.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 45.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 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. Step-by-step derivation

      1. associate--l+ 35.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 35.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 35.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 33.5%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 33.5%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 33.5%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 33.5%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 33.5%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 33.5%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if 2.2500000000000001e-27 < y2

   1. Initial program 12.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 12.4%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 13.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 13.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 13.9%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 15.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.6%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.6%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in y5 around inf 47.2%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.5 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.95 \cdot 10^{-236}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;y2 \leq -5.5 \cdot 10^{-290}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)\\ \mathbf{elif}\;y2 \leq -2 \cdot 10^{-309}:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;y2 \leq 4.1 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.25 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]

Alternative 27: 30.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+236}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i)))))
        (t_2 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -1.35e+44)
     t_2
     (if (<= b 2.1e-299)
       t_1
       (if (<= b 1.55e-264)
         (* y (* y3 (* a (- y5))))
         (if (<= b 2.4e-23)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= b 7e+99)
             t_1
             (if (<= b 9.5e+236) (* c (* y2 (- (* x y0) (* t y4)))) 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 * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.35e+44) {
		tmp = t_2;
	} else if (b <= 2.1e-299) {
		tmp = t_1;
	} else if (b <= 1.55e-264) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 2.4e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 7e+99) {
		tmp = t_1;
	} else if (b <= 9.5e+236) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} 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 * (y * ((y3 * y4) - (x * i)))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-1.35d+44)) then
        tmp = t_2
    else if (b <= 2.1d-299) then
        tmp = t_1
    else if (b <= 1.55d-264) then
        tmp = y * (y3 * (a * -y5))
    else if (b <= 2.4d-23) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 7d+99) then
        tmp = t_1
    else if (b <= 9.5d+236) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    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 * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -1.35e+44) {
		tmp = t_2;
	} else if (b <= 2.1e-299) {
		tmp = t_1;
	} else if (b <= 1.55e-264) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 2.4e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 7e+99) {
		tmp = t_1;
	} else if (b <= 9.5e+236) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} 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 * (y * ((y3 * y4) - (x * i)))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -1.35e+44:
		tmp = t_2
	elif b <= 2.1e-299:
		tmp = t_1
	elif b <= 1.55e-264:
		tmp = y * (y3 * (a * -y5))
	elif b <= 2.4e-23:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 7e+99:
		tmp = t_1
	elif b <= 9.5e+236:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	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(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -1.35e+44)
		tmp = t_2;
	elseif (b <= 2.1e-299)
		tmp = t_1;
	elseif (b <= 1.55e-264)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (b <= 2.4e-23)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 7e+99)
		tmp = t_1;
	elseif (b <= 9.5e+236)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	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 * (y * ((y3 * y4) - (x * i)));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -1.35e+44)
		tmp = t_2;
	elseif (b <= 2.1e-299)
		tmp = t_1;
	elseif (b <= 1.55e-264)
		tmp = y * (y3 * (a * -y5));
	elseif (b <= 2.4e-23)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 7e+99)
		tmp = t_1;
	elseif (b <= 9.5e+236)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	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[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e+44], t$95$2, If[LessEqual[b, 2.1e-299], t$95$1, If[LessEqual[b, 1.55e-264], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-23], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+99], t$95$1, If[LessEqual[b, 9.5e+236], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.35e44 or 9.4999999999999999e236 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -1.35e44 < b < 2.1000000000000001e-299 or 2.39999999999999996e-23 < b < 6.9999999999999995e99

   1. Initial program 39.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 39.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 39.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 39.2%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if 2.1000000000000001e-299 < b < 1.5500000000000001e-264

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 45.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 45.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 55.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.4%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 55.4%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around 0 55.4%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 55.4%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 55.4%

          \[\leadsto -a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   12. Simplified 55.4%

       \[\leadsto \color{blue}{-a \cdot \left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   13. Taylor expanded in a around 0 64.1%

       \[\leadsto -\color{blue}{y \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 64.1%

          \[\leadsto -y \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot a\right)} \]

       2. associate-*l* 64.2%

          \[\leadsto -y \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   15. Simplified 64.2%

       \[\leadsto -\color{blue}{y \cdot \left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   if 1.5500000000000001e-264 < b < 2.39999999999999996e-23

   1. Initial program 20.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 57.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 57.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 57.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 57.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 38.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 6.9999999999999995e99 < b < 9.4999999999999999e236

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 28.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 28.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 28.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 28.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 40.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-264}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+99}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+236}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 28: 31.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i)))))
        (t_2 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -3.2e+44)
     t_2
     (if (<= b 2e-299)
       t_1
       (if (<= b 6e-263)
         (* y (* y3 (* a (- y5))))
         (if (<= b 1.15e-23)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= b 1.06e+99)
             t_1
             (if (<= b 1.2e+237) (* y4 (* t (- (* b j) (* c y2)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -3.2e+44) {
		tmp = t_2;
	} else if (b <= 2e-299) {
		tmp = t_1;
	} else if (b <= 6e-263) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1.15e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.06e+99) {
		tmp = t_1;
	} else if (b <= 1.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * (y * ((y3 * y4) - (x * i)))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-3.2d+44)) then
        tmp = t_2
    else if (b <= 2d-299) then
        tmp = t_1
    else if (b <= 6d-263) then
        tmp = y * (y3 * (a * -y5))
    else if (b <= 1.15d-23) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 1.06d+99) then
        tmp = t_1
    else if (b <= 1.2d+237) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    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 * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -3.2e+44) {
		tmp = t_2;
	} else if (b <= 2e-299) {
		tmp = t_1;
	} else if (b <= 6e-263) {
		tmp = y * (y3 * (a * -y5));
	} else if (b <= 1.15e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 1.06e+99) {
		tmp = t_1;
	} else if (b <= 1.2e+237) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * (y * ((y3 * y4) - (x * i)))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -3.2e+44:
		tmp = t_2
	elif b <= 2e-299:
		tmp = t_1
	elif b <= 6e-263:
		tmp = y * (y3 * (a * -y5))
	elif b <= 1.15e-23:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 1.06e+99:
		tmp = t_1
	elif b <= 1.2e+237:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -3.2e+44)
		tmp = t_2;
	elseif (b <= 2e-299)
		tmp = t_1;
	elseif (b <= 6e-263)
		tmp = Float64(y * Float64(y3 * Float64(a * Float64(-y5))));
	elseif (b <= 1.15e-23)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 1.06e+99)
		tmp = t_1;
	elseif (b <= 1.2e+237)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	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 * (y * ((y3 * y4) - (x * i)));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -3.2e+44)
		tmp = t_2;
	elseif (b <= 2e-299)
		tmp = t_1;
	elseif (b <= 6e-263)
		tmp = y * (y3 * (a * -y5));
	elseif (b <= 1.15e-23)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 1.06e+99)
		tmp = t_1;
	elseif (b <= 1.2e+237)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	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[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+44], t$95$2, If[LessEqual[b, 2e-299], t$95$1, If[LessEqual[b, 6e-263], N[(y * N[(y3 * N[(a * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-23], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e+99], t$95$1, If[LessEqual[b, 1.2e+237], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.20000000000000004e44 or 1.1999999999999999e237 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -3.20000000000000004e44 < b < 1.99999999999999998e-299 or 1.15000000000000005e-23 < b < 1.05999999999999999e99

   1. Initial program 39.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 39.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 39.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 39.2%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if 1.99999999999999998e-299 < b < 6.0000000000000001e-263

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 45.8%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 45.8%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 45.8%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 55.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.4%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 55.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 55.4%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around 0 55.4%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 55.4%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 55.4%

          \[\leadsto -a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   12. Simplified 55.4%

       \[\leadsto \color{blue}{-a \cdot \left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   13. Taylor expanded in a around 0 64.1%

       \[\leadsto -\color{blue}{y \cdot \left(a \cdot \left(y3 \cdot y5\right)\right)} \]
   14. Step-by-step derivation

       1. *-commutative 64.1%

          \[\leadsto -y \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot a\right)} \]

       2. associate-*l* 64.2%

          \[\leadsto -y \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   15. Simplified 64.2%

       \[\leadsto -\color{blue}{y \cdot \left(y3 \cdot \left(y5 \cdot a\right)\right)} \]

   if 6.0000000000000001e-263 < b < 1.15000000000000005e-23

   1. Initial program 20.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 20.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 20.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 57.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 57.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 57.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 57.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 38.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 1.05999999999999999e99 < b < 1.1999999999999999e237

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-263}:\\ \;\;\;\;y \cdot \left(y3 \cdot \left(a \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+99}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+237}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 29: 31.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+236}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y (- (* y3 y4) (* x i)))))
        (t_2 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= b -2.2e+44)
     t_2
     (if (<= b 2.1e-299)
       t_1
       (if (<= b 1.35e-179)
         (* y2 (* y1 (- (* k y4) (* x a))))
         (if (<= b 1.28e-23)
           (* c (* y0 (- (* x y2) (* z y3))))
           (if (<= b 5.5e+101)
             t_1
             (if (<= b 9.8e+236) (* y4 (* t (- (* b j) (* c y2)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -2.2e+44) {
		tmp = t_2;
	} else if (b <= 2.1e-299) {
		tmp = t_1;
	} else if (b <= 1.35e-179) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.28e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 5.5e+101) {
		tmp = t_1;
	} else if (b <= 9.8e+236) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * (y * ((y3 * y4) - (x * i)))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    if (b <= (-2.2d+44)) then
        tmp = t_2
    else if (b <= 2.1d-299) then
        tmp = t_1
    else if (b <= 1.35d-179) then
        tmp = y2 * (y1 * ((k * y4) - (x * a)))
    else if (b <= 1.28d-23) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (b <= 5.5d+101) then
        tmp = t_1
    else if (b <= 9.8d+236) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    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 * (y * ((y3 * y4) - (x * i)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (b <= -2.2e+44) {
		tmp = t_2;
	} else if (b <= 2.1e-299) {
		tmp = t_1;
	} else if (b <= 1.35e-179) {
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	} else if (b <= 1.28e-23) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (b <= 5.5e+101) {
		tmp = t_1;
	} else if (b <= 9.8e+236) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} 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 * (y * ((y3 * y4) - (x * i)))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if b <= -2.2e+44:
		tmp = t_2
	elif b <= 2.1e-299:
		tmp = t_1
	elif b <= 1.35e-179:
		tmp = y2 * (y1 * ((k * y4) - (x * a)))
	elif b <= 1.28e-23:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif b <= 5.5e+101:
		tmp = t_1
	elif b <= 9.8e+236:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (b <= -2.2e+44)
		tmp = t_2;
	elseif (b <= 2.1e-299)
		tmp = t_1;
	elseif (b <= 1.35e-179)
		tmp = Float64(y2 * Float64(y1 * Float64(Float64(k * y4) - Float64(x * a))));
	elseif (b <= 1.28e-23)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (b <= 5.5e+101)
		tmp = t_1;
	elseif (b <= 9.8e+236)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	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 * (y * ((y3 * y4) - (x * i)));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (b <= -2.2e+44)
		tmp = t_2;
	elseif (b <= 2.1e-299)
		tmp = t_1;
	elseif (b <= 1.35e-179)
		tmp = y2 * (y1 * ((k * y4) - (x * a)));
	elseif (b <= 1.28e-23)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (b <= 5.5e+101)
		tmp = t_1;
	elseif (b <= 9.8e+236)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	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[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+44], t$95$2, If[LessEqual[b, 2.1e-299], t$95$1, If[LessEqual[b, 1.35e-179], N[(y2 * N[(y1 * N[(N[(k * y4), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.28e-23], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+101], t$95$1, If[LessEqual[b, 9.8e+236], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.19999999999999996e44 or 9.8e236 < b

   1. Initial program 21.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 21.8%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 24.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 50.9%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 50.9%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -2.19999999999999996e44 < b < 2.1000000000000001e-299 or 1.28000000000000005e-23 < b < 5.50000000000000018e101

   1. Initial program 39.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 39.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 39.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 39.2%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 39.2%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 39.2%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if 2.1000000000000001e-299 < b < 1.34999999999999994e-179

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 24.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 24.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 52.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 52.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 52.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 52.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 52.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in y2 around inf 48.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(k \cdot y4 - a \cdot x\right) \cdot y2\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 48.3%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(k \cdot y4 - a \cdot x\right)\right) \cdot y2} \]

      2. *-commutative 48.3%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{y4 \cdot k} - a \cdot x\right)\right) \cdot y2 \]

      3. *-commutative 48.3%

         \[\leadsto \left(y1 \cdot \left(y4 \cdot k - \color{blue}{x \cdot a}\right)\right) \cdot y2 \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(y4 \cdot k - x \cdot a\right)\right) \cdot y2} \]

   if 1.34999999999999994e-179 < b < 1.28000000000000005e-23

   1. Initial program 23.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 23.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 60.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 60.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 60.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 60.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 44.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]

   if 5.50000000000000018e101 < b < 9.8e236

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+44}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-179}:\\ \;\;\;\;y2 \cdot \left(y1 \cdot \left(k \cdot y4 - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+101}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+236}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 30: 30.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.82 \cdot 10^{+171}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-274}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-190}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+162}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.82e+171)
   (* (* j y1) (- (* x i) (* y3 y4)))
   (if (<= j -1.35e-47)
     (* y0 (* b (- (* z k) (* x j))))
     (if (<= j -1.45e-274)
       (* c (* y (- (* y3 y4) (* x i))))
       (if (<= j 3.7e-190)
         (* c (* i (- (* z t) (* x y))))
         (if (<= j 1.12e+162)
           (* y4 (* c (- (* y y3) (* t y2))))
           (* y4 (* t (- (* b j) (* c 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 (j <= -1.82e+171) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (j <= -1.35e-47) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (j <= -1.45e-274) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (j <= 3.7e-190) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (j <= 1.12e+162) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else {
		tmp = y4 * (t * ((b * j) - (c * 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 (j <= (-1.82d+171)) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (j <= (-1.35d-47)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (j <= (-1.45d-274)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (j <= 3.7d-190) then
        tmp = c * (i * ((z * t) - (x * y)))
    else if (j <= 1.12d+162) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else
        tmp = y4 * (t * ((b * j) - (c * 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 (j <= -1.82e+171) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (j <= -1.35e-47) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (j <= -1.45e-274) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (j <= 3.7e-190) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else if (j <= 1.12e+162) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else {
		tmp = y4 * (t * ((b * j) - (c * 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 j <= -1.82e+171:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif j <= -1.35e-47:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif j <= -1.45e-274:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif j <= 3.7e-190:
		tmp = c * (i * ((z * t) - (x * y)))
	elif j <= 1.12e+162:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	else:
		tmp = y4 * (t * ((b * j) - (c * 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 (j <= -1.82e+171)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (j <= -1.35e-47)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (j <= -1.45e-274)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (j <= 3.7e-190)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	elseif (j <= 1.12e+162)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * 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 (j <= -1.82e+171)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (j <= -1.35e-47)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (j <= -1.45e-274)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (j <= 3.7e-190)
		tmp = c * (i * ((z * t) - (x * y)));
	elseif (j <= 1.12e+162)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	else
		tmp = y4 * (t * ((b * j) - (c * 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[j, -1.82e+171], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.35e-47], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.45e-274], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.7e-190], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e+162], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.81999999999999996e171

   1. Initial program 3.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 3.6%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 3.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

   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 43.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 43.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 43.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in j around inf 65.1%

      \[\leadsto \color{blue}{y1 \cdot \left(j \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 68.3%

         \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(i \cdot x + -1 \cdot \left(y4 \cdot y3\right)\right)} \]

      2. mul-1-neg 68.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(i \cdot x + \color{blue}{\left(-y4 \cdot y3\right)}\right) \]

      3. unsub-neg 68.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \color{blue}{\left(i \cdot x - y4 \cdot y3\right)} \]

      4. *-commutative 68.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(\color{blue}{x \cdot i} - y4 \cdot y3\right) \]

      5. *-commutative 68.3%

         \[\leadsto \left(y1 \cdot j\right) \cdot \left(x \cdot i - \color{blue}{y3 \cdot y4}\right) \]

   9. Simplified 68.3%

      \[\leadsto \color{blue}{\left(y1 \cdot j\right) \cdot \left(x \cdot i - y3 \cdot y4\right)} \]

   if -1.81999999999999996e171 < j < -1.3499999999999999e-47

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. +-commutative 34.0%

         \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) + \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      2. fma-def 37.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y4 \cdot y1 - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right)} \]

      3. *-commutative 37.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, \color{blue}{y1 \cdot y4} - y5 \cdot y0, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

      4. *-commutative 37.4%

         \[\leadsto \mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - \color{blue}{y0 \cdot y5}, \left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) \]

   3. Simplified 40.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.0%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 40.3%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{z \cdot k} - j \cdot x\right) \cdot b\right) \]

      2. *-commutative 40.3%

         \[\leadsto y0 \cdot \left(\left(z \cdot k - \color{blue}{x \cdot j}\right) \cdot b\right) \]

   9. Simplified 40.3%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(z \cdot k - x \cdot j\right) \cdot b\right)} \]

   if -1.3499999999999999e-47 < j < -1.44999999999999988e-274

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 33.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 33.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 46.7%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 46.7%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 46.7%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 46.7%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 46.7%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if -1.44999999999999988e-274 < j < 3.7000000000000002e-190

   1. Initial program 47.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 47.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 47.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 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. Step-by-step derivation

      1. associate--l+ 39.5%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 37.3%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 37.3%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 37.3%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 37.3%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if 3.7000000000000002e-190 < j < 1.12000000000000008e162

   1. Initial program 35.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 46.5%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.5%

         \[\leadsto y4 \cdot \left(c \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 46.5%

         \[\leadsto y4 \cdot \left(c \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 46.5%

      \[\leadsto y4 \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 1.12000000000000008e162 < j

   1. Initial program 3.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 3.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 3.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 21.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 47.0%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.82 \cdot 10^{+171}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-47}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-274}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{-190}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+162}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \end{array} \]

Alternative 31: 22.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-20}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-38}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(y \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-182}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 620000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -1.5e+36)
   (* c (* y4 (* y y3)))
   (if (<= y -2.9e-20)
     (* c (* y2 (* t (- y4))))
     (if (<= y -1.3e-38)
       (* (* x i) (* y (- c)))
       (if (<= y -8.6e-182)
         (* y0 (* c (* x y2)))
         (if (<= y 620000.0) (* i (* (* z t) c)) (* a (* (* x y) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.5e+36) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= -2.9e-20) {
		tmp = c * (y2 * (t * -y4));
	} else if (y <= -1.3e-38) {
		tmp = (x * i) * (y * -c);
	} else if (y <= -8.6e-182) {
		tmp = y0 * (c * (x * y2));
	} else if (y <= 620000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-1.5d+36)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= (-2.9d-20)) then
        tmp = c * (y2 * (t * -y4))
    else if (y <= (-1.3d-38)) then
        tmp = (x * i) * (y * -c)
    else if (y <= (-8.6d-182)) then
        tmp = y0 * (c * (x * y2))
    else if (y <= 620000.0d0) then
        tmp = i * ((z * t) * c)
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -1.5e+36) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= -2.9e-20) {
		tmp = c * (y2 * (t * -y4));
	} else if (y <= -1.3e-38) {
		tmp = (x * i) * (y * -c);
	} else if (y <= -8.6e-182) {
		tmp = y0 * (c * (x * y2));
	} else if (y <= 620000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -1.5e+36:
		tmp = c * (y4 * (y * y3))
	elif y <= -2.9e-20:
		tmp = c * (y2 * (t * -y4))
	elif y <= -1.3e-38:
		tmp = (x * i) * (y * -c)
	elif y <= -8.6e-182:
		tmp = y0 * (c * (x * y2))
	elif y <= 620000.0:
		tmp = i * ((z * t) * c)
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -1.5e+36)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= -2.9e-20)
		tmp = Float64(c * Float64(y2 * Float64(t * Float64(-y4))));
	elseif (y <= -1.3e-38)
		tmp = Float64(Float64(x * i) * Float64(y * Float64(-c)));
	elseif (y <= -8.6e-182)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (y <= 620000.0)
		tmp = Float64(i * Float64(Float64(z * t) * c));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -1.5e+36)
		tmp = c * (y4 * (y * y3));
	elseif (y <= -2.9e-20)
		tmp = c * (y2 * (t * -y4));
	elseif (y <= -1.3e-38)
		tmp = (x * i) * (y * -c);
	elseif (y <= -8.6e-182)
		tmp = y0 * (c * (x * y2));
	elseif (y <= 620000.0)
		tmp = i * ((z * t) * c);
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -1.5e+36], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e-20], N[(c * N[(y2 * N[(t * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-38], N[(N[(x * i), $MachinePrecision] * N[(y * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.6e-182], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 620000.0], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.5e36

   1. Initial program 22.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 22.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 22.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 49.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 49.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 49.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 49.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 44.6%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 38.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -1.5e36 < y < -2.9e-20

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 33.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.5%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 33.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 33.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 40.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x - y4 \cdot t\right) \cdot y2\right)} \]

   8. Taylor expanded in y0 around 0 47.5%

      \[\leadsto c \cdot \left(\color{blue}{\left(-1 \cdot \left(y4 \cdot t\right)\right)} \cdot y2\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 47.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(-y4 \cdot t\right)} \cdot y2\right) \]

      2. distribute-rgt-neg-in 47.5%

         \[\leadsto c \cdot \left(\color{blue}{\left(y4 \cdot \left(-t\right)\right)} \cdot y2\right) \]

   10. Simplified 47.5%

       \[\leadsto c \cdot \left(\color{blue}{\left(y4 \cdot \left(-t\right)\right)} \cdot y2\right) \]

   if -2.9e-20 < y < -1.30000000000000005e-38

   1. Initial program 15.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 15.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 15.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 42.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 42.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 57.9%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.9%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 57.9%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 57.9%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   10. Taylor expanded in z around 0 58.1%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot \left(y \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 58.1%

          \[\leadsto \color{blue}{-c \cdot \left(i \cdot \left(y \cdot x\right)\right)} \]

       2. associate-*r* 58.1%

          \[\leadsto -c \cdot \color{blue}{\left(\left(i \cdot y\right) \cdot x\right)} \]

       3. *-commutative 58.1%

          \[\leadsto -c \cdot \left(\color{blue}{\left(y \cdot i\right)} \cdot x\right) \]

       4. associate-*r* 58.1%

          \[\leadsto -c \cdot \color{blue}{\left(y \cdot \left(i \cdot x\right)\right)} \]

       5. associate-*r* 58.1%

          \[\leadsto -\color{blue}{\left(c \cdot y\right) \cdot \left(i \cdot x\right)} \]

       6. *-commutative 58.1%

          \[\leadsto -\left(c \cdot y\right) \cdot \color{blue}{\left(x \cdot i\right)} \]

   12. Simplified 58.1%

       \[\leadsto \color{blue}{-\left(c \cdot y\right) \cdot \left(x \cdot i\right)} \]

   if -1.30000000000000005e-38 < y < -8.6e-182

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 50.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 50.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 50.7%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y0 around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 33.4%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot x\right)\right) \cdot c} \]

      2. associate-*l* 33.4%

         \[\leadsto \color{blue}{y0 \cdot \left(\left(y2 \cdot x\right) \cdot c\right)} \]

      3. *-commutative 33.4%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(x \cdot y2\right)} \cdot c\right) \]

   10. Simplified 33.4%

       \[\leadsto \color{blue}{y0 \cdot \left(\left(x \cdot y2\right) \cdot c\right)} \]

   if -8.6e-182 < y < 6.2e5

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 35.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 35.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 35.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 35.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 32.2%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in z around inf 24.4%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 24.4%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 25.6%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   10. Simplified 25.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   if 6.2e5 < y

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 42.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 42.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \cdot a \]
   8. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto \color{blue}{\left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \cdot a \]

      2. *-commutative 42.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot y} - t \cdot z\right) \cdot b\right) \cdot a \]

      3. *-commutative 42.4%

         \[\leadsto \left(\left(x \cdot y - \color{blue}{z \cdot t}\right) \cdot b\right) \cdot a \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(x \cdot y - z \cdot t\right) \cdot b\right)} \cdot a \]

   10. Taylor expanded in x around inf 40.8%

       \[\leadsto \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \cdot a \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-20}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(t \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-38}:\\ \;\;\;\;\left(x \cdot i\right) \cdot \left(y \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-182}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 620000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 32: 21.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.75 \cdot 10^{-180}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 180000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -8.2e-22)
   (* c (* y4 (* y y3)))
   (if (<= y -2.5e-88)
     (* a (* y (* y3 (- y5))))
     (if (<= y -3.75e-180)
       (* y0 (* c (* x y2)))
       (if (<= y 180000.0) (* i (* (* z t) c)) (* a (* (* x y) b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -8.2e-22) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= -2.5e-88) {
		tmp = a * (y * (y3 * -y5));
	} else if (y <= -3.75e-180) {
		tmp = y0 * (c * (x * y2));
	} else if (y <= 180000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-8.2d-22)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= (-2.5d-88)) then
        tmp = a * (y * (y3 * -y5))
    else if (y <= (-3.75d-180)) then
        tmp = y0 * (c * (x * y2))
    else if (y <= 180000.0d0) then
        tmp = i * ((z * t) * c)
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -8.2e-22) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= -2.5e-88) {
		tmp = a * (y * (y3 * -y5));
	} else if (y <= -3.75e-180) {
		tmp = y0 * (c * (x * y2));
	} else if (y <= 180000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -8.2e-22:
		tmp = c * (y4 * (y * y3))
	elif y <= -2.5e-88:
		tmp = a * (y * (y3 * -y5))
	elif y <= -3.75e-180:
		tmp = y0 * (c * (x * y2))
	elif y <= 180000.0:
		tmp = i * ((z * t) * c)
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -8.2e-22)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= -2.5e-88)
		tmp = Float64(a * Float64(y * Float64(y3 * Float64(-y5))));
	elseif (y <= -3.75e-180)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	elseif (y <= 180000.0)
		tmp = Float64(i * Float64(Float64(z * t) * c));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -8.2e-22)
		tmp = c * (y4 * (y * y3));
	elseif (y <= -2.5e-88)
		tmp = a * (y * (y3 * -y5));
	elseif (y <= -3.75e-180)
		tmp = y0 * (c * (x * y2));
	elseif (y <= 180000.0)
		tmp = i * ((z * t) * c);
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -8.2e-22], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-88], N[(a * N[(y * N[(y3 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.75e-180], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 180000.0], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.1999999999999999e-22

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 46.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.2%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.2%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 44.0%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 34.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -8.1999999999999999e-22 < y < -2.50000000000000004e-88

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 29.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 30.0%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 30.0%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 30.0%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 30.0%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 30.0%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 44.4%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 44.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 44.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 44.4%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 44.4%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 44.4%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around 0 43.8%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 43.8%

          \[\leadsto \color{blue}{-a \cdot \left(y \cdot \left(y3 \cdot y5\right)\right)} \]

       2. *-commutative 43.8%

          \[\leadsto -a \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   12. Simplified 43.8%

       \[\leadsto \color{blue}{-a \cdot \left(\left(y3 \cdot y5\right) \cdot y\right)} \]

   if -2.50000000000000004e-88 < y < -3.75000000000000008e-180

   1. Initial program 28.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 28.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 53.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 53.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 53.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 53.2%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y0 around inf 42.6%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 42.6%

         \[\leadsto \color{blue}{\left(y0 \cdot \left(y2 \cdot x\right)\right) \cdot c} \]

      2. associate-*l* 42.6%

         \[\leadsto \color{blue}{y0 \cdot \left(\left(y2 \cdot x\right) \cdot c\right)} \]

      3. *-commutative 42.6%

         \[\leadsto y0 \cdot \left(\color{blue}{\left(x \cdot y2\right)} \cdot c\right) \]

   10. Simplified 42.6%

       \[\leadsto \color{blue}{y0 \cdot \left(\left(x \cdot y2\right) \cdot c\right)} \]

   if -3.75000000000000008e-180 < y < 1.8e5

   1. Initial program 34.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 35.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 35.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 35.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 35.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 32.2%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in z around inf 24.4%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 24.4%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 25.6%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   10. Simplified 25.6%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   if 1.8e5 < y

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 42.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 42.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \cdot a \]
   8. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto \color{blue}{\left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \cdot a \]

      2. *-commutative 42.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot y} - t \cdot z\right) \cdot b\right) \cdot a \]

      3. *-commutative 42.4%

         \[\leadsto \left(\left(x \cdot y - \color{blue}{z \cdot t}\right) \cdot b\right) \cdot a \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(x \cdot y - z \cdot t\right) \cdot b\right)} \cdot a \]

   10. Taylor expanded in x around inf 40.8%

       \[\leadsto \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \cdot a \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(y \cdot \left(y3 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y \leq -3.75 \cdot 10^{-180}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 180000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 33: 27.8% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.35 \cdot 10^{-29} \lor \neg \left(y3 \leq 7.2 \cdot 10^{+196}\right):\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -1.35e-29) (not (<= y3 7.2e+196)))
   (* c (* y4 (* y y3)))
   (* c (* i (- (* z t) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -1.35e-29) || !(y3 <= 7.2e+196)) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = c * (i * ((z * t) - (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y3 <= (-1.35d-29)) .or. (.not. (y3 <= 7.2d+196))) then
        tmp = c * (y4 * (y * y3))
    else
        tmp = c * (i * ((z * t) - (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -1.35e-29) || !(y3 <= 7.2e+196)) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = c * (i * ((z * t) - (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y3 <= -1.35e-29) or not (y3 <= 7.2e+196):
		tmp = c * (y4 * (y * y3))
	else:
		tmp = c * (i * ((z * t) - (x * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y3 <= -1.35e-29) || !(y3 <= 7.2e+196))
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	else
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y3 <= -1.35e-29) || ~((y3 <= 7.2e+196)))
		tmp = c * (y4 * (y * y3));
	else
		tmp = c * (i * ((z * t) - (x * y)));
	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[y3, -1.35e-29], N[Not[LessEqual[y3, 7.2e+196]], $MachinePrecision]], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < -1.35000000000000011e-29 or 7.20000000000000015e196 < y3

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 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. Step-by-step derivation

      1. associate--l+ 46.1%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.1%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 41.0%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 36.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -1.35000000000000011e-29 < y3 < 7.20000000000000015e196

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 36.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 36.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 36.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 36.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 32.3%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.3%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 32.3%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 32.3%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.35 \cdot 10^{-29} \lor \neg \left(y3 \leq 7.2 \cdot 10^{+196}\right):\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \end{array} \]

Alternative 34: 29.5% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.7 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 3.45 \cdot 10^{+193}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.7e-29)
   (* c (* y (- (* y3 y4) (* x i))))
   (if (<= y3 3.45e+193)
     (* c (* i (- (* z t) (* x y))))
     (* c (* y4 (* y y3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.7e-29) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y3 <= 3.45e+193) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else {
		tmp = c * (y4 * (y * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-1.7d-29)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y3 <= 3.45d+193) then
        tmp = c * (i * ((z * t) - (x * y)))
    else
        tmp = c * (y4 * (y * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.7e-29) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y3 <= 3.45e+193) {
		tmp = c * (i * ((z * t) - (x * y)));
	} else {
		tmp = c * (y4 * (y * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -1.7e-29:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y3 <= 3.45e+193:
		tmp = c * (i * ((z * t) - (x * y)))
	else:
		tmp = c * (y4 * (y * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -1.7e-29)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y3 <= 3.45e+193)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	else
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -1.7e-29)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y3 <= 3.45e+193)
		tmp = c * (i * ((z * t) - (x * y)));
	else
		tmp = c * (y4 * (y * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -1.7e-29], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.45e+193], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -1.69999999999999986e-29

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 43.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 39.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 39.0%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 39.0%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 39.0%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 39.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if -1.69999999999999986e-29 < y3 < 3.45e193

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 36.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 36.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 36.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 36.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 32.3%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.3%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 32.3%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 32.3%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if 3.45e193 < y3

   1. Initial program 19.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 19.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 19.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 52.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 52.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 52.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 52.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 48.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 43.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.7 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 3.45 \cdot 10^{+193}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]

Alternative 35: 30.0% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.25 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+191}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.25e-29)
   (* c (* y (- (* y3 y4) (* x i))))
   (if (<= y3 1.4e+191)
     (* c (* i (- (* z t) (* x y))))
     (* 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 tmp;
	if (y3 <= -1.25e-29) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y3 <= 1.4e+191) {
		tmp = c * (i * ((z * t) - (x * y)));
	} 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) :: tmp
    if (y3 <= (-1.25d-29)) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (y3 <= 1.4d+191) then
        tmp = c * (i * ((z * t) - (x * y)))
    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 tmp;
	if (y3 <= -1.25e-29) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (y3 <= 1.4e+191) {
		tmp = c * (i * ((z * t) - (x * y)));
	} 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):
	tmp = 0
	if y3 <= -1.25e-29:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif y3 <= 1.4e+191:
		tmp = c * (i * ((z * t) - (x * y)))
	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)
	tmp = 0.0
	if (y3 <= -1.25e-29)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (y3 <= 1.4e+191)
		tmp = Float64(c * Float64(i * Float64(Float64(z * t) - Float64(x * y))));
	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)
	tmp = 0.0;
	if (y3 <= -1.25e-29)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (y3 <= 1.4e+191)
		tmp = c * (i * ((z * t) - (x * y)));
	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_] := If[LessEqual[y3, -1.25e-29], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.4e+191], N[(c * N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y3 < -1.24999999999999996e-29

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 43.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 43.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 43.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 43.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y around -inf 39.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y4 \cdot y3 + -1 \cdot \left(i \cdot x\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.0%

         \[\leadsto c \cdot \left(y \cdot \left(y4 \cdot y3 + \color{blue}{\left(-i \cdot x\right)}\right)\right) \]

      2. unsub-neg 39.0%

         \[\leadsto c \cdot \left(y \cdot \color{blue}{\left(y4 \cdot y3 - i \cdot x\right)}\right) \]

      3. *-commutative 39.0%

         \[\leadsto c \cdot \left(y \cdot \left(\color{blue}{y3 \cdot y4} - i \cdot x\right)\right) \]

      4. *-commutative 39.0%

         \[\leadsto c \cdot \left(y \cdot \left(y3 \cdot y4 - \color{blue}{x \cdot i}\right)\right) \]

   9. Simplified 39.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)} \]

   if -1.24999999999999996e-29 < y3 < 1.3999999999999999e191

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 36.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 36.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 36.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 36.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 32.5%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.5%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 32.5%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 32.5%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   if 1.3999999999999999e191 < y3

   1. Initial program 18.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 18.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 18.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 55.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 55.0%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 55.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 55.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y0 around -inf 47.0%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.25 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+191}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \end{array} \]

Alternative 36: 22.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 380000000:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (* y y3)))))
   (if (<= y -1.5e-34)
     t_1
     (if (<= y -2.2e-179)
       (* c (* y0 (* x y2)))
       (if (<= y 380000000.0) (* c (* (* z t) i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * (y * y3));
	double tmp;
	if (y <= -1.5e-34) {
		tmp = t_1;
	} else if (y <= -2.2e-179) {
		tmp = c * (y0 * (x * y2));
	} else if (y <= 380000000.0) {
		tmp = c * ((z * t) * i);
	} 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 * (y4 * (y * y3))
    if (y <= (-1.5d-34)) then
        tmp = t_1
    else if (y <= (-2.2d-179)) then
        tmp = c * (y0 * (x * y2))
    else if (y <= 380000000.0d0) then
        tmp = c * ((z * t) * i)
    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 * (y4 * (y * y3));
	double tmp;
	if (y <= -1.5e-34) {
		tmp = t_1;
	} else if (y <= -2.2e-179) {
		tmp = c * (y0 * (x * y2));
	} else if (y <= 380000000.0) {
		tmp = c * ((z * t) * i);
	} 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 * (y4 * (y * y3))
	tmp = 0
	if y <= -1.5e-34:
		tmp = t_1
	elif y <= -2.2e-179:
		tmp = c * (y0 * (x * y2))
	elif y <= 380000000.0:
		tmp = c * ((z * t) * i)
	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(y4 * Float64(y * y3)))
	tmp = 0.0
	if (y <= -1.5e-34)
		tmp = t_1;
	elseif (y <= -2.2e-179)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y <= 380000000.0)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	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 * (y4 * (y * y3));
	tmp = 0.0;
	if (y <= -1.5e-34)
		tmp = t_1;
	elseif (y <= -2.2e-179)
		tmp = c * (y0 * (x * y2));
	elseif (y <= 380000000.0)
		tmp = c * ((z * t) * i);
	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[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e-34], t$95$1, If[LessEqual[y, -2.2e-179], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 380000000.0], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5e-34 or 3.8e8 < y

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 25.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 38.8%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 31.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -1.5e-34 < y < -2.20000000000000005e-179

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 52.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 52.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 52.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 52.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y4 around 0 45.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around inf 32.3%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -2.20000000000000005e-179 < y < 3.8e8

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 35.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 35.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 35.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 35.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 26.5%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 26.5%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 26.5%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 26.5%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   10. Taylor expanded in z around inf 24.1%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 24.1%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 24.1%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 380000000:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]

Alternative 37: 22.1% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3300000000000:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -1.8e-34)
   (* c (* y4 (* y y3)))
   (if (<= y -1.06e-179)
     (* c (* y0 (* x y2)))
     (if (<= y 3300000000000.0) (* c (* (* z t) i)) (* c (* y3 (* y 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 (y <= -1.8e-34) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= -1.06e-179) {
		tmp = c * (y0 * (x * y2));
	} else if (y <= 3300000000000.0) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = c * (y3 * (y * 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 (y <= (-1.8d-34)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= (-1.06d-179)) then
        tmp = c * (y0 * (x * y2))
    else if (y <= 3300000000000.0d0) then
        tmp = c * ((z * t) * i)
    else
        tmp = c * (y3 * (y * 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 (y <= -1.8e-34) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= -1.06e-179) {
		tmp = c * (y0 * (x * y2));
	} else if (y <= 3300000000000.0) {
		tmp = c * ((z * t) * i);
	} else {
		tmp = c * (y3 * (y * 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 y <= -1.8e-34:
		tmp = c * (y4 * (y * y3))
	elif y <= -1.06e-179:
		tmp = c * (y0 * (x * y2))
	elif y <= 3300000000000.0:
		tmp = c * ((z * t) * i)
	else:
		tmp = c * (y3 * (y * 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 (y <= -1.8e-34)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= -1.06e-179)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y <= 3300000000000.0)
		tmp = Float64(c * Float64(Float64(z * t) * i));
	else
		tmp = Float64(c * Float64(y3 * Float64(y * 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 (y <= -1.8e-34)
		tmp = c * (y4 * (y * y3));
	elseif (y <= -1.06e-179)
		tmp = c * (y0 * (x * y2));
	elseif (y <= 3300000000000.0)
		tmp = c * ((z * t) * i);
	else
		tmp = c * (y3 * (y * 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[y, -1.8e-34], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.06e-179], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3300000000000.0], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.80000000000000004e-34

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 24.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 43.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 34.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -1.80000000000000004e-34 < y < -1.0599999999999999e-179

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 52.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 52.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 52.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 52.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y4 around 0 45.8%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around inf 32.3%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -1.0599999999999999e-179 < y < 3.3e12

   1. Initial program 35.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 35.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 35.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 35.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 35.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 35.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 35.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 26.5%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 26.5%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 26.5%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 26.5%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   10. Taylor expanded in z around inf 24.1%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 24.1%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 24.1%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if 3.3e12 < y

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 27.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 29.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 29.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 29.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 29.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 31.8%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 25.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 30.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   10. Simplified 30.6%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-34}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3300000000000:\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 38: 21.6% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 82000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -4.6e-30)
   (* c (* y4 (* y y3)))
   (if (<= y 82000.0)
     (* i (* (* z t) c))
     (if (<= y 2.75e+216) (* y (* a (* x b))) (* c (* y3 (* y 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 (y <= -4.6e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 82000.0) {
		tmp = i * ((z * t) * c);
	} else if (y <= 2.75e+216) {
		tmp = y * (a * (x * b));
	} else {
		tmp = c * (y3 * (y * 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 (y <= (-4.6d-30)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= 82000.0d0) then
        tmp = i * ((z * t) * c)
    else if (y <= 2.75d+216) then
        tmp = y * (a * (x * b))
    else
        tmp = c * (y3 * (y * 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 (y <= -4.6e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 82000.0) {
		tmp = i * ((z * t) * c);
	} else if (y <= 2.75e+216) {
		tmp = y * (a * (x * b));
	} else {
		tmp = c * (y3 * (y * 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 y <= -4.6e-30:
		tmp = c * (y4 * (y * y3))
	elif y <= 82000.0:
		tmp = i * ((z * t) * c)
	elif y <= 2.75e+216:
		tmp = y * (a * (x * b))
	else:
		tmp = c * (y3 * (y * 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 (y <= -4.6e-30)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= 82000.0)
		tmp = Float64(i * Float64(Float64(z * t) * c));
	elseif (y <= 2.75e+216)
		tmp = Float64(y * Float64(a * Float64(x * b)));
	else
		tmp = Float64(c * Float64(y3 * Float64(y * 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 (y <= -4.6e-30)
		tmp = c * (y4 * (y * y3));
	elseif (y <= 82000.0)
		tmp = i * ((z * t) * c);
	elseif (y <= 2.75e+216)
		tmp = y * (a * (x * b));
	else
		tmp = c * (y3 * (y * 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[y, -4.6e-30], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 82000.0], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+216], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.59999999999999968e-30

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 44.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 35.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -4.59999999999999968e-30 < y < 82000

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 32.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 32.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 36.2%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in z around inf 22.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 22.3%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 23.9%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   10. Simplified 23.9%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   if 82000 < y < 2.75e216

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 36.5%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.5%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.7%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 45.7%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around inf 37.5%

       \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 37.5%

          \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(x \cdot b\right)}\right) \]

   12. Simplified 37.5%

       \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(x \cdot b\right)\right)} \]

   if 2.75e216 < y

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 37.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 37.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 37.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 37.4%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 48.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   10. Simplified 48.4%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 82000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 39: 22.1% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 80000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+215}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -5.4e-30)
   (* c (* y4 (* y y3)))
   (if (<= y 80000.0)
     (* i (* (* z t) c))
     (if (<= y 3.1e+215) (* (* y a) (* x b)) (* c (* y3 (* y 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 (y <= -5.4e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 80000.0) {
		tmp = i * ((z * t) * c);
	} else if (y <= 3.1e+215) {
		tmp = (y * a) * (x * b);
	} else {
		tmp = c * (y3 * (y * 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 (y <= (-5.4d-30)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= 80000.0d0) then
        tmp = i * ((z * t) * c)
    else if (y <= 3.1d+215) then
        tmp = (y * a) * (x * b)
    else
        tmp = c * (y3 * (y * 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 (y <= -5.4e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 80000.0) {
		tmp = i * ((z * t) * c);
	} else if (y <= 3.1e+215) {
		tmp = (y * a) * (x * b);
	} else {
		tmp = c * (y3 * (y * 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 y <= -5.4e-30:
		tmp = c * (y4 * (y * y3))
	elif y <= 80000.0:
		tmp = i * ((z * t) * c)
	elif y <= 3.1e+215:
		tmp = (y * a) * (x * b)
	else:
		tmp = c * (y3 * (y * 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 (y <= -5.4e-30)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= 80000.0)
		tmp = Float64(i * Float64(Float64(z * t) * c));
	elseif (y <= 3.1e+215)
		tmp = Float64(Float64(y * a) * Float64(x * b));
	else
		tmp = Float64(c * Float64(y3 * Float64(y * 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 (y <= -5.4e-30)
		tmp = c * (y4 * (y * y3));
	elseif (y <= 80000.0)
		tmp = i * ((z * t) * c);
	elseif (y <= 3.1e+215)
		tmp = (y * a) * (x * b);
	else
		tmp = c * (y3 * (y * 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[y, -5.4e-30], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 80000.0], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+215], N[(N[(y * a), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.39999999999999975e-30

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 44.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 35.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -5.39999999999999975e-30 < y < 8e4

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 32.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 32.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 36.2%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in z around inf 22.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 22.3%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 23.9%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   10. Simplified 23.9%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   if 8e4 < y < 3.0999999999999999e215

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 36.5%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 36.5%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 36.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 36.5%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 36.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.7%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. +-commutative 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)} \]

      3. mul-1-neg 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right) \]

      4. unsub-neg 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)} \]

      5. *-commutative 45.7%

         \[\leadsto \left(a \cdot y\right) \cdot \left(\color{blue}{x \cdot b} - y3 \cdot y5\right) \]

   9. Simplified 45.7%

      \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(x \cdot b - y3 \cdot y5\right)} \]

   10. Taylor expanded in x around inf 40.0%

       \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(b \cdot x\right)} \]
   11. Step-by-step derivation

       1. *-commutative 40.0%

          \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(x \cdot b\right)} \]

   12. Simplified 40.0%

       \[\leadsto \left(a \cdot y\right) \cdot \color{blue}{\left(x \cdot b\right)} \]

   if 3.0999999999999999e215 < y

   1. Initial program 36.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 36.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 37.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.4%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 37.4%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 37.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 37.4%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 48.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   10. Simplified 48.4%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 80000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+215}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 40: 22.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+26} \lor \neg \left(z \leq 2.1 \cdot 10^{+22}\right):\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= z -1.8e+26) (not (<= z 2.1e+22)))
   (* c (* (* z t) 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 ((z <= -1.8e+26) || !(z <= 2.1e+22)) {
		tmp = c * ((z * t) * 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 ((z <= (-1.8d+26)) .or. (.not. (z <= 2.1d+22))) then
        tmp = c * ((z * t) * 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 ((z <= -1.8e+26) || !(z <= 2.1e+22)) {
		tmp = c * ((z * t) * 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 (z <= -1.8e+26) or not (z <= 2.1e+22):
		tmp = c * ((z * t) * 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 ((z <= -1.8e+26) || !(z <= 2.1e+22))
		tmp = Float64(c * Float64(Float64(z * t) * 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 ((z <= -1.8e+26) || ~((z <= 2.1e+22)))
		tmp = c * ((z * t) * 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[Or[LessEqual[z, -1.8e+26], N[Not[LessEqual[z, 2.1e+22]], $MachinePrecision]], N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000012e26 or 2.0999999999999998e22 < z

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 25.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 31.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 31.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 31.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 31.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in i around inf 34.9%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

      2. *-commutative 34.9%

         \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

   9. Simplified 34.9%

      \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

   10. Taylor expanded in z around inf 32.3%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 32.3%

          \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

   12. Simplified 32.3%

       \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

   if -1.80000000000000012e26 < z < 2.0999999999999998e22

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 32.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 32.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 45.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 45.7%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 45.7%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 45.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y4 around 0 32.3%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - i \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y2 around inf 20.0%

      \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+26} \lor \neg \left(z \leq 2.1 \cdot 10^{+22}\right):\\ \;\;\;\;c \cdot \left(\left(z \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 41: 21.9% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -6.5e-30)
   (* c (* y4 (* y y3)))
   (if (<= y 1.28e+126) (* i (* (* z t) c)) (* c (* y3 (* y 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 (y <= -6.5e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 1.28e+126) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = c * (y3 * (y * 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 (y <= (-6.5d-30)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= 1.28d+126) then
        tmp = i * ((z * t) * c)
    else
        tmp = c * (y3 * (y * 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 (y <= -6.5e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 1.28e+126) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = c * (y3 * (y * 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 y <= -6.5e-30:
		tmp = c * (y4 * (y * y3))
	elif y <= 1.28e+126:
		tmp = i * ((z * t) * c)
	else:
		tmp = c * (y3 * (y * 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 (y <= -6.5e-30)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= 1.28e+126)
		tmp = Float64(i * Float64(Float64(z * t) * c));
	else
		tmp = Float64(c * Float64(y3 * Float64(y * 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 (y <= -6.5e-30)
		tmp = c * (y4 * (y * y3));
	elseif (y <= 1.28e+126)
		tmp = i * ((z * t) * c);
	else
		tmp = c * (y3 * (y * 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[y, -6.5e-30], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.28e+126], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(y * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000005e-30

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 44.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 35.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -6.5000000000000005e-30 < y < 1.27999999999999993e126

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 31.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 36.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 36.9%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 36.9%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 36.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 34.8%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in z around inf 21.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 21.1%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 23.2%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   10. Simplified 23.2%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   if 1.27999999999999993e126 < y

   1. Initial program 30.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 30.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 33.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.8%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 33.8%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 28.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(y4 \cdot y\right) \cdot y3\right)} \]

   10. Simplified 37.5%

       \[\leadsto \color{blue}{c \cdot \left(\left(y4 \cdot y\right) \cdot y3\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+126}:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4\right)\right)\\ \end{array} \]

Alternative 42: 22.0% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 840000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -8.5e-30)
   (* c (* y4 (* y y3)))
   (if (<= y 840000.0) (* i (* (* z t) c)) (* a (* x (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -8.5e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 840000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-8.5d-30)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= 840000.0d0) then
        tmp = i * ((z * t) * c)
    else
        tmp = a * (x * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -8.5e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 840000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * (x * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -8.5e-30:
		tmp = c * (y4 * (y * y3))
	elif y <= 840000.0:
		tmp = i * ((z * t) * c)
	else:
		tmp = a * (x * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -8.5e-30)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= 840000.0)
		tmp = Float64(i * Float64(Float64(z * t) * c));
	else
		tmp = Float64(a * Float64(x * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -8.5e-30)
		tmp = c * (y4 * (y * y3));
	elseif (y <= 840000.0)
		tmp = i * ((z * t) * c);
	else
		tmp = a * (x * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -8.5e-30], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 840000.0], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999931e-30

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 44.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 35.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -8.49999999999999931e-30 < y < 8.4e5

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 32.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 32.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 36.2%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in z around inf 22.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 22.3%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 23.9%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   10. Simplified 23.9%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   if 8.4e5 < y

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 42.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 42.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \cdot a \]
   8. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto \color{blue}{\left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \cdot a \]

      2. *-commutative 42.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot y} - t \cdot z\right) \cdot b\right) \cdot a \]

      3. *-commutative 42.4%

         \[\leadsto \left(\left(x \cdot y - \color{blue}{z \cdot t}\right) \cdot b\right) \cdot a \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(x \cdot y - z \cdot t\right) \cdot b\right)} \cdot a \]

   10. Taylor expanded in x around inf 35.6%

       \[\leadsto \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \cdot a \]
   11. Step-by-step derivation

       1. *-commutative 35.6%

          \[\leadsto \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \cdot a \]

       2. *-commutative 35.6%

          \[\leadsto \left(\color{blue}{\left(x \cdot b\right)} \cdot y\right) \cdot a \]

       3. associate-*l* 39.1%

          \[\leadsto \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \cdot a \]

   12. Simplified 39.1%

       \[\leadsto \color{blue}{\left(x \cdot \left(b \cdot y\right)\right)} \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 840000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(y \cdot b\right)\right)\\ \end{array} \]

Alternative 43: 21.9% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 440000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -6.5e-30)
   (* c (* y4 (* y y3)))
   (if (<= y 440000.0) (* i (* (* z t) c)) (* a (* (* x y) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -6.5e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 440000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-6.5d-30)) then
        tmp = c * (y4 * (y * y3))
    else if (y <= 440000.0d0) then
        tmp = i * ((z * t) * c)
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -6.5e-30) {
		tmp = c * (y4 * (y * y3));
	} else if (y <= 440000.0) {
		tmp = i * ((z * t) * c);
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -6.5e-30:
		tmp = c * (y4 * (y * y3))
	elif y <= 440000.0:
		tmp = i * ((z * t) * c)
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -6.5e-30)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y <= 440000.0)
		tmp = Float64(i * Float64(Float64(z * t) * c));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -6.5e-30)
		tmp = c * (y4 * (y * y3));
	elseif (y <= 440000.0)
		tmp = i * ((z * t) * c);
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -6.5e-30], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 440000.0], N[(i * N[(N[(z * t), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000005e-30

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 24.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 c around inf 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.3%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 46.3%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 44.1%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in y3 around inf 35.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -6.5000000000000005e-30 < y < 4.4e5

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 32.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   3. Simplified 32.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in c around inf 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.6%

         \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. mul-1-neg 39.6%

         \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   6. Simplified 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   7. Taylor expanded in y2 around inf 36.2%

      \[\leadsto c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(\color{blue}{y0 \cdot \left(y2 \cdot x\right)} - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

   8. Taylor expanded in z around inf 22.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 22.3%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*l* 23.9%

         \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   10. Simplified 23.9%

       \[\leadsto \color{blue}{i \cdot \left(\left(t \cdot z\right) \cdot c\right)} \]

   if 4.4e5 < y

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Step-by-step derivation

      1. associate-+l- 29.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

   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 a around inf 42.1%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 42.1%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in b around inf 42.4%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \cdot a \]
   8. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto \color{blue}{\left(\left(y \cdot x - t \cdot z\right) \cdot b\right)} \cdot a \]

      2. *-commutative 42.4%

         \[\leadsto \left(\left(\color{blue}{x \cdot y} - t \cdot z\right) \cdot b\right) \cdot a \]

      3. *-commutative 42.4%

         \[\leadsto \left(\left(x \cdot y - \color{blue}{z \cdot t}\right) \cdot b\right) \cdot a \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{\left(\left(x \cdot y - z \cdot t\right) \cdot b\right)} \cdot a \]

   10. Taylor expanded in x around inf 40.8%

       \[\leadsto \left(\color{blue}{\left(y \cdot x\right)} \cdot b\right) \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 440000:\\ \;\;\;\;i \cdot \left(\left(z \cdot t\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 44: 17.1% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(\left(z \cdot t\right) \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* c (* (* z t) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return c * ((z * t) * i);
}

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 = c * ((z * t) * i)
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 c * ((z * t) * i);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return c * ((z * t) * i)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(c * Float64(Float64(z * t) * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = c * ((z * t) * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(c * N[(N[(z * t), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.4%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
2. Step-by-step derivation

   1. associate-+l- 29.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\right)} \]

3. Simplified 29.4%

   \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

4. Taylor expanded in c around inf 39.6%

   \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + y0 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
5. Step-by-step derivation

   1. associate--l+ 39.6%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   2. mul-1-neg 39.6%

      \[\leadsto c \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right)} + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) \]

6. Simplified 39.6%

   \[\leadsto \color{blue}{c \cdot \left(\left(-i \cdot \left(y \cdot x - t \cdot z\right)\right) + \left(y0 \cdot \left(y2 \cdot x - y3 \cdot z\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

7. Taylor expanded in i around inf 27.9%

   \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z - y \cdot x\right)\right)} \]
8. Step-by-step derivation

   1. *-commutative 27.9%

      \[\leadsto c \cdot \left(i \cdot \left(\color{blue}{z \cdot t} - y \cdot x\right)\right) \]

   2. *-commutative 27.9%

      \[\leadsto c \cdot \left(i \cdot \left(z \cdot t - \color{blue}{x \cdot y}\right)\right) \]

9. Simplified 27.9%

   \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t - x \cdot y\right)\right)} \]

10. Taylor expanded in z around inf 17.9%

    \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(t \cdot z\right)\right)} \]
11. Step-by-step derivation

    1. *-commutative 17.9%

       \[\leadsto c \cdot \left(i \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

12. Simplified 17.9%

    \[\leadsto c \cdot \color{blue}{\left(i \cdot \left(z \cdot t\right)\right)} \]

13. Final simplification 17.9%

    \[\leadsto c \cdot \left(\left(z \cdot t\right) \cdot i\right) \]

Developer target: 28.1% 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 2023176 
(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)))))