Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.8% → 41.3%

Time: 1.2min

Alternatives: 38

Speedup: 2.3×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.8% 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: 41.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := t \cdot y2 - y \cdot y3\\ t_3 := j \cdot y3 - k \cdot y2\\ t_4 := y5 \cdot \left(a \cdot t\_2 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t\_3\right)\right)\\ t_5 := x \cdot y2 - z \cdot y3\\ t_6 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t\_5 + y4 \cdot t\_3\right)\right)\\ t_7 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;y5 \leq -9.5 \cdot 10^{+163}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq -1.18 \cdot 10^{+23}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_1 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_7\right)\\ \mathbf{elif}\;y5 \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y5 \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t\_5\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 0.0102:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot t\_7\right)\\ \mathbf{elif}\;y5 \leq 4.8 \cdot 10^{+109}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y5 \leq 2.15 \cdot 10^{+167}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;y5 \leq 5.5 \cdot 10^{+223}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot t\_1 + t\_2 \cdot t\_7\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y1 y4) (* y0 y5)))
        (t_2 (- (* t y2) (* y y3)))
        (t_3 (- (* j y3) (* k y2)))
        (t_4 (* y5 (+ (* a t_2) (+ (* i (- (* y k) (* t j))) (* y0 t_3)))))
        (t_5 (- (* x y2) (* z y3)))
        (t_6 (* y1 (- (* i (- (* x j) (* z k))) (+ (* a t_5) (* y4 t_3)))))
        (t_7 (- (* a y5) (* c y4))))
   (if (<= y5 -9.5e+163)
     t_4
     (if (<= y5 -1.18e+23)
       (* y2 (+ (+ (* k t_1) (* x (- (* c y0) (* a y1)))) (* t t_7)))
       (if (<= y5 -3.2e-50)
         t_6
         (if (<= y5 8.2e-159)
           (*
            c
            (+
             (+ (* i (- (* z t) (* x y))) (* y0 t_5))
             (* y4 (- (* y y3) (* t y2)))))
           (if (<= y5 0.0102)
             (*
              t
              (+
               (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
               (* y2 t_7)))
             (if (<= y5 4.8e+109)
               t_6
               (if (<= y5 2.15e+167)
                 (* (* j y5) (- (* y0 y3) (* t i)))
                 (if (<= y5 5.5e+223)
                   (+
                    (* b (* y4 (- (* t j) (* y k))))
                    (+ (* (- (* k y2) (* j y3)) t_1) (* t_2 t_7)))
                   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 = (y1 * y4) - (y0 * y5);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	double t_5 = (x * y2) - (z * y3);
	double t_6 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_5) + (y4 * t_3)));
	double t_7 = (a * y5) - (c * y4);
	double tmp;
	if (y5 <= -9.5e+163) {
		tmp = t_4;
	} else if (y5 <= -1.18e+23) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * t_7));
	} else if (y5 <= -3.2e-50) {
		tmp = t_6;
	} else if (y5 <= 8.2e-159) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_5)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 0.0102) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_7));
	} else if (y5 <= 4.8e+109) {
		tmp = t_6;
	} else if (y5 <= 2.15e+167) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (y5 <= 5.5e+223) {
		tmp = (b * (y4 * ((t * j) - (y * k)))) + ((((k * y2) - (j * y3)) * t_1) + (t_2 * t_7));
	} 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) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = (y1 * y4) - (y0 * y5)
    t_2 = (t * y2) - (y * y3)
    t_3 = (j * y3) - (k * y2)
    t_4 = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_3)))
    t_5 = (x * y2) - (z * y3)
    t_6 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_5) + (y4 * t_3)))
    t_7 = (a * y5) - (c * y4)
    if (y5 <= (-9.5d+163)) then
        tmp = t_4
    else if (y5 <= (-1.18d+23)) then
        tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * t_7))
    else if (y5 <= (-3.2d-50)) then
        tmp = t_6
    else if (y5 <= 8.2d-159) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_5)) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 0.0102d0) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_7))
    else if (y5 <= 4.8d+109) then
        tmp = t_6
    else if (y5 <= 2.15d+167) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (y5 <= 5.5d+223) then
        tmp = (b * (y4 * ((t * j) - (y * k)))) + ((((k * y2) - (j * y3)) * t_1) + (t_2 * t_7))
    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 = (y1 * y4) - (y0 * y5);
	double t_2 = (t * y2) - (y * y3);
	double t_3 = (j * y3) - (k * y2);
	double t_4 = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	double t_5 = (x * y2) - (z * y3);
	double t_6 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_5) + (y4 * t_3)));
	double t_7 = (a * y5) - (c * y4);
	double tmp;
	if (y5 <= -9.5e+163) {
		tmp = t_4;
	} else if (y5 <= -1.18e+23) {
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * t_7));
	} else if (y5 <= -3.2e-50) {
		tmp = t_6;
	} else if (y5 <= 8.2e-159) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_5)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 0.0102) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_7));
	} else if (y5 <= 4.8e+109) {
		tmp = t_6;
	} else if (y5 <= 2.15e+167) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (y5 <= 5.5e+223) {
		tmp = (b * (y4 * ((t * j) - (y * k)))) + ((((k * y2) - (j * y3)) * t_1) + (t_2 * t_7));
	} 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 = (y1 * y4) - (y0 * y5)
	t_2 = (t * y2) - (y * y3)
	t_3 = (j * y3) - (k * y2)
	t_4 = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_3)))
	t_5 = (x * y2) - (z * y3)
	t_6 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_5) + (y4 * t_3)))
	t_7 = (a * y5) - (c * y4)
	tmp = 0
	if y5 <= -9.5e+163:
		tmp = t_4
	elif y5 <= -1.18e+23:
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * t_7))
	elif y5 <= -3.2e-50:
		tmp = t_6
	elif y5 <= 8.2e-159:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_5)) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 0.0102:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_7))
	elif y5 <= 4.8e+109:
		tmp = t_6
	elif y5 <= 2.15e+167:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif y5 <= 5.5e+223:
		tmp = (b * (y4 * ((t * j) - (y * k)))) + ((((k * y2) - (j * y3)) * t_1) + (t_2 * t_7))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	t_3 = Float64(Float64(j * y3) - Float64(k * y2))
	t_4 = Float64(y5 * Float64(Float64(a * t_2) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_3))))
	t_5 = Float64(Float64(x * y2) - Float64(z * y3))
	t_6 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_5) + Float64(y4 * t_3))))
	t_7 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (y5 <= -9.5e+163)
		tmp = t_4;
	elseif (y5 <= -1.18e+23)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_1) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * t_7)));
	elseif (y5 <= -3.2e-50)
		tmp = t_6;
	elseif (y5 <= 8.2e-159)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_5)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 0.0102)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * t_7)));
	elseif (y5 <= 4.8e+109)
		tmp = t_6;
	elseif (y5 <= 2.15e+167)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (y5 <= 5.5e+223)
		tmp = Float64(Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1) + Float64(t_2 * t_7)));
	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 = (y1 * y4) - (y0 * y5);
	t_2 = (t * y2) - (y * y3);
	t_3 = (j * y3) - (k * y2);
	t_4 = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_3)));
	t_5 = (x * y2) - (z * y3);
	t_6 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_5) + (y4 * t_3)));
	t_7 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (y5 <= -9.5e+163)
		tmp = t_4;
	elseif (y5 <= -1.18e+23)
		tmp = y2 * (((k * t_1) + (x * ((c * y0) - (a * y1)))) + (t * t_7));
	elseif (y5 <= -3.2e-50)
		tmp = t_6;
	elseif (y5 <= 8.2e-159)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_5)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 0.0102)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_7));
	elseif (y5 <= 4.8e+109)
		tmp = t_6;
	elseif (y5 <= 2.15e+167)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (y5 <= 5.5e+223)
		tmp = (b * (y4 * ((t * j) - (y * k)))) + ((((k * y2) - (j * y3)) * t_1) + (t_2 * t_7));
	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[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(a * t$95$2), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$5), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -9.5e+163], t$95$4, If[LessEqual[y5, -1.18e+23], N[(y2 * N[(N[(N[(k * t$95$1), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.2e-50], t$95$6, If[LessEqual[y5, 8.2e-159], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 0.0102], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.8e+109], t$95$6, If[LessEqual[y5, 2.15e+167], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.5e+223], N[(N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$2 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y5 < -9.50000000000000053e163 or 5.4999999999999999e223 < y5

   1. Initial program 24.6%

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

   3. Simplified 24.6%

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

   5. Taylor expanded in y5 around -inf 73.5%

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

   if -9.50000000000000053e163 < y5 < -1.18e23

   1. Initial program 19.2%

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

   3. Taylor expanded in y2 around inf 66.0%

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

   if -1.18e23 < y5 < -3.2e-50 or 0.010200000000000001 < y5 < 4.79999999999999975e109

   1. Initial program 39.2%

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

   3. Simplified 39.2%

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

   5. Taylor expanded in y1 around inf 58.9%

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

   if -3.2e-50 < y5 < 8.20000000000000029e-159

   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. Add Preprocessing

   3. Taylor expanded in c around inf 59.2%

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

   if 8.20000000000000029e-159 < y5 < 0.010200000000000001

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   5. Taylor expanded in t around inf 71.2%

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

   if 4.79999999999999975e109 < y5 < 2.1500000000000001e167

   1. Initial program 21.4%

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

   3. Simplified 26.6%

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

   5. Taylor expanded in y5 around -inf 48.1%

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

   6. Taylor expanded in j around inf 69.1%

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

      1. *-commutative 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-*l* 64.1%

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

      4. +-commutative 64.1%

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

      5. mul-1-neg 64.1%

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

      6. unsub-neg 64.1%

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

      7. *-commutative 64.1%

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

   8. Simplified 64.1%

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

   if 2.1500000000000001e167 < y5 < 5.4999999999999999e223

   1. Initial program 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in y4 around inf 79.8%

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

      1. *-commutative 79.8%

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

   7. Simplified 79.8%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(t \cdot j - k \cdot y\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -9.5 \cdot 10^{+163}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -1.18 \cdot 10^{+23}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -3.2 \cdot 10^{-50}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 8.2 \cdot 10^{-159}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 0.0102:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 4.8 \cdot 10^{+109}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.15 \cdot 10^{+167}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;y5 \leq 5.5 \cdot 10^{+223}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + \left(\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(t \cdot y2 - y \cdot y3\right) \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * t_1)) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + (y4 * ((y * y3) - (t * y2)))) / y0) + 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 = (x * y2) - (z * y3);
	double t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * t_1)) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + (y4 * ((y * y3) - (t * y2)))) / y0) + 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 = (x * y2) - (z * y3)
	t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * t_1)) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = y0 * (c * ((((t * (z * i)) + (y4 * ((y * y3) - (t * y2)))) / y0) + 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(x * y2) - Float64(z * y3))
	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(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(Float64(Float64(c * y0) - Float64(a * y1)) * t_1)) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))) / y0) + 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 = (x * y2) - (z * y3);
	t_2 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((c * y0) - (a * y1)) * t_1)) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = y0 * (c * ((((t * (z * i)) + (y4 * ((y * y3) - (t * y2)))) / y0) + 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[(x * y2), $MachinePrecision] - N[(z * y3), $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[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$1), $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] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y0), $MachinePrecision] + 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 93.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 39.6%

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

   4. Taylor expanded in x around 0 38.4%

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

      1. *-commutative 38.4%

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

   6. Simplified 38.4%

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

   7. Taylor expanded in y0 around inf 35.3%

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

      1. +-commutative 35.3%

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

      2. associate-/l* 37.7%

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

      3. distribute-lft-out 41.4%

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

      4. associate-*r* 42.0%

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

      5. *-commutative 42.0%

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

      6. associate-*l* 42.6%

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

      7. *-commutative 42.6%

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

      8. *-commutative 42.6%

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

      9. *-commutative 42.6%

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

      10. *-commutative 42.6%

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

   9. Simplified 42.6%

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

4. Final simplification 61.3%

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

Alternative 3: 41.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := t \cdot j - y \cdot k\\ t_5 := y4 \cdot t\_1\\ t_6 := c \cdot \left(\left(y0 \cdot t\_3 - \left(x \cdot y\right) \cdot i\right) + t\_5\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+173}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -3.45 \cdot 10^{+112}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -4.7 \cdot 10^{+59}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -1080000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_4 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_1\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-69}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-209}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_4\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + t\_5}{y0} + t\_3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2)))))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (- (* t j) (* y k)))
        (t_5 (* y4 t_1))
        (t_6 (* c (+ (- (* y0 t_3) (* (* x y) i)) t_5))))
   (if (<= c -3e+173)
     t_6
     (if (<= c -3.45e+112)
       (* (- (* z i) (* y2 y4)) (* t c))
       (if (<= c -4.7e+59)
         t_6
         (if (<= c -1080000000000.0)
           (* y4 (+ (+ (* b t_4) (* y1 (- (* k y2) (* j y3)))) (* c t_1)))
           (if (<= c -9.5e-69)
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
               (* t (- (* a y5) (* c y4)))))
             (if (<= c -5.6e-195)
               (* b (* x (- (* y a) (* j y0))))
               (if (<= c 1.7e-308)
                 t_2
                 (if (<= c 2.2e-209)
                   (*
                    b
                    (+
                     (+ (* a (- (* x y) (* z t))) (* y4 t_4))
                     (* y0 (- (* z k) (* x j)))))
                   (if (<= c 4.5e+34)
                     t_2
                     (*
                      y0
                      (* c (+ (/ (+ (* t (* z i)) t_5) y0) t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (t * j) - (y * k);
	double t_5 = y4 * t_1;
	double t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5);
	double tmp;
	if (c <= -3e+173) {
		tmp = t_6;
	} else if (c <= -3.45e+112) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -4.7e+59) {
		tmp = t_6;
	} else if (c <= -1080000000000.0) {
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	} else if (c <= -9.5e-69) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -5.6e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= 1.7e-308) {
		tmp = t_2;
	} else if (c <= 2.2e-209) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 4.5e+34) {
		tmp = t_2;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    t_3 = (x * y2) - (z * y3)
    t_4 = (t * j) - (y * k)
    t_5 = y4 * t_1
    t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5)
    if (c <= (-3d+173)) then
        tmp = t_6
    else if (c <= (-3.45d+112)) then
        tmp = ((z * i) - (y2 * y4)) * (t * c)
    else if (c <= (-4.7d+59)) then
        tmp = t_6
    else if (c <= (-1080000000000.0d0)) then
        tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
    else if (c <= (-9.5d-69)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= (-5.6d-195)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (c <= 1.7d-308) then
        tmp = t_2
    else if (c <= 2.2d-209) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))))
    else if (c <= 4.5d+34) then
        tmp = t_2
    else
        tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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 = (y * y3) - (t * y2);
	double t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = (t * j) - (y * k);
	double t_5 = y4 * t_1;
	double t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5);
	double tmp;
	if (c <= -3e+173) {
		tmp = t_6;
	} else if (c <= -3.45e+112) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -4.7e+59) {
		tmp = t_6;
	} else if (c <= -1080000000000.0) {
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	} else if (c <= -9.5e-69) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -5.6e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= 1.7e-308) {
		tmp = t_2;
	} else if (c <= 2.2e-209) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 4.5e+34) {
		tmp = t_2;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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 = (y * y3) - (t * y2)
	t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	t_3 = (x * y2) - (z * y3)
	t_4 = (t * j) - (y * k)
	t_5 = y4 * t_1
	t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5)
	tmp = 0
	if c <= -3e+173:
		tmp = t_6
	elif c <= -3.45e+112:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	elif c <= -4.7e+59:
		tmp = t_6
	elif c <= -1080000000000.0:
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
	elif c <= -9.5e-69:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif c <= -5.6e-195:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif c <= 1.7e-308:
		tmp = t_2
	elif c <= 2.2e-209:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))))
	elif c <= 4.5e+34:
		tmp = t_2
	else:
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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(y * y3) - Float64(t * y2))
	t_2 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(y4 * t_1)
	t_6 = Float64(c * Float64(Float64(Float64(y0 * t_3) - Float64(Float64(x * y) * i)) + t_5))
	tmp = 0.0
	if (c <= -3e+173)
		tmp = t_6;
	elseif (c <= -3.45e+112)
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(t * c));
	elseif (c <= -4.7e+59)
		tmp = t_6;
	elseif (c <= -1080000000000.0)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_4) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_1)));
	elseif (c <= -9.5e-69)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -5.6e-195)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (c <= 1.7e-308)
		tmp = t_2;
	elseif (c <= 2.2e-209)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_4)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (c <= 4.5e+34)
		tmp = t_2;
	else
		tmp = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + t_5) / y0) + 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 = (y * y3) - (t * y2);
	t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	t_3 = (x * y2) - (z * y3);
	t_4 = (t * j) - (y * k);
	t_5 = y4 * t_1;
	t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5);
	tmp = 0.0;
	if (c <= -3e+173)
		tmp = t_6;
	elseif (c <= -3.45e+112)
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	elseif (c <= -4.7e+59)
		tmp = t_6;
	elseif (c <= -1080000000000.0)
		tmp = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	elseif (c <= -9.5e-69)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= -5.6e-195)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (c <= 1.7e-308)
		tmp = t_2;
	elseif (c <= 2.2e-209)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))));
	elseif (c <= 4.5e+34)
		tmp = t_2;
	else
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(c * N[(N[(N[(y0 * t$95$3), $MachinePrecision] - N[(N[(x * y), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+173], t$95$6, If[LessEqual[c, -3.45e+112], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.7e+59], t$95$6, If[LessEqual[c, -1080000000000.0], N[(y4 * N[(N[(N[(b * t$95$4), $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[c, -9.5e-69], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.6e-195], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e-308], t$95$2, If[LessEqual[c, 2.2e-209], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e+34], t$95$2, N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision] / y0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -2.9999999999999998e173 or -3.45e112 < c < -4.7e59

   1. Initial program 23.1%

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

   3. Taylor expanded in c around inf 62.1%

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

   4. Taylor expanded in x around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

      4. distribute-rgt-neg-in 64.6%

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

   6. Simplified 64.6%

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

   if -2.9999999999999998e173 < c < -3.45e112

   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. Add Preprocessing

   3. Taylor expanded in c around inf 72.7%

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

   4. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in t around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*r* 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-*l* 82.4%

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

   9. Simplified 82.4%

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

   if -4.7e59 < c < -1.08e12

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   5. Taylor expanded in y4 around inf 69.9%

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

   if -1.08e12 < c < -9.50000000000000094e-69

   1. Initial program 18.8%

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

   3. Taylor expanded in y2 around inf 75.2%

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

   if -9.50000000000000094e-69 < c < -5.60000000000000007e-195

   1. Initial program 28.8%

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

   3. Simplified 28.8%

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

   5. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 54.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -5.60000000000000007e-195 < c < 1.7000000000000002e-308 or 2.2000000000000001e-209 < c < 4.5e34

   1. Initial program 45.4%

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

   3. Simplified 46.7%

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

   5. Taylor expanded in y5 around -inf 58.0%

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

   if 1.7000000000000002e-308 < c < 2.2000000000000001e-209

   1. Initial program 25.5%

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

   3. Simplified 25.5%

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

   5. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 4.5e34 < c

   1. Initial program 37.5%

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

   3. Taylor expanded in c around inf 61.3%

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

   4. Taylor expanded in x around 0 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in y0 around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate-/l* 62.7%

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

      3. distribute-lft-out 69.8%

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

      4. associate-*r* 68.1%

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

      5. *-commutative 68.1%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

      8. *-commutative 69.8%

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

      9. *-commutative 69.8%

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

      10. *-commutative 69.8%

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

   9. Simplified 69.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(i \cdot z\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot y4}{y0} + \left(y2 \cdot x - y3 \cdot z\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.45 \cdot 10^{+112}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -4.7 \cdot 10^{+59}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1080000000000:\\ \;\;\;\;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}\;c \leq -9.5 \cdot 10^{-69}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-308}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-209}:\\ \;\;\;\;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}\;c \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 40.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := y4 \cdot t\_1\\ t_5 := c \cdot \left(\left(y0 \cdot t\_3 - \left(x \cdot y\right) \cdot i\right) + t\_4\right)\\ \mathbf{if}\;c \leq -4.1 \cdot 10^{+173}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+112}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;c \leq -490000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_1\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-69}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 10^{-209}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + t\_4}{y0} + t\_3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2)))))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (* y4 t_1))
        (t_5 (* c (+ (- (* y0 t_3) (* (* x y) i)) t_4))))
   (if (<= c -4.1e+173)
     t_5
     (if (<= c -1.65e+112)
       (* (- (* z i) (* y2 y4)) (* t c))
       (if (<= c -8.2e+55)
         t_5
         (if (<= c -490000000000.0)
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
             (* c t_1)))
           (if (<= c -2.7e-69)
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
               (* t (- (* a y5) (* c y4)))))
             (if (<= c -6e-195)
               (* b (* x (- (* y a) (* j y0))))
               (if (<= c 4.2e-301)
                 t_2
                 (if (<= c 1e-209)
                   (* b (* j (- (* t y4) (* x y0))))
                   (if (<= c 3.1e+34)
                     t_2
                     (*
                      y0
                      (* c (+ (/ (+ (* t (* z i)) t_4) y0) t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y4 * t_1;
	double t_5 = c * (((y0 * t_3) - ((x * y) * i)) + t_4);
	double tmp;
	if (c <= -4.1e+173) {
		tmp = t_5;
	} else if (c <= -1.65e+112) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -8.2e+55) {
		tmp = t_5;
	} else if (c <= -490000000000.0) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	} else if (c <= -2.7e-69) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -6e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= 4.2e-301) {
		tmp = t_2;
	} else if (c <= 1e-209) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (c <= 3.1e+34) {
		tmp = t_2;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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 = (y * y3) - (t * y2)
    t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    t_3 = (x * y2) - (z * y3)
    t_4 = y4 * t_1
    t_5 = c * (((y0 * t_3) - ((x * y) * i)) + t_4)
    if (c <= (-4.1d+173)) then
        tmp = t_5
    else if (c <= (-1.65d+112)) then
        tmp = ((z * i) - (y2 * y4)) * (t * c)
    else if (c <= (-8.2d+55)) then
        tmp = t_5
    else if (c <= (-490000000000.0d0)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
    else if (c <= (-2.7d-69)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= (-6d-195)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (c <= 4.2d-301) then
        tmp = t_2
    else if (c <= 1d-209) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (c <= 3.1d+34) then
        tmp = t_2
    else
        tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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 = (y * y3) - (t * y2);
	double t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y4 * t_1;
	double t_5 = c * (((y0 * t_3) - ((x * y) * i)) + t_4);
	double tmp;
	if (c <= -4.1e+173) {
		tmp = t_5;
	} else if (c <= -1.65e+112) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -8.2e+55) {
		tmp = t_5;
	} else if (c <= -490000000000.0) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	} else if (c <= -2.7e-69) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -6e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= 4.2e-301) {
		tmp = t_2;
	} else if (c <= 1e-209) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (c <= 3.1e+34) {
		tmp = t_2;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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 = (y * y3) - (t * y2)
	t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	t_3 = (x * y2) - (z * y3)
	t_4 = y4 * t_1
	t_5 = c * (((y0 * t_3) - ((x * y) * i)) + t_4)
	tmp = 0
	if c <= -4.1e+173:
		tmp = t_5
	elif c <= -1.65e+112:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	elif c <= -8.2e+55:
		tmp = t_5
	elif c <= -490000000000.0:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
	elif c <= -2.7e-69:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif c <= -6e-195:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif c <= 4.2e-301:
		tmp = t_2
	elif c <= 1e-209:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif c <= 3.1e+34:
		tmp = t_2
	else:
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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(y * y3) - Float64(t * y2))
	t_2 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(y4 * t_1)
	t_5 = Float64(c * Float64(Float64(Float64(y0 * t_3) - Float64(Float64(x * y) * i)) + t_4))
	tmp = 0.0
	if (c <= -4.1e+173)
		tmp = t_5;
	elseif (c <= -1.65e+112)
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(t * c));
	elseif (c <= -8.2e+55)
		tmp = t_5;
	elseif (c <= -490000000000.0)
		tmp = 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)));
	elseif (c <= -2.7e-69)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -6e-195)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (c <= 4.2e-301)
		tmp = t_2;
	elseif (c <= 1e-209)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (c <= 3.1e+34)
		tmp = t_2;
	else
		tmp = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + t_4) / y0) + 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 = (y * y3) - (t * y2);
	t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	t_3 = (x * y2) - (z * y3);
	t_4 = y4 * t_1;
	t_5 = c * (((y0 * t_3) - ((x * y) * i)) + t_4);
	tmp = 0.0;
	if (c <= -4.1e+173)
		tmp = t_5;
	elseif (c <= -1.65e+112)
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	elseif (c <= -8.2e+55)
		tmp = t_5;
	elseif (c <= -490000000000.0)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	elseif (c <= -2.7e-69)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= -6e-195)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (c <= 4.2e-301)
		tmp = t_2;
	elseif (c <= 1e-209)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (c <= 3.1e+34)
		tmp = t_2;
	else
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(c * N[(N[(N[(y0 * t$95$3), $MachinePrecision] - N[(N[(x * y), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.1e+173], t$95$5, If[LessEqual[c, -1.65e+112], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e+55], t$95$5, If[LessEqual[c, -490000000000.0], 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[c, -2.7e-69], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6e-195], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e-301], t$95$2, If[LessEqual[c, 1e-209], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.1e+34], t$95$2, N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] / y0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -4.09999999999999976e173 or -1.64999999999999995e112 < c < -8.19999999999999962e55

   1. Initial program 23.1%

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

   3. Taylor expanded in c around inf 62.1%

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

   4. Taylor expanded in x around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

      4. distribute-rgt-neg-in 64.6%

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

   6. Simplified 64.6%

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

   if -4.09999999999999976e173 < c < -1.64999999999999995e112

   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. Add Preprocessing

   3. Taylor expanded in c around inf 72.7%

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

   4. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in t around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*r* 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-*l* 82.4%

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

   9. Simplified 82.4%

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

   if -8.19999999999999962e55 < c < -4.9e11

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   5. Taylor expanded in y4 around inf 69.9%

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

   if -4.9e11 < c < -2.6999999999999997e-69

   1. Initial program 18.8%

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

   3. Taylor expanded in y2 around inf 75.2%

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

   if -2.6999999999999997e-69 < c < -6e-195

   1. Initial program 28.8%

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

   3. Simplified 28.8%

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

   5. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 54.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -6e-195 < c < 4.1999999999999997e-301 or 1e-209 < c < 3.09999999999999977e34

   1. Initial program 45.4%

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

   3. Simplified 46.7%

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

   5. Taylor expanded in y5 around -inf 58.0%

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

   if 4.1999999999999997e-301 < c < 1e-209

   1. Initial program 25.5%

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

   3. Simplified 25.5%

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

   5. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 41.8%

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

   if 3.09999999999999977e34 < c

   1. Initial program 37.5%

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

   3. Taylor expanded in c around inf 61.3%

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

   4. Taylor expanded in x around 0 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in y0 around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate-/l* 62.7%

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

      3. distribute-lft-out 69.8%

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

      4. associate-*r* 68.1%

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

      5. *-commutative 68.1%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

      8. *-commutative 69.8%

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

      9. *-commutative 69.8%

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

      10. *-commutative 69.8%

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

   9. Simplified 69.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(i \cdot z\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot y4}{y0} + \left(y2 \cdot x - y3 \cdot z\right)\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+112}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -490000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-69}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-301}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;c \leq 10^{-209}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+34}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_1\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ t_5 := y4 \cdot t\_1\\ t_6 := c \cdot \left(\left(y0 \cdot t\_3 - \left(x \cdot y\right) \cdot i\right) + t\_5\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+173}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+55}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;c \leq -900000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-244}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+35}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + t\_5}{y0} + t\_3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y y3) (* t y2)))
        (t_2
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c t_1))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4))))))
        (t_5 (* y4 t_1))
        (t_6 (* c (+ (- (* y0 t_3) (* (* x y) i)) t_5))))
   (if (<= c -3e+173)
     t_6
     (if (<= c -3.4e+110)
       (* (- (* z i) (* y2 y4)) (* t c))
       (if (<= c -3.1e+55)
         t_6
         (if (<= c -900000000000.0)
           t_2
           (if (<= c -2.3e-61)
             t_4
             (if (<= c -6.2e-195)
               (* b (* x (- (* y a) (* j y0))))
               (if (<= c -3e-244)
                 (* (* j y5) (- (* y0 y3) (* t i)))
                 (if (<= c 2.5e-221)
                   t_2
                   (if (<= c 6e+35)
                     t_4
                     (*
                      y0
                      (* c (+ (/ (+ (* t (* z i)) t_5) y0) t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * y3) - (t * y2);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_5 = y4 * t_1;
	double t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5);
	double tmp;
	if (c <= -3e+173) {
		tmp = t_6;
	} else if (c <= -3.4e+110) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -3.1e+55) {
		tmp = t_6;
	} else if (c <= -900000000000.0) {
		tmp = t_2;
	} else if (c <= -2.3e-61) {
		tmp = t_4;
	} else if (c <= -6.2e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= -3e-244) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (c <= 2.5e-221) {
		tmp = t_2;
	} else if (c <= 6e+35) {
		tmp = t_4;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
    t_3 = (x * y2) - (z * y3)
    t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    t_5 = y4 * t_1
    t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5)
    if (c <= (-3d+173)) then
        tmp = t_6
    else if (c <= (-3.4d+110)) then
        tmp = ((z * i) - (y2 * y4)) * (t * c)
    else if (c <= (-3.1d+55)) then
        tmp = t_6
    else if (c <= (-900000000000.0d0)) then
        tmp = t_2
    else if (c <= (-2.3d-61)) then
        tmp = t_4
    else if (c <= (-6.2d-195)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (c <= (-3d-244)) then
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    else if (c <= 2.5d-221) then
        tmp = t_2
    else if (c <= 6d+35) then
        tmp = t_4
    else
        tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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 = (y * y3) - (t * y2);
	double t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double t_5 = y4 * t_1;
	double t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5);
	double tmp;
	if (c <= -3e+173) {
		tmp = t_6;
	} else if (c <= -3.4e+110) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -3.1e+55) {
		tmp = t_6;
	} else if (c <= -900000000000.0) {
		tmp = t_2;
	} else if (c <= -2.3e-61) {
		tmp = t_4;
	} else if (c <= -6.2e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= -3e-244) {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	} else if (c <= 2.5e-221) {
		tmp = t_2;
	} else if (c <= 6e+35) {
		tmp = t_4;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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 = (y * y3) - (t * y2)
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1))
	t_3 = (x * y2) - (z * y3)
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	t_5 = y4 * t_1
	t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5)
	tmp = 0
	if c <= -3e+173:
		tmp = t_6
	elif c <= -3.4e+110:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	elif c <= -3.1e+55:
		tmp = t_6
	elif c <= -900000000000.0:
		tmp = t_2
	elif c <= -2.3e-61:
		tmp = t_4
	elif c <= -6.2e-195:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif c <= -3e-244:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	elif c <= 2.5e-221:
		tmp = t_2
	elif c <= 6e+35:
		tmp = t_4
	else:
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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(y * y3) - Float64(t * y2))
	t_2 = 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)))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	t_5 = Float64(y4 * t_1)
	t_6 = Float64(c * Float64(Float64(Float64(y0 * t_3) - Float64(Float64(x * y) * i)) + t_5))
	tmp = 0.0
	if (c <= -3e+173)
		tmp = t_6;
	elseif (c <= -3.4e+110)
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(t * c));
	elseif (c <= -3.1e+55)
		tmp = t_6;
	elseif (c <= -900000000000.0)
		tmp = t_2;
	elseif (c <= -2.3e-61)
		tmp = t_4;
	elseif (c <= -6.2e-195)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (c <= -3e-244)
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	elseif (c <= 2.5e-221)
		tmp = t_2;
	elseif (c <= 6e+35)
		tmp = t_4;
	else
		tmp = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + t_5) / y0) + 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 = (y * y3) - (t * y2);
	t_2 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_1));
	t_3 = (x * y2) - (z * y3);
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	t_5 = y4 * t_1;
	t_6 = c * (((y0 * t_3) - ((x * y) * i)) + t_5);
	tmp = 0.0;
	if (c <= -3e+173)
		tmp = t_6;
	elseif (c <= -3.4e+110)
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	elseif (c <= -3.1e+55)
		tmp = t_6;
	elseif (c <= -900000000000.0)
		tmp = t_2;
	elseif (c <= -2.3e-61)
		tmp = t_4;
	elseif (c <= -6.2e-195)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (c <= -3e-244)
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	elseif (c <= 2.5e-221)
		tmp = t_2;
	elseif (c <= 6e+35)
		tmp = t_4;
	else
		tmp = y0 * (c * ((((t * (z * i)) + t_5) / y0) + 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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(c * N[(N[(N[(y0 * t$95$3), $MachinePrecision] - N[(N[(x * y), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+173], t$95$6, If[LessEqual[c, -3.4e+110], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.1e+55], t$95$6, If[LessEqual[c, -900000000000.0], t$95$2, If[LessEqual[c, -2.3e-61], t$95$4, If[LessEqual[c, -6.2e-195], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3e-244], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e-221], t$95$2, If[LessEqual[c, 6e+35], t$95$4, N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision] / y0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -2.9999999999999998e173 or -3.4000000000000001e110 < c < -3.09999999999999994e55

   1. Initial program 23.1%

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

   3. Taylor expanded in c around inf 62.1%

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

   4. Taylor expanded in x around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. distribute-rgt-neg-in 64.6%

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

      4. distribute-rgt-neg-in 64.6%

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

   6. Simplified 64.6%

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

   if -2.9999999999999998e173 < c < -3.4000000000000001e110

   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. Add Preprocessing

   3. Taylor expanded in c around inf 72.7%

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

   4. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in t around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*r* 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-*l* 82.4%

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

   9. Simplified 82.4%

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

   if -3.09999999999999994e55 < c < -9e11 or -3.0000000000000001e-244 < c < 2.49999999999999998e-221

   1. Initial program 46.5%

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

   3. Simplified 46.5%

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

   5. Taylor expanded in y4 around inf 54.2%

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

   if -9e11 < c < -2.29999999999999992e-61 or 2.49999999999999998e-221 < c < 5.99999999999999981e35

   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. Add Preprocessing

   3. Taylor expanded in y2 around inf 52.2%

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

   if -2.29999999999999992e-61 < c < -6.20000000000000005e-195

   1. Initial program 28.8%

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

   3. Simplified 28.8%

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

   5. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 54.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -6.20000000000000005e-195 < c < -3.0000000000000001e-244

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in y5 around -inf 60.0%

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

   6. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if 5.99999999999999981e35 < c

   1. Initial program 37.5%

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

   3. Taylor expanded in c around inf 61.3%

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

   4. Taylor expanded in x around 0 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in y0 around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate-/l* 62.7%

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

      3. distribute-lft-out 69.8%

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

      4. associate-*r* 68.1%

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

      5. *-commutative 68.1%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

      8. *-commutative 69.8%

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

      9. *-commutative 69.8%

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

      10. *-commutative 69.8%

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

   9. Simplified 69.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(i \cdot z\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot y4}{y0} + \left(y2 \cdot x - y3 \cdot z\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -900000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-244}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-221}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+35}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot y3 - k \cdot y2\\ t_2 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t\_1\right)\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot t\_3 + y4 \cdot t\_1\right)\right)\\ t_5 := a \cdot y5 - c \cdot y4\\ t_6 := t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot t\_5\right)\\ \mathbf{if}\;y5 \leq -6 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_5\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq 2.45 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t\_3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2400:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y5 \leq 1.45 \cdot 10^{+75}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y5 \leq 3.3 \cdot 10^{+103}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;y5 \leq 1.1 \cdot 10^{+138}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j y3) (* k y2)))
        (t_2
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i (- (* y k) (* t j))) (* y0 t_1)))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (* y1 (- (* i (- (* x j) (* z k))) (+ (* a t_3) (* y4 t_1)))))
        (t_5 (- (* a y5) (* c y4)))
        (t_6
         (*
          t
          (+
           (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
           (* y2 t_5)))))
   (if (<= y5 -6e+164)
     t_2
     (if (<= y5 -2.3e+18)
       (*
        y2
        (+
         (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
         (* t t_5)))
       (if (<= y5 -2.8e-49)
         t_4
         (if (<= y5 2.45e-163)
           (*
            c
            (+
             (+ (* i (- (* z t) (* x y))) (* y0 t_3))
             (* y4 (- (* y y3) (* t y2)))))
           (if (<= y5 2400.0)
             t_6
             (if (<= y5 1.45e+75)
               t_4
               (if (<= y5 3.3e+103)
                 t_6
                 (if (<= y5 1.1e+138) (* y0 (* y5 t_1)) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y3) - (k * y2);
	double t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * t_1)));
	double t_5 = (a * y5) - (c * y4);
	double t_6 = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_5));
	double tmp;
	if (y5 <= -6e+164) {
		tmp = t_2;
	} else if (y5 <= -2.3e+18) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_5));
	} else if (y5 <= -2.8e-49) {
		tmp = t_4;
	} else if (y5 <= 2.45e-163) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 2400.0) {
		tmp = t_6;
	} else if (y5 <= 1.45e+75) {
		tmp = t_4;
	} else if (y5 <= 3.3e+103) {
		tmp = t_6;
	} else if (y5 <= 1.1e+138) {
		tmp = y0 * (y5 * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (j * y3) - (k * y2)
    t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)))
    t_3 = (x * y2) - (z * y3)
    t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * t_1)))
    t_5 = (a * y5) - (c * y4)
    t_6 = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_5))
    if (y5 <= (-6d+164)) then
        tmp = t_2
    else if (y5 <= (-2.3d+18)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_5))
    else if (y5 <= (-2.8d-49)) then
        tmp = t_4
    else if (y5 <= 2.45d-163) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 2400.0d0) then
        tmp = t_6
    else if (y5 <= 1.45d+75) then
        tmp = t_4
    else if (y5 <= 3.3d+103) then
        tmp = t_6
    else if (y5 <= 1.1d+138) then
        tmp = y0 * (y5 * t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y3) - (k * y2);
	double t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * t_1)));
	double t_5 = (a * y5) - (c * y4);
	double t_6 = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_5));
	double tmp;
	if (y5 <= -6e+164) {
		tmp = t_2;
	} else if (y5 <= -2.3e+18) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_5));
	} else if (y5 <= -2.8e-49) {
		tmp = t_4;
	} else if (y5 <= 2.45e-163) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 2400.0) {
		tmp = t_6;
	} else if (y5 <= 1.45e+75) {
		tmp = t_4;
	} else if (y5 <= 3.3e+103) {
		tmp = t_6;
	} else if (y5 <= 1.1e+138) {
		tmp = y0 * (y5 * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y3) - (k * y2)
	t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)))
	t_3 = (x * y2) - (z * y3)
	t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * t_1)))
	t_5 = (a * y5) - (c * y4)
	t_6 = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_5))
	tmp = 0
	if y5 <= -6e+164:
		tmp = t_2
	elif y5 <= -2.3e+18:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_5))
	elif y5 <= -2.8e-49:
		tmp = t_4
	elif y5 <= 2.45e-163:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 2400.0:
		tmp = t_6
	elif y5 <= 1.45e+75:
		tmp = t_4
	elif y5 <= 3.3e+103:
		tmp = t_6
	elif y5 <= 1.1e+138:
		tmp = y0 * (y5 * t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * y3) - Float64(k * y2))
	t_2 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_1))))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(y1 * Float64(Float64(i * Float64(Float64(x * j) - Float64(z * k))) - Float64(Float64(a * t_3) + Float64(y4 * t_1))))
	t_5 = Float64(Float64(a * y5) - Float64(c * y4))
	t_6 = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * t_5)))
	tmp = 0.0
	if (y5 <= -6e+164)
		tmp = t_2;
	elseif (y5 <= -2.3e+18)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * t_5)));
	elseif (y5 <= -2.8e-49)
		tmp = t_4;
	elseif (y5 <= 2.45e-163)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_3)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 2400.0)
		tmp = t_6;
	elseif (y5 <= 1.45e+75)
		tmp = t_4;
	elseif (y5 <= 3.3e+103)
		tmp = t_6;
	elseif (y5 <= 1.1e+138)
		tmp = Float64(y0 * Float64(y5 * t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * y3) - (k * y2);
	t_2 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	t_3 = (x * y2) - (z * y3);
	t_4 = y1 * ((i * ((x * j) - (z * k))) - ((a * t_3) + (y4 * t_1)));
	t_5 = (a * y5) - (c * y4);
	t_6 = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_5));
	tmp = 0.0;
	if (y5 <= -6e+164)
		tmp = t_2;
	elseif (y5 <= -2.3e+18)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_5));
	elseif (y5 <= -2.8e-49)
		tmp = t_4;
	elseif (y5 <= 2.45e-163)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 2400.0)
		tmp = t_6;
	elseif (y5 <= 1.45e+75)
		tmp = t_4;
	elseif (y5 <= 3.3e+103)
		tmp = t_6;
	elseif (y5 <= 1.1e+138)
		tmp = y0 * (y5 * t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -6e+164], t$95$2, If[LessEqual[y5, -2.3e+18], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.8e-49], t$95$4, If[LessEqual[y5, 2.45e-163], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2400.0], t$95$6, If[LessEqual[y5, 1.45e+75], t$95$4, If[LessEqual[y5, 3.3e+103], t$95$6, If[LessEqual[y5, 1.1e+138], N[(y0 * N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -6.00000000000000001e164 or 1.1e138 < y5

   1. Initial program 31.0%

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

   3. Simplified 32.4%

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

   5. Taylor expanded in y5 around -inf 65.7%

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

   if -6.00000000000000001e164 < y5 < -2.3e18

   1. Initial program 19.2%

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

   3. Taylor expanded in y2 around inf 66.0%

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

   if -2.3e18 < y5 < -2.79999999999999997e-49 or 2400 < y5 < 1.4499999999999999e75

   1. Initial program 43.0%

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

   3. Simplified 43.0%

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

   5. Taylor expanded in y1 around inf 60.4%

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

   if -2.79999999999999997e-49 < y5 < 2.4500000000000001e-163

   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. Add Preprocessing

   3. Taylor expanded in c around inf 59.2%

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

   if 2.4500000000000001e-163 < y5 < 2400 or 1.4499999999999999e75 < y5 < 3.30000000000000009e103

   1. Initial program 34.2%

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

   3. Simplified 34.2%

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

   5. Taylor expanded in t around inf 74.2%

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

   if 3.30000000000000009e103 < y5 < 1.1e138

   1. Initial program 10.6%

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

   3. Simplified 10.6%

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

   5. Taylor expanded in y0 around inf 60.9%

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

   6. Taylor expanded in y5 around inf 61.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 61.2%

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

   8. Simplified 61.2%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -6 \cdot 10^{+164}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 2.45 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2400:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.45 \cdot 10^{+75}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right) - \left(a \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq 3.3 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 1.1 \cdot 10^{+138}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_3 := y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + t\_2}{y0} + t\_1\right)\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-45}:\\ \;\;\;\;\left(k \cdot y5\right) \cdot \left(y \cdot i - y0 \cdot y2\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-180}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-201}:\\ \;\;\;\;y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+129}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+232}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot t\_1 + i \cdot \left(z \cdot t\right)\right) + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2 (* y4 (- (* y y3) (* t y2))))
        (t_3 (* y0 (* c (+ (/ (+ (* t (* z i)) t_2) y0) t_1)))))
   (if (<= b -3.4e+137)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= b -6.5e-17)
       (* a (* b (- (* x y) (* z t))))
       (if (<= b -8.2e-45)
         (* (* k y5) (- (* y i) (* y0 y2)))
         (if (<= b -6e-180)
           t_3
           (if (<= b -1.3e-201)
             (* y2 (- (/ (* j (* y0 (* y3 y5))) y2) (* k (* y0 y5))))
             (if (<= b 1.1e+129)
               t_3
               (if (<= b 1.5e+167)
                 (* t (* y5 (- (* a y2) (* i j))))
                 (if (<= b 2.5e+232)
                   (* c (+ (+ (* y0 t_1) (* i (* z t))) t_2))
                   (* b (* j (- (* t y4) (* x y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = y4 * ((y * y3) - (t * y2));
	double t_3 = y0 * (c * ((((t * (z * i)) + t_2) / y0) + t_1));
	double tmp;
	if (b <= -3.4e+137) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -6.5e-17) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -8.2e-45) {
		tmp = (k * y5) * ((y * i) - (y0 * y2));
	} else if (b <= -6e-180) {
		tmp = t_3;
	} else if (b <= -1.3e-201) {
		tmp = y2 * (((j * (y0 * (y3 * y5))) / y2) - (k * (y0 * y5)));
	} else if (b <= 1.1e+129) {
		tmp = t_3;
	} else if (b <= 1.5e+167) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (b <= 2.5e+232) {
		tmp = c * (((y0 * t_1) + (i * (z * t))) + t_2);
	} else {
		tmp = b * (j * ((t * y4) - (x * 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) :: t_3
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = y4 * ((y * y3) - (t * y2))
    t_3 = y0 * (c * ((((t * (z * i)) + t_2) / y0) + t_1))
    if (b <= (-3.4d+137)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (b <= (-6.5d-17)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-8.2d-45)) then
        tmp = (k * y5) * ((y * i) - (y0 * y2))
    else if (b <= (-6d-180)) then
        tmp = t_3
    else if (b <= (-1.3d-201)) then
        tmp = y2 * (((j * (y0 * (y3 * y5))) / y2) - (k * (y0 * y5)))
    else if (b <= 1.1d+129) then
        tmp = t_3
    else if (b <= 1.5d+167) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (b <= 2.5d+232) then
        tmp = c * (((y0 * t_1) + (i * (z * t))) + t_2)
    else
        tmp = b * (j * ((t * y4) - (x * 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 = (x * y2) - (z * y3);
	double t_2 = y4 * ((y * y3) - (t * y2));
	double t_3 = y0 * (c * ((((t * (z * i)) + t_2) / y0) + t_1));
	double tmp;
	if (b <= -3.4e+137) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -6.5e-17) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -8.2e-45) {
		tmp = (k * y5) * ((y * i) - (y0 * y2));
	} else if (b <= -6e-180) {
		tmp = t_3;
	} else if (b <= -1.3e-201) {
		tmp = y2 * (((j * (y0 * (y3 * y5))) / y2) - (k * (y0 * y5)));
	} else if (b <= 1.1e+129) {
		tmp = t_3;
	} else if (b <= 1.5e+167) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (b <= 2.5e+232) {
		tmp = c * (((y0 * t_1) + (i * (z * t))) + t_2);
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (x * y2) - (z * y3)
	t_2 = y4 * ((y * y3) - (t * y2))
	t_3 = y0 * (c * ((((t * (z * i)) + t_2) / y0) + t_1))
	tmp = 0
	if b <= -3.4e+137:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif b <= -6.5e-17:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -8.2e-45:
		tmp = (k * y5) * ((y * i) - (y0 * y2))
	elif b <= -6e-180:
		tmp = t_3
	elif b <= -1.3e-201:
		tmp = y2 * (((j * (y0 * (y3 * y5))) / y2) - (k * (y0 * y5)))
	elif b <= 1.1e+129:
		tmp = t_3
	elif b <= 1.5e+167:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif b <= 2.5e+232:
		tmp = c * (((y0 * t_1) + (i * (z * t))) + t_2)
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(x * y2) - Float64(z * y3))
	t_2 = Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))
	t_3 = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + t_2) / y0) + t_1)))
	tmp = 0.0
	if (b <= -3.4e+137)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -6.5e-17)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -8.2e-45)
		tmp = Float64(Float64(k * y5) * Float64(Float64(y * i) - Float64(y0 * y2)));
	elseif (b <= -6e-180)
		tmp = t_3;
	elseif (b <= -1.3e-201)
		tmp = Float64(y2 * Float64(Float64(Float64(j * Float64(y0 * Float64(y3 * y5))) / y2) - Float64(k * Float64(y0 * y5))));
	elseif (b <= 1.1e+129)
		tmp = t_3;
	elseif (b <= 1.5e+167)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (b <= 2.5e+232)
		tmp = Float64(c * Float64(Float64(Float64(y0 * t_1) + Float64(i * Float64(z * t))) + t_2));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * 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 = (x * y2) - (z * y3);
	t_2 = y4 * ((y * y3) - (t * y2));
	t_3 = y0 * (c * ((((t * (z * i)) + t_2) / y0) + t_1));
	tmp = 0.0;
	if (b <= -3.4e+137)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (b <= -6.5e-17)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -8.2e-45)
		tmp = (k * y5) * ((y * i) - (y0 * y2));
	elseif (b <= -6e-180)
		tmp = t_3;
	elseif (b <= -1.3e-201)
		tmp = y2 * (((j * (y0 * (y3 * y5))) / y2) - (k * (y0 * y5)));
	elseif (b <= 1.1e+129)
		tmp = t_3;
	elseif (b <= 1.5e+167)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (b <= 2.5e+232)
		tmp = c * (((y0 * t_1) + (i * (z * t))) + t_2);
	else
		tmp = b * (j * ((t * y4) - (x * 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[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / y0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+137], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e-17], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.2e-45], N[(N[(k * y5), $MachinePrecision] * N[(N[(y * i), $MachinePrecision] - N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6e-180], t$95$3, If[LessEqual[b, -1.3e-201], N[(y2 * N[(N[(N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y2), $MachinePrecision] - N[(k * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+129], t$95$3, If[LessEqual[b, 1.5e+167], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+232], N[(c * N[(N[(N[(y0 * t$95$1), $MachinePrecision] + N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -3.39999999999999986e137

   1. Initial program 35.9%

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

   3. Simplified 35.9%

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

   5. Taylor expanded in b around inf 68.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 61.1%

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

   if -3.39999999999999986e137 < b < -6.4999999999999996e-17

   1. Initial program 37.5%

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

   3. Simplified 37.5%

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

   5. Taylor expanded in b around inf 34.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. distribute-lft-neg-out 47.6%

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

      3. +-commutative 47.6%

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

      4. *-commutative 47.6%

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

      5. cancel-sign-sub-inv 47.6%

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

      6. *-commutative 47.6%

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

   8. Simplified 47.6%

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

   if -6.4999999999999996e-17 < b < -8.1999999999999998e-45

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   5. Taylor expanded in k around inf 62.3%

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

   6. Taylor expanded in y5 around inf 62.9%

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

      1. associate-*r* 62.7%

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

      2. +-commutative 62.7%

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

      3. mul-1-neg 62.7%

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

      4. unsub-neg 62.7%

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

      5. *-commutative 62.7%

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

   8. Simplified 62.7%

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

   if -8.1999999999999998e-45 < b < -6.0000000000000001e-180 or -1.29999999999999991e-201 < b < 1.1e129

   1. Initial program 38.9%

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

   3. Taylor expanded in c around inf 53.0%

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

   4. Taylor expanded in x around 0 49.8%

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

      1. *-commutative 49.8%

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

   6. Simplified 49.8%

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

   7. Taylor expanded in y0 around inf 47.1%

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

      1. +-commutative 47.1%

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

      2. associate-/l* 49.0%

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

      3. distribute-lft-out 54.4%

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

      4. associate-*r* 55.0%

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

      5. *-commutative 55.0%

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

      6. associate-*l* 55.7%

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

      7. *-commutative 55.7%

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

      8. *-commutative 55.7%

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

      9. *-commutative 55.7%

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

      10. *-commutative 55.7%

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

   9. Simplified 55.7%

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

   if -6.0000000000000001e-180 < b < -1.29999999999999991e-201

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in y0 around inf 23.4%

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

   6. Taylor expanded in y5 around inf 46.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 46.0%

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

   8. Simplified 46.0%

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

   9. Taylor expanded in y2 around inf 56.8%

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

   if 1.1e129 < b < 1.50000000000000006e167

   1. Initial program 15.4%

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

   3. Simplified 15.4%

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

   5. Taylor expanded in y5 around -inf 47.1%

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

   6. Taylor expanded in t around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. *-commutative 54.6%

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

   8. Simplified 54.6%

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

   if 1.50000000000000006e167 < b < 2.49999999999999993e232

   1. Initial program 38.5%

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

   3. Taylor expanded in c around inf 70.7%

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

   4. Taylor expanded in x around 0 69.7%

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

      1. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   if 2.49999999999999993e232 < b

   1. Initial program 7.1%

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

   3. Simplified 7.1%

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

   5. Taylor expanded in b around inf 64.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 72.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-45}:\\ \;\;\;\;\left(k \cdot y5\right) \cdot \left(y \cdot i - y0 \cdot y2\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-180}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-201}:\\ \;\;\;\;y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+129}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+232}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{+224}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -1.95 \cdot 10^{+217}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;k \leq -4.9 \cdot 10^{+100}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -6.4 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-130}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3.25 \cdot 10^{+209}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -9.5e+224)
   (* b (* z (- (* k y0) (* t a))))
   (if (<= k -1.95e+217)
     (* y0 (* y3 (- (* j y5) (* z c))))
     (if (<= k -4.9e+100)
       (* k (* y (- (* i y5) (* b y4))))
       (if (<= k -6.4e-44)
         (* c (* z (- (* t i) (* y0 y3))))
         (if (<= k 7.8e-248)
           (* t (* y5 (- (* a y2) (* i j))))
           (if (<= k 5e-130)
             (* (- (* z i) (* y2 y4)) (* t c))
             (if (<= k 5e-14)
               (* c (* y0 (- (* x y2) (* z y3))))
               (if (<= k 1.6e+48)
                 (* j (* y0 (- (* y3 y5) (* x b))))
                 (if (<= k 4.2e+95)
                   (* a (* b (- (* x y) (* z t))))
                   (if (<= k 7.5e+135)
                     (* y (* y5 (- (* i k) (* a y3))))
                     (if (<= k 3.25e+209)
                       (* (* k y4) (- (* y1 y2) (* y b)))
                       (* (* k y2) (- (* y1 y4) (* y0 y5)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -9.5e+224) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -1.95e+217) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (k <= -4.9e+100) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (k <= -6.4e-44) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (k <= 7.8e-248) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (k <= 5e-130) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (k <= 5e-14) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (k <= 1.6e+48) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (k <= 4.2e+95) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (k <= 7.5e+135) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (k <= 3.25e+209) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else {
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (k <= (-9.5d+224)) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else if (k <= (-1.95d+217)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (k <= (-4.9d+100)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (k <= (-6.4d-44)) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (k <= 7.8d-248) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (k <= 5d-130) then
        tmp = ((z * i) - (y2 * y4)) * (t * c)
    else if (k <= 5d-14) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (k <= 1.6d+48) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (k <= 4.2d+95) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (k <= 7.5d+135) then
        tmp = y * (y5 * ((i * k) - (a * y3)))
    else if (k <= 3.25d+209) then
        tmp = (k * y4) * ((y1 * y2) - (y * b))
    else
        tmp = (k * y2) * ((y1 * y4) - (y0 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -9.5e+224) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else if (k <= -1.95e+217) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (k <= -4.9e+100) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (k <= -6.4e-44) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (k <= 7.8e-248) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (k <= 5e-130) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (k <= 5e-14) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (k <= 1.6e+48) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (k <= 4.2e+95) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (k <= 7.5e+135) {
		tmp = y * (y5 * ((i * k) - (a * y3)));
	} else if (k <= 3.25e+209) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else {
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -9.5e+224:
		tmp = b * (z * ((k * y0) - (t * a)))
	elif k <= -1.95e+217:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif k <= -4.9e+100:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif k <= -6.4e-44:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif k <= 7.8e-248:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif k <= 5e-130:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	elif k <= 5e-14:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif k <= 1.6e+48:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif k <= 4.2e+95:
		tmp = a * (b * ((x * y) - (z * t)))
	elif k <= 7.5e+135:
		tmp = y * (y5 * ((i * k) - (a * y3)))
	elif k <= 3.25e+209:
		tmp = (k * y4) * ((y1 * y2) - (y * b))
	else:
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -9.5e+224)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	elseif (k <= -1.95e+217)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (k <= -4.9e+100)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (k <= -6.4e-44)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (k <= 7.8e-248)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (k <= 5e-130)
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(t * c));
	elseif (k <= 5e-14)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (k <= 1.6e+48)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (k <= 4.2e+95)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (k <= 7.5e+135)
		tmp = Float64(y * Float64(y5 * Float64(Float64(i * k) - Float64(a * y3))));
	elseif (k <= 3.25e+209)
		tmp = Float64(Float64(k * y4) * Float64(Float64(y1 * y2) - Float64(y * b)));
	else
		tmp = Float64(Float64(k * y2) * Float64(Float64(y1 * y4) - Float64(y0 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (k <= -9.5e+224)
		tmp = b * (z * ((k * y0) - (t * a)));
	elseif (k <= -1.95e+217)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (k <= -4.9e+100)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (k <= -6.4e-44)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (k <= 7.8e-248)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (k <= 5e-130)
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	elseif (k <= 5e-14)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (k <= 1.6e+48)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (k <= 4.2e+95)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (k <= 7.5e+135)
		tmp = y * (y5 * ((i * k) - (a * y3)));
	elseif (k <= 3.25e+209)
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	else
		tmp = (k * y2) * ((y1 * y4) - (y0 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[k, -9.5e+224], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.95e+217], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.9e+100], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -6.4e-44], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.8e-248], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5e-130], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5e-14], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.6e+48], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.2e+95], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.5e+135], N[(y * N[(y5 * N[(N[(i * k), $MachinePrecision] - N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.25e+209], N[(N[(k * y4), $MachinePrecision] * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * y2), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if k < -9.5000000000000002e224

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in b around inf 40.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in z around inf 55.4%

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(-1 \cdot \left(a \cdot t\right) - -1 \cdot \left(k \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 55.4%

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

      2. *-commutative 55.4%

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

   8. Simplified 55.4%

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

   if -9.5000000000000002e224 < k < -1.94999999999999997e217

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in y0 around inf 83.6%

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

   6. Taylor expanded in y3 around -inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. distribute-rgt-neg-in 83.6%

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

      3. +-commutative 83.6%

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

      4. mul-1-neg 83.6%

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

      5. unsub-neg 83.6%

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

      6. *-commutative 83.6%

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

      7. *-commutative 83.6%

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

   8. Simplified 83.6%

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

   if -1.94999999999999997e217 < k < -4.89999999999999967e100

   1. Initial program 26.3%

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

   3. Simplified 26.3%

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

   5. Taylor expanded in k around inf 57.9%

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

   6. Taylor expanded in y around inf 53.3%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 53.3%

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

      2. distribute-rgt-neg-in 53.3%

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

      3. *-commutative 53.3%

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

      4. distribute-rgt-neg-in 53.3%

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

      5. *-commutative 53.3%

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

      6. *-commutative 53.3%

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

   8. Simplified 53.3%

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

   if -4.89999999999999967e100 < k < -6.3999999999999999e-44

   1. Initial program 32.5%

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

   3. Taylor expanded in c around inf 56.3%

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

   4. Taylor expanded in x around 0 56.5%

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

      1. *-commutative 56.5%

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

   6. Simplified 56.5%

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

   7. Taylor expanded in z around inf 48.7%

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

   if -6.3999999999999999e-44 < k < 7.800000000000001e-248

   1. Initial program 47.3%

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

   3. Simplified 48.7%

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

   5. Taylor expanded in y5 around -inf 42.0%

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

   6. Taylor expanded in t around inf 46.5%

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

      1. *-commutative 46.5%

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

      2. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if 7.800000000000001e-248 < k < 4.9999999999999996e-130

   1. Initial program 35.8%

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

   3. Taylor expanded in c around inf 39.4%

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

   4. Taylor expanded in x around 0 39.6%

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

      1. *-commutative 39.6%

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

   6. Simplified 39.6%

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

   7. Taylor expanded in t around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-*r* 52.8%

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

      3. *-commutative 52.8%

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

      4. associate-*l* 56.0%

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

   9. Simplified 56.0%

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

   if 4.9999999999999996e-130 < k < 5.0000000000000002e-14

   1. Initial program 30.0%

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

   3. Simplified 30.0%

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

   5. Taylor expanded in y0 around inf 41.1%

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

   6. Taylor expanded in c around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. *-commutative 60.6%

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

   8. Simplified 60.6%

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

   if 5.0000000000000002e-14 < k < 1.6000000000000001e48

   1. Initial program 35.7%

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

   3. Simplified 35.7%

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

   5. Taylor expanded in y0 around inf 57.1%

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

   6. Taylor expanded in j around inf 64.7%

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

      1. *-commutative 64.7%

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

   8. Simplified 64.7%

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

   if 1.6000000000000001e48 < k < 4.2e95

   1. Initial program 12.5%

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

   3. Simplified 12.5%

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

   5. Taylor expanded in b around inf 25.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-lft-neg-out 63.2%

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

      3. +-commutative 63.2%

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

      4. *-commutative 63.2%

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

      5. cancel-sign-sub-inv 63.2%

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

      6. *-commutative 63.2%

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

   8. Simplified 63.2%

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

   if 4.2e95 < k < 7.49999999999999947e135

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   5. Taylor expanded in y5 around -inf 38.6%

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

   6. Taylor expanded in y around inf 75.1%

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

      1. distribute-lft-out-- 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

   8. Simplified 75.1%

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

   if 7.49999999999999947e135 < k < 3.24999999999999987e209

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in k around inf 47.4%

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

   6. Taylor expanded in y4 around inf 74.1%

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

      1. associate-*r* 74.1%

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

      2. +-commutative 74.1%

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

      3. mul-1-neg 74.1%

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

      4. unsub-neg 74.1%

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

      5. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   if 3.24999999999999987e209 < k

   1. Initial program 36.4%

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

   3. Simplified 36.4%

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

   5. Taylor expanded in k around inf 50.3%

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

   6. Taylor expanded in y2 around inf 59.9%

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

      1. associate-*r* 59.9%

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

   8. Simplified 59.9%

      \[\leadsto \color{blue}{\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
3. Recombined 12 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{+224}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -1.95 \cdot 10^{+217}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;k \leq -4.9 \cdot 10^{+100}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -6.4 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 7.8 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-130}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.6 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 4.2 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;k \leq 7.5 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(y5 \cdot \left(i \cdot k - a \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 3.25 \cdot 10^{+209}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := t \cdot j - y \cdot k\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := y4 \cdot t\_3\\ t_5 := y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t\_1\right) + t\_4\right)\\ \mathbf{elif}\;c \leq -2450000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t\_2 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_3\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-71}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-303}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-208}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t\_2\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+34}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + t\_4}{y0} + t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2 (- (* t j) (* y k)))
        (t_3 (- (* y y3) (* t y2)))
        (t_4 (* y4 t_3))
        (t_5
         (*
          y5
          (+
           (* a (- (* t y2) (* y y3)))
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))))
   (if (<= c -1e+60)
     (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_1)) t_4))
     (if (<= c -2450000000000.0)
       (* y4 (+ (+ (* b t_2) (* y1 (- (* k y2) (* j y3)))) (* c t_3)))
       (if (<= c -8.2e-71)
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= c -5.5e-195)
           (* b (* x (- (* y a) (* j y0))))
           (if (<= c -1.4e-303)
             t_5
             (if (<= c 3.8e-208)
               (*
                b
                (+
                 (+ (* a (- (* x y) (* z t))) (* y4 t_2))
                 (* y0 (- (* z k) (* x j)))))
               (if (<= c 5.1e+34)
                 t_5
                 (* y0 (* c (+ (/ (+ (* t (* z i)) t_4) y0) t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * t_3;
	double t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (c <= -1e+60) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_4);
	} else if (c <= -2450000000000.0) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (c <= -8.2e-71) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -5.5e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= -1.4e-303) {
		tmp = t_5;
	} else if (c <= 3.8e-208) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 5.1e+34) {
		tmp = t_5;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (x * y2) - (z * y3)
    t_2 = (t * j) - (y * k)
    t_3 = (y * y3) - (t * y2)
    t_4 = y4 * t_3
    t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    if (c <= (-1d+60)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_4)
    else if (c <= (-2450000000000.0d0)) then
        tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
    else if (c <= (-8.2d-71)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= (-5.5d-195)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (c <= (-1.4d-303)) then
        tmp = t_5
    else if (c <= 3.8d-208) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
    else if (c <= 5.1d+34) then
        tmp = t_5
    else
        tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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 = (x * y2) - (z * y3);
	double t_2 = (t * j) - (y * k);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * t_3;
	double t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (c <= -1e+60) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_4);
	} else if (c <= -2450000000000.0) {
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	} else if (c <= -8.2e-71) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= -5.5e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= -1.4e-303) {
		tmp = t_5;
	} else if (c <= 3.8e-208) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	} else if (c <= 5.1e+34) {
		tmp = t_5;
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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 = (x * y2) - (z * y3)
	t_2 = (t * j) - (y * k)
	t_3 = (y * y3) - (t * y2)
	t_4 = y4 * t_3
	t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	tmp = 0
	if c <= -1e+60:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_4)
	elif c <= -2450000000000.0:
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3))
	elif c <= -8.2e-71:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif c <= -5.5e-195:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif c <= -1.4e-303:
		tmp = t_5
	elif c <= 3.8e-208:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))))
	elif c <= 5.1e+34:
		tmp = t_5
	else:
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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(x * y2) - Float64(z * y3))
	t_2 = Float64(Float64(t * j) - Float64(y * k))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(y4 * t_3)
	t_5 = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	tmp = 0.0
	if (c <= -1e+60)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_1)) + t_4));
	elseif (c <= -2450000000000.0)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_2) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * t_3)));
	elseif (c <= -8.2e-71)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= -5.5e-195)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (c <= -1.4e-303)
		tmp = t_5;
	elseif (c <= 3.8e-208)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_2)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (c <= 5.1e+34)
		tmp = t_5;
	else
		tmp = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + t_4) / y0) + 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 = (x * y2) - (z * y3);
	t_2 = (t * j) - (y * k);
	t_3 = (y * y3) - (t * y2);
	t_4 = y4 * t_3;
	t_5 = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	tmp = 0.0;
	if (c <= -1e+60)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_4);
	elseif (c <= -2450000000000.0)
		tmp = y4 * (((b * t_2) + (y1 * ((k * y2) - (j * y3)))) + (c * t_3));
	elseif (c <= -8.2e-71)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= -5.5e-195)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (c <= -1.4e-303)
		tmp = t_5;
	elseif (c <= 3.8e-208)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_2)) + (y0 * ((z * k) - (x * j))));
	elseif (c <= 5.1e+34)
		tmp = t_5;
	else
		tmp = y0 * (c * ((((t * (z * i)) + t_4) / y0) + 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[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+60], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2450000000000.0], N[(y4 * N[(N[(N[(b * t$95$2), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e-71], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.5e-195], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.4e-303], t$95$5, If[LessEqual[c, 3.8e-208], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.1e+34], t$95$5, N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] / y0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -9.9999999999999995e59

   1. Initial program 26.2%

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

   3. Taylor expanded in c around inf 64.4%

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

   if -9.9999999999999995e59 < c < -2.45e12

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   5. Taylor expanded in y4 around inf 69.9%

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

   if -2.45e12 < c < -8.19999999999999987e-71

   1. Initial program 18.8%

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

   3. Taylor expanded in y2 around inf 75.2%

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

   if -8.19999999999999987e-71 < c < -5.5000000000000003e-195

   1. Initial program 28.8%

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

   3. Simplified 28.8%

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

   5. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 54.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -5.5000000000000003e-195 < c < -1.4e-303 or 3.80000000000000011e-208 < c < 5.10000000000000036e34

   1. Initial program 45.4%

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

   3. Simplified 46.7%

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

   5. Taylor expanded in y5 around -inf 58.0%

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

   if -1.4e-303 < c < 3.80000000000000011e-208

   1. Initial program 25.5%

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

   3. Simplified 25.5%

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

   5. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 5.10000000000000036e34 < c

   1. Initial program 37.5%

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

   3. Taylor expanded in c around inf 61.3%

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

   4. Taylor expanded in x around 0 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in y0 around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate-/l* 62.7%

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

      3. distribute-lft-out 69.8%

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

      4. associate-*r* 68.1%

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

      5. *-commutative 68.1%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

      8. *-commutative 69.8%

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

      9. *-commutative 69.8%

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

      10. *-commutative 69.8%

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

   9. Simplified 69.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(i \cdot z\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot y4}{y0} + \left(y2 \cdot x - y3 \cdot z\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2450000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-71}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-303}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-208}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+34}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ t_2 := \left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ t_3 := \left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;k \leq -1.35 \cdot 10^{+208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq -4.3 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -3.55 \cdot 10^{+93}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.8 \cdot 10^{-68}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;k \leq -4.1 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{-267}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-223}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* t (- (* j y4) (* z a)))))
        (t_2 (* (- (* z i) (* y2 y4)) (* t c)))
        (t_3 (* (* k y2) (- (* y1 y4) (* y0 y5)))))
   (if (<= k -1.35e+208)
     t_3
     (if (<= k -4.3e+188)
       t_1
       (if (<= k -3.55e+93)
         (* k (* y (- (* i y5) (* b y4))))
         (if (<= k -1.8e-68)
           (* (* t i) (* z c))
           (if (<= k -4.1e-159)
             t_1
             (if (<= k -4.5e-267)
               t_2
               (if (<= k 1.05e-223)
                 (* y0 (* y3 (- (* j y5) (* z c))))
                 (if (<= k 1.5e-129)
                   t_2
                   (if (<= k 5e-5)
                     (* c (* y0 (- (* x y2) (* z y3))))
                     (if (<= k 9.5e+154) t_1 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 = b * (t * ((j * y4) - (z * a)));
	double t_2 = ((z * i) - (y2 * y4)) * (t * c);
	double t_3 = (k * y2) * ((y1 * y4) - (y0 * y5));
	double tmp;
	if (k <= -1.35e+208) {
		tmp = t_3;
	} else if (k <= -4.3e+188) {
		tmp = t_1;
	} else if (k <= -3.55e+93) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (k <= -1.8e-68) {
		tmp = (t * i) * (z * c);
	} else if (k <= -4.1e-159) {
		tmp = t_1;
	} else if (k <= -4.5e-267) {
		tmp = t_2;
	} else if (k <= 1.05e-223) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (k <= 1.5e-129) {
		tmp = t_2;
	} else if (k <= 5e-5) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (k <= 9.5e+154) {
		tmp = t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = b * (t * ((j * y4) - (z * a)))
    t_2 = ((z * i) - (y2 * y4)) * (t * c)
    t_3 = (k * y2) * ((y1 * y4) - (y0 * y5))
    if (k <= (-1.35d+208)) then
        tmp = t_3
    else if (k <= (-4.3d+188)) then
        tmp = t_1
    else if (k <= (-3.55d+93)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (k <= (-1.8d-68)) then
        tmp = (t * i) * (z * c)
    else if (k <= (-4.1d-159)) then
        tmp = t_1
    else if (k <= (-4.5d-267)) then
        tmp = t_2
    else if (k <= 1.05d-223) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (k <= 1.5d-129) then
        tmp = t_2
    else if (k <= 5d-5) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (k <= 9.5d+154) then
        tmp = t_1
    else
        tmp = 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 = b * (t * ((j * y4) - (z * a)));
	double t_2 = ((z * i) - (y2 * y4)) * (t * c);
	double t_3 = (k * y2) * ((y1 * y4) - (y0 * y5));
	double tmp;
	if (k <= -1.35e+208) {
		tmp = t_3;
	} else if (k <= -4.3e+188) {
		tmp = t_1;
	} else if (k <= -3.55e+93) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (k <= -1.8e-68) {
		tmp = (t * i) * (z * c);
	} else if (k <= -4.1e-159) {
		tmp = t_1;
	} else if (k <= -4.5e-267) {
		tmp = t_2;
	} else if (k <= 1.05e-223) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (k <= 1.5e-129) {
		tmp = t_2;
	} else if (k <= 5e-5) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (k <= 9.5e+154) {
		tmp = t_1;
	} else {
		tmp = 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 = b * (t * ((j * y4) - (z * a)))
	t_2 = ((z * i) - (y2 * y4)) * (t * c)
	t_3 = (k * y2) * ((y1 * y4) - (y0 * y5))
	tmp = 0
	if k <= -1.35e+208:
		tmp = t_3
	elif k <= -4.3e+188:
		tmp = t_1
	elif k <= -3.55e+93:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif k <= -1.8e-68:
		tmp = (t * i) * (z * c)
	elif k <= -4.1e-159:
		tmp = t_1
	elif k <= -4.5e-267:
		tmp = t_2
	elif k <= 1.05e-223:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif k <= 1.5e-129:
		tmp = t_2
	elif k <= 5e-5:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif k <= 9.5e+154:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))))
	t_2 = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(t * c))
	t_3 = Float64(Float64(k * y2) * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	tmp = 0.0
	if (k <= -1.35e+208)
		tmp = t_3;
	elseif (k <= -4.3e+188)
		tmp = t_1;
	elseif (k <= -3.55e+93)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (k <= -1.8e-68)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	elseif (k <= -4.1e-159)
		tmp = t_1;
	elseif (k <= -4.5e-267)
		tmp = t_2;
	elseif (k <= 1.05e-223)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (k <= 1.5e-129)
		tmp = t_2;
	elseif (k <= 5e-5)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (k <= 9.5e+154)
		tmp = t_1;
	else
		tmp = 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 = b * (t * ((j * y4) - (z * a)));
	t_2 = ((z * i) - (y2 * y4)) * (t * c);
	t_3 = (k * y2) * ((y1 * y4) - (y0 * y5));
	tmp = 0.0;
	if (k <= -1.35e+208)
		tmp = t_3;
	elseif (k <= -4.3e+188)
		tmp = t_1;
	elseif (k <= -3.55e+93)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (k <= -1.8e-68)
		tmp = (t * i) * (z * c);
	elseif (k <= -4.1e-159)
		tmp = t_1;
	elseif (k <= -4.5e-267)
		tmp = t_2;
	elseif (k <= 1.05e-223)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (k <= 1.5e-129)
		tmp = t_2;
	elseif (k <= 5e-5)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (k <= 9.5e+154)
		tmp = t_1;
	else
		tmp = 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[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.35e+208], t$95$3, If[LessEqual[k, -4.3e+188], t$95$1, If[LessEqual[k, -3.55e+93], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1.8e-68], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.1e-159], t$95$1, If[LessEqual[k, -4.5e-267], t$95$2, If[LessEqual[k, 1.05e-223], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.5e-129], t$95$2, If[LessEqual[k, 5e-5], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.5e+154], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -1.35e208 or 9.5000000000000001e154 < k

   1. Initial program 30.0%

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

   3. Simplified 30.0%

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

   5. Taylor expanded in k around inf 45.5%

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

   6. Taylor expanded in y2 around inf 47.8%

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

      1. associate-*r* 49.4%

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

   8. Simplified 49.4%

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

   if -1.35e208 < k < -4.29999999999999985e188 or -1.80000000000000004e-68 < k < -4.10000000000000014e-159 or 5.00000000000000024e-5 < k < 9.5000000000000001e154

   1. Initial program 31.2%

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

   3. Simplified 31.2%

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

   5. Taylor expanded in b around inf 46.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in t around -inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. *-commutative 58.1%

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

      3. distribute-rgt-neg-in 58.1%

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

      4. +-commutative 58.1%

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

      5. mul-1-neg 58.1%

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

      6. unsub-neg 58.1%

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

      7. *-commutative 58.1%

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

      8. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if -4.29999999999999985e188 < k < -3.5500000000000002e93

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in k around inf 66.6%

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

   6. Taylor expanded in y around inf 50.6%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 50.6%

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

      2. distribute-rgt-neg-in 50.6%

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

      3. *-commutative 50.6%

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

      4. distribute-rgt-neg-in 50.6%

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

      5. *-commutative 50.6%

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

      6. *-commutative 50.6%

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

   8. Simplified 50.6%

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

   if -3.5500000000000002e93 < k < -1.80000000000000004e-68

   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. Add Preprocessing

   3. Taylor expanded in c around inf 55.9%

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

   4. Taylor expanded in x around 0 56.1%

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

      1. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in i around inf 34.5%

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

      1. *-commutative 34.5%

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

      2. associate-*r* 41.4%

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

      3. associate-*l* 41.7%

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

      4. *-commutative 41.7%

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

   9. Simplified 41.7%

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

   if -4.10000000000000014e-159 < k < -4.4999999999999999e-267 or 1.04999999999999991e-223 < k < 1.4999999999999999e-129

   1. Initial program 34.5%

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

   3. Taylor expanded in c around inf 46.9%

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

   4. Taylor expanded in x around 0 44.9%

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

      1. *-commutative 44.9%

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

   6. Simplified 44.9%

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

   7. Taylor expanded in t around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. associate-*r* 49.4%

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

      3. *-commutative 49.4%

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

      4. associate-*l* 53.4%

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

   9. Simplified 53.4%

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

   if -4.4999999999999999e-267 < k < 1.04999999999999991e-223

   1. Initial program 53.7%

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

   3. Simplified 53.7%

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

   5. Taylor expanded in y0 around inf 47.4%

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

   6. Taylor expanded in y3 around -inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-rgt-neg-in 51.3%

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

      3. +-commutative 51.3%

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

      4. mul-1-neg 51.3%

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

      5. unsub-neg 51.3%

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

      6. *-commutative 51.3%

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

      7. *-commutative 51.3%

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

   8. Simplified 51.3%

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

   if 1.4999999999999999e-129 < k < 5.00000000000000024e-5

   1. Initial program 34.8%

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

   3. Simplified 34.8%

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

   5. Taylor expanded in y0 around inf 48.8%

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

   6. Taylor expanded in c around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. *-commutative 57.2%

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

   8. Simplified 57.2%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.35 \cdot 10^{+208}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;k \leq -4.3 \cdot 10^{+188}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -3.55 \cdot 10^{+93}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1.8 \cdot 10^{-68}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;k \leq -4.1 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;k \leq -4.5 \cdot 10^{-267}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{-223}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;k \leq 5 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + t\_1}{y0} + t\_2\right)\right)\\ t_4 := y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{if}\;c \leq -7.3 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot t\_2 - \left(x \cdot y\right) \cdot i\right) + t\_1\right)\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{+119}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -255000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-68}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+34}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (- (* y y3) (* t y2))))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (* y0 (* c (+ (/ (+ (* t (* z i)) t_1) y0) t_2))))
        (t_4
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))))
   (if (<= c -7.3e+173)
     (* c (+ (- (* y0 t_2) (* (* x y) i)) t_1))
     (if (<= c -6.4e+119)
       (* (- (* z i) (* y2 y4)) (* t c))
       (if (<= c -255000000000.0)
         t_3
         (if (<= c -1.45e-68)
           t_4
           (if (<= c -4.8e-195)
             (* b (* x (- (* y a) (* j y0))))
             (if (<= c 2.15e+34) t_4 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 = y4 * ((y * y3) - (t * y2));
	double t_2 = (x * y2) - (z * y3);
	double t_3 = y0 * (c * ((((t * (z * i)) + t_1) / y0) + t_2));
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (c <= -7.3e+173) {
		tmp = c * (((y0 * t_2) - ((x * y) * i)) + t_1);
	} else if (c <= -6.4e+119) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -255000000000.0) {
		tmp = t_3;
	} else if (c <= -1.45e-68) {
		tmp = t_4;
	} else if (c <= -4.8e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= 2.15e+34) {
		tmp = t_4;
	} else {
		tmp = 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 = y4 * ((y * y3) - (t * y2))
    t_2 = (x * y2) - (z * y3)
    t_3 = y0 * (c * ((((t * (z * i)) + t_1) / y0) + t_2))
    t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    if (c <= (-7.3d+173)) then
        tmp = c * (((y0 * t_2) - ((x * y) * i)) + t_1)
    else if (c <= (-6.4d+119)) then
        tmp = ((z * i) - (y2 * y4)) * (t * c)
    else if (c <= (-255000000000.0d0)) then
        tmp = t_3
    else if (c <= (-1.45d-68)) then
        tmp = t_4
    else if (c <= (-4.8d-195)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (c <= 2.15d+34) then
        tmp = t_4
    else
        tmp = 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 = y4 * ((y * y3) - (t * y2));
	double t_2 = (x * y2) - (z * y3);
	double t_3 = y0 * (c * ((((t * (z * i)) + t_1) / y0) + t_2));
	double t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	double tmp;
	if (c <= -7.3e+173) {
		tmp = c * (((y0 * t_2) - ((x * y) * i)) + t_1);
	} else if (c <= -6.4e+119) {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	} else if (c <= -255000000000.0) {
		tmp = t_3;
	} else if (c <= -1.45e-68) {
		tmp = t_4;
	} else if (c <= -4.8e-195) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (c <= 2.15e+34) {
		tmp = t_4;
	} else {
		tmp = 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 = y4 * ((y * y3) - (t * y2))
	t_2 = (x * y2) - (z * y3)
	t_3 = y0 * (c * ((((t * (z * i)) + t_1) / y0) + t_2))
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	tmp = 0
	if c <= -7.3e+173:
		tmp = c * (((y0 * t_2) - ((x * y) * i)) + t_1)
	elif c <= -6.4e+119:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	elif c <= -255000000000.0:
		tmp = t_3
	elif c <= -1.45e-68:
		tmp = t_4
	elif c <= -4.8e-195:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif c <= 2.15e+34:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + t_1) / y0) + t_2)))
	t_4 = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))))
	tmp = 0.0
	if (c <= -7.3e+173)
		tmp = Float64(c * Float64(Float64(Float64(y0 * t_2) - Float64(Float64(x * y) * i)) + t_1));
	elseif (c <= -6.4e+119)
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(t * c));
	elseif (c <= -255000000000.0)
		tmp = t_3;
	elseif (c <= -1.45e-68)
		tmp = t_4;
	elseif (c <= -4.8e-195)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (c <= 2.15e+34)
		tmp = t_4;
	else
		tmp = 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 = y4 * ((y * y3) - (t * y2));
	t_2 = (x * y2) - (z * y3);
	t_3 = y0 * (c * ((((t * (z * i)) + t_1) / y0) + t_2));
	t_4 = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	tmp = 0.0;
	if (c <= -7.3e+173)
		tmp = c * (((y0 * t_2) - ((x * y) * i)) + t_1);
	elseif (c <= -6.4e+119)
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	elseif (c <= -255000000000.0)
		tmp = t_3;
	elseif (c <= -1.45e-68)
		tmp = t_4;
	elseif (c <= -4.8e-195)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (c <= 2.15e+34)
		tmp = t_4;
	else
		tmp = 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[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / y0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.3e+173], N[(c * N[(N[(N[(y0 * t$95$2), $MachinePrecision] - N[(N[(x * y), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.4e+119], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -255000000000.0], t$95$3, If[LessEqual[c, -1.45e-68], t$95$4, If[LessEqual[c, -4.8e-195], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.15e+34], t$95$4, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.2999999999999995e173

   1. Initial program 23.1%

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

   3. Taylor expanded in c around inf 65.4%

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

   4. Taylor expanded in x around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

      4. distribute-rgt-neg-in 69.2%

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

   6. Simplified 69.2%

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

   if -7.2999999999999995e173 < c < -6.39999999999999979e119

   1. Initial program 34.2%

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

   3. Taylor expanded in c around inf 66.7%

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

   4. Taylor expanded in x around 0 66.7%

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

      1. *-commutative 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in t around inf 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*r* 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-*l* 89.1%

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

   9. Simplified 89.1%

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

   if -6.39999999999999979e119 < c < -2.55e11 or 2.14999999999999997e34 < c

   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. Add Preprocessing

   3. Taylor expanded in c around inf 55.4%

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

   4. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in y0 around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. associate-/l* 56.5%

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

      3. distribute-lft-out 63.6%

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

      4. associate-*r* 62.4%

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

      5. *-commutative 62.4%

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

      6. associate-*l* 63.6%

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

      7. *-commutative 63.6%

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

      8. *-commutative 63.6%

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

      9. *-commutative 63.6%

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

      10. *-commutative 63.6%

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

   9. Simplified 63.6%

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

   if -2.55e11 < c < -1.45e-68 or -4.8e-195 < c < 2.14999999999999997e34

   1. Initial program 37.8%

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

   3. Taylor expanded in y2 around inf 46.0%

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

   if -1.45e-68 < c < -4.8e-195

   1. Initial program 28.8%

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

   3. Simplified 28.8%

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

   5. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 54.2%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

   8. Simplified 54.2%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.3 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -6.4 \cdot 10^{+119}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -255000000000:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-68}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+34}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{-270}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;a \leq 10^{-234}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-81}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(t \cdot \frac{z \cdot i}{y2}\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          c
          (+
           (+ (* y0 (- (* x y2) (* z y3))) (* i (* z t)))
           (* y4 (- (* y y3) (* t y2)))))))
   (if (<= a -2.4e+89)
     (* t (* y5 (- (* a y2) (* i j))))
     (if (<= a -2e-85)
       t_1
       (if (<= a -4.4e-166)
         (* k (* z (- (* b y0) (* i y1))))
         (if (<= a -3.25e-270)
           (* (* y0 y2) (- (* x c) (* k y5)))
           (if (<= a 1e-234)
             (* b (* j (- (* t y4) (* x y0))))
             (if (<= a 3.8e-81)
               (* y2 (- (* c (* t (/ (* z i) y2))) (* c (* t y4))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * (z * t))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (a <= -2.4e+89) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (a <= -2e-85) {
		tmp = t_1;
	} else if (a <= -4.4e-166) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (a <= -3.25e-270) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (a <= 1e-234) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 3.8e-81) {
		tmp = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * (z * t))) + (y4 * ((y * y3) - (t * y2))))
    if (a <= (-2.4d+89)) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (a <= (-2d-85)) then
        tmp = t_1
    else if (a <= (-4.4d-166)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (a <= (-3.25d-270)) then
        tmp = (y0 * y2) * ((x * c) - (k * y5))
    else if (a <= 1d-234) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (a <= 3.8d-81) then
        tmp = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * (z * t))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (a <= -2.4e+89) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (a <= -2e-85) {
		tmp = t_1;
	} else if (a <= -4.4e-166) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (a <= -3.25e-270) {
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	} else if (a <= 1e-234) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (a <= 3.8e-81) {
		tmp = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * (z * t))) + (y4 * ((y * y3) - (t * y2))))
	tmp = 0
	if a <= -2.4e+89:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif a <= -2e-85:
		tmp = t_1
	elif a <= -4.4e-166:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif a <= -3.25e-270:
		tmp = (y0 * y2) * ((x * c) - (k * y5))
	elif a <= 1e-234:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif a <= 3.8e-81:
		tmp = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(i * Float64(z * t))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (a <= -2.4e+89)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (a <= -2e-85)
		tmp = t_1;
	elseif (a <= -4.4e-166)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (a <= -3.25e-270)
		tmp = Float64(Float64(y0 * y2) * Float64(Float64(x * c) - Float64(k * y5)));
	elseif (a <= 1e-234)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (a <= 3.8e-81)
		tmp = Float64(y2 * Float64(Float64(c * Float64(t * Float64(Float64(z * i) / y2))) - Float64(c * Float64(t * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (((y0 * ((x * y2) - (z * y3))) + (i * (z * t))) + (y4 * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (a <= -2.4e+89)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (a <= -2e-85)
		tmp = t_1;
	elseif (a <= -4.4e-166)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (a <= -3.25e-270)
		tmp = (y0 * y2) * ((x * c) - (k * y5));
	elseif (a <= 1e-234)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (a <= 3.8e-81)
		tmp = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+89], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e-85], t$95$1, If[LessEqual[a, -4.4e-166], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.25e-270], N[(N[(y0 * y2), $MachinePrecision] * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-234], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e-81], N[(y2 * N[(N[(c * N[(t * N[(N[(z * i), $MachinePrecision] / y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.40000000000000004e89

   1. Initial program 24.9%

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

   3. Simplified 24.9%

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

   5. Taylor expanded in y5 around -inf 36.2%

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

   6. Taylor expanded in t around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. *-commutative 53.9%

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

   8. Simplified 53.9%

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

   if -2.40000000000000004e89 < a < -2e-85 or 3.7999999999999999e-81 < a

   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. Add Preprocessing

   3. Taylor expanded in c around inf 56.5%

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

   4. Taylor expanded in x around 0 56.6%

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

      1. *-commutative 56.6%

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

   6. Simplified 56.6%

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

   if -2e-85 < a < -4.4000000000000002e-166

   1. Initial program 38.1%

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

   3. Simplified 38.1%

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

   5. Taylor expanded in k around inf 43.1%

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

   6. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   if -4.4000000000000002e-166 < a < -3.25e-270

   1. Initial program 41.9%

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

   3. Simplified 41.9%

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

   5. Taylor expanded in y0 around inf 44.7%

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

   6. Taylor expanded in y2 around inf 43.0%

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

      1. associate-*r* 43.0%

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

      2. *-commutative 43.0%

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

      3. +-commutative 43.0%

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

      4. mul-1-neg 43.0%

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

      5. unsub-neg 43.0%

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

      6. *-commutative 43.0%

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

   8. Simplified 43.0%

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

   if -3.25e-270 < a < 9.9999999999999996e-235

   1. Initial program 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in b around inf 75.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 59.1%

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

   if 9.9999999999999996e-235 < a < 3.7999999999999999e-81

   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. Add Preprocessing

   3. Taylor expanded in c around inf 42.6%

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

   4. Taylor expanded in x around 0 31.0%

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

      1. *-commutative 31.0%

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

   6. Simplified 31.0%

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

   7. Taylor expanded in t around inf 37.2%

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

      1. *-commutative 37.2%

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

      2. associate-*r* 34.6%

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

      3. *-commutative 34.6%

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

      4. associate-*l* 31.9%

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

   9. Simplified 31.9%

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

   10. Taylor expanded in y2 around -inf 34.1%

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

       1. mul-1-neg 34.1%

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

       2. *-commutative 34.1%

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

       3. distribute-rgt-neg-in 34.1%

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

       4. +-commutative 34.1%

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

       5. mul-1-neg 34.1%

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

       6. unsub-neg 34.1%

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

       7. associate-/l* 34.1%

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

       8. associate-*r* 37.0%

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

       9. *-commutative 37.0%

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

       10. associate-*l* 37.0%

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

       11. associate-/l* 42.7%

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

   12. Simplified 42.7%

       \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot y4\right) - c \cdot \left(t \cdot \frac{i \cdot z}{y2}\right)\right) \cdot \left(-y2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-85}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-166}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq -3.25 \cdot 10^{-270}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c - k \cdot y5\right)\\ \mathbf{elif}\;a \leq 10^{-234}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-81}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(t \cdot \frac{z \cdot i}{y2}\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + i \cdot \left(z \cdot t\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := y5 \cdot \left(a \cdot t\_1 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ t_3 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;y5 \leq -3.3 \cdot 10^{+163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq -50000000:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_3\right)\\ \mathbf{elif}\;y5 \leq -9 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot t\_1\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t y2) (* y y3)))
        (t_2
         (*
          y5
          (+
           (* a t_1)
           (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2)))))))
        (t_3 (- (* a y5) (* c y4))))
   (if (<= y5 -3.3e+163)
     t_2
     (if (<= y5 -50000000.0)
       (*
        y2
        (+
         (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
         (* t t_3)))
       (if (<= y5 -9e-51)
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 t_1)))
         (if (<= y5 9e-169)
           (*
            c
            (+
             (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
             (* y4 (- (* y y3) (* t y2)))))
           (if (<= y5 2.5e+102)
             (*
              t
              (+
               (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
               (* y2 t_3)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * y2) - (y * y3);
	double t_2 = y5 * ((a * t_1) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double t_3 = (a * y5) - (c * y4);
	double tmp;
	if (y5 <= -3.3e+163) {
		tmp = t_2;
	} else if (y5 <= -50000000.0) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3));
	} else if (y5 <= -9e-51) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_1));
	} else if (y5 <= 9e-169) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 2.5e+102) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_3));
	} 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 = (t * y2) - (y * y3)
    t_2 = y5 * ((a * t_1) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    t_3 = (a * y5) - (c * y4)
    if (y5 <= (-3.3d+163)) then
        tmp = t_2
    else if (y5 <= (-50000000.0d0)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3))
    else if (y5 <= (-9d-51)) then
        tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_1))
    else if (y5 <= 9d-169) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 2.5d+102) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_3))
    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 = (t * y2) - (y * y3);
	double t_2 = y5 * ((a * t_1) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	double t_3 = (a * y5) - (c * y4);
	double tmp;
	if (y5 <= -3.3e+163) {
		tmp = t_2;
	} else if (y5 <= -50000000.0) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3));
	} else if (y5 <= -9e-51) {
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_1));
	} else if (y5 <= 9e-169) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 2.5e+102) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_3));
	} 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 = (t * y2) - (y * y3)
	t_2 = y5 * ((a * t_1) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	t_3 = (a * y5) - (c * y4)
	tmp = 0
	if y5 <= -3.3e+163:
		tmp = t_2
	elif y5 <= -50000000.0:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3))
	elif y5 <= -9e-51:
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_1))
	elif y5 <= 9e-169:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 2.5e+102:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_3))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(y5 * Float64(Float64(a * t_1) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (y5 <= -3.3e+163)
		tmp = t_2;
	elseif (y5 <= -50000000.0)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * t_3)));
	elseif (y5 <= -9e-51)
		tmp = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * t_1)));
	elseif (y5 <= 9e-169)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 2.5e+102)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * t_3)));
	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 = (t * y2) - (y * y3);
	t_2 = y5 * ((a * t_1) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	t_3 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (y5 <= -3.3e+163)
		tmp = t_2;
	elseif (y5 <= -50000000.0)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3));
	elseif (y5 <= -9e-51)
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_1));
	elseif (y5 <= 9e-169)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 2.5e+102)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_3));
	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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y5 * N[(N[(a * t$95$1), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.3e+163], t$95$2, If[LessEqual[y5, -50000000.0], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9e-51], N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9e-169], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.5e+102], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -3.3e163 or 2.5e102 < y5

   1. Initial program 28.5%

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

   3. Simplified 29.7%

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

   5. Taylor expanded in y5 around -inf 62.7%

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

   if -3.3e163 < y5 < -5e7

   1. Initial program 18.5%

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

   3. Taylor expanded in y2 around inf 63.6%

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

   if -5e7 < y5 < -8.99999999999999948e-51

   1. Initial program 44.1%

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

   3. Taylor expanded in a around inf 57.2%

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

   if -8.99999999999999948e-51 < y5 < 8.9999999999999997e-169

   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. Add Preprocessing

   3. Taylor expanded in c around inf 59.2%

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

   if 8.9999999999999997e-169 < y5 < 2.5e102

   1. Initial program 37.5%

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

   3. Simplified 37.5%

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

   5. Taylor expanded in t around inf 57.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.3 \cdot 10^{+163}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y5 \leq -50000000:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -9 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-169}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 2.5 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y2 - z \cdot y3\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := y4 \cdot t\_2\\ \mathbf{if}\;c \leq -5.4 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t\_1\right) + t\_3\right)\\ \mathbf{elif}\;c \leq -500000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot t\_2\right)\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{-59}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-223}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + t\_3}{y0} + t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* x y2) (* z y3)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (* y4 t_2)))
   (if (<= c -5.4e+53)
     (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_1)) t_3))
     (if (<= c -500000000000.0)
       (*
        y4
        (+
         (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
         (* c t_2)))
       (if (<= c -9.6e-59)
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= c 3e-223)
           (*
            j
            (+
             (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
             (* x (- (* i y1) (* b y0)))))
           (if (<= c 9.5e+33)
             (*
              y5
              (+
               (* a (- (* t y2) (* y y3)))
               (+ (* i (- (* y k) (* t j))) (* y0 (- (* j y3) (* k y2))))))
             (* y0 (* c (+ (/ (+ (* t (* z i)) t_3) y0) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (x * y2) - (z * y3);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = y4 * t_2;
	double tmp;
	if (c <= -5.4e+53) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_3);
	} else if (c <= -500000000000.0) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	} else if (c <= -9.6e-59) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= 3e-223) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (c <= 9.5e+33) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_3) / y0) + 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 = (x * y2) - (z * y3)
    t_2 = (y * y3) - (t * y2)
    t_3 = y4 * t_2
    if (c <= (-5.4d+53)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_3)
    else if (c <= (-500000000000.0d0)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
    else if (c <= (-9.6d-59)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (c <= 3d-223) then
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    else if (c <= 9.5d+33) then
        tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
    else
        tmp = y0 * (c * ((((t * (z * i)) + t_3) / y0) + 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 = (x * y2) - (z * y3);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = y4 * t_2;
	double tmp;
	if (c <= -5.4e+53) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_3);
	} else if (c <= -500000000000.0) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	} else if (c <= -9.6e-59) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (c <= 3e-223) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (c <= 9.5e+33) {
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	} else {
		tmp = y0 * (c * ((((t * (z * i)) + t_3) / y0) + 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 = (x * y2) - (z * y3)
	t_2 = (y * y3) - (t * y2)
	t_3 = y4 * t_2
	tmp = 0
	if c <= -5.4e+53:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_3)
	elif c <= -500000000000.0:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2))
	elif c <= -9.6e-59:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif c <= 3e-223:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	elif c <= 9.5e+33:
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))))
	else:
		tmp = y0 * (c * ((((t * (z * i)) + t_3) / y0) + 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(x * y2) - Float64(z * y3))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(y4 * t_2)
	tmp = 0.0
	if (c <= -5.4e+53)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_1)) + t_3));
	elseif (c <= -500000000000.0)
		tmp = 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_2)));
	elseif (c <= -9.6e-59)
		tmp = Float64(y2 * Float64(Float64(Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (c <= 3e-223)
		tmp = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= 9.5e+33)
		tmp = Float64(y5 * Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	else
		tmp = Float64(y0 * Float64(c * Float64(Float64(Float64(Float64(t * Float64(z * i)) + t_3) / y0) + 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 = (x * y2) - (z * y3);
	t_2 = (y * y3) - (t * y2);
	t_3 = y4 * t_2;
	tmp = 0.0;
	if (c <= -5.4e+53)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_1)) + t_3);
	elseif (c <= -500000000000.0)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * t_2));
	elseif (c <= -9.6e-59)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (c <= 3e-223)
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	elseif (c <= 9.5e+33)
		tmp = y5 * ((a * ((t * y2) - (y * y3))) + ((i * ((y * k) - (t * j))) + (y0 * ((j * y3) - (k * y2)))));
	else
		tmp = y0 * (c * ((((t * (z * i)) + t_3) / y0) + 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[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y4 * t$95$2), $MachinePrecision]}, If[LessEqual[c, -5.4e+53], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -500000000000.0], 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$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.6e-59], N[(y2 * N[(N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e-223], N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e+33], N[(y5 * N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(N[(N[(N[(t * N[(z * i), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] / y0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.40000000000000039e53

   1. Initial program 26.2%

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

   3. Taylor expanded in c around inf 64.4%

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

   if -5.40000000000000039e53 < c < -5e11

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   5. Taylor expanded in y4 around inf 69.9%

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

   if -5e11 < c < -9.6000000000000006e-59

   1. Initial program 18.8%

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

   3. Taylor expanded in y2 around inf 75.2%

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

   if -9.6000000000000006e-59 < c < 2.99999999999999991e-223

   1. Initial program 36.8%

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

   3. Simplified 36.8%

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

   5. Taylor expanded in j around inf 50.7%

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

   if 2.99999999999999991e-223 < c < 9.5000000000000003e33

   1. Initial program 39.7%

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

   3. Simplified 41.3%

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

   5. Taylor expanded in y5 around -inf 49.9%

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

   if 9.5000000000000003e33 < c

   1. Initial program 37.5%

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

   3. Taylor expanded in c around inf 61.3%

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

   4. Taylor expanded in x around 0 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in y0 around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. associate-/l* 62.7%

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

      3. distribute-lft-out 69.8%

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

      4. associate-*r* 68.1%

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

      5. *-commutative 68.1%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

      8. *-commutative 69.8%

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

      9. *-commutative 69.8%

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

      10. *-commutative 69.8%

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

   9. Simplified 69.8%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(i \cdot z\right) - \left(y2 \cdot t - y3 \cdot y\right) \cdot y4}{y0} + \left(y2 \cdot x - y3 \cdot z\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.4 \cdot 10^{+53}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -500000000000:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{-59}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-223}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(\frac{t \cdot \left(z \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)}{y0} + \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -2.1 \cdot 10^{+224}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{+104}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -5.7 \cdot 10^{+47}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-14}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.9 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.2 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -2.1e+224)
   (* k (* z (- (* b y0) (* i y1))))
   (if (<= y1 -1.55e+104)
     (* (* k y4) (- (* y1 y2) (* y b)))
     (if (<= y1 -5.7e+47)
       (* y0 (* y3 (- (* j y5) (* z c))))
       (if (<= y1 -5.6e-14)
         (* y0 (* y5 (- (* j y3) (* k y2))))
         (if (<= y1 -2.25e-234)
           (* j (* y0 (- (* y3 y5) (* x b))))
           (if (<= y1 4.9e-293)
             (* a (* b (- (* x y) (* z t))))
             (if (<= y1 6.6e-261)
               (* b (* j (- (* t y4) (* x y0))))
               (if (<= y1 4.2e-84)
                 (* b (* y0 (- (* z k) (* x j))))
                 (* (- (* z i) (* y2 y4)) (* 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 tmp;
	if (y1 <= -2.1e+224) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -1.55e+104) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -5.7e+47) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (y1 <= -5.6e-14) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (y1 <= -2.25e-234) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 4.9e-293) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 6.6e-261) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 4.2e-84) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = ((z * i) - (y2 * y4)) * (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) :: tmp
    if (y1 <= (-2.1d+224)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y1 <= (-1.55d+104)) then
        tmp = (k * y4) * ((y1 * y2) - (y * b))
    else if (y1 <= (-5.7d+47)) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (y1 <= (-5.6d-14)) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (y1 <= (-2.25d-234)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y1 <= 4.9d-293) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 6.6d-261) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 4.2d-84) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = ((z * i) - (y2 * y4)) * (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 tmp;
	if (y1 <= -2.1e+224) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -1.55e+104) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -5.7e+47) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (y1 <= -5.6e-14) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (y1 <= -2.25e-234) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 4.9e-293) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 6.6e-261) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 4.2e-84) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -2.1e+224:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y1 <= -1.55e+104:
		tmp = (k * y4) * ((y1 * y2) - (y * b))
	elif y1 <= -5.7e+47:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif y1 <= -5.6e-14:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif y1 <= -2.25e-234:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y1 <= 4.9e-293:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 6.6e-261:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 4.2e-84:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -2.1e+224)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y1 <= -1.55e+104)
		tmp = Float64(Float64(k * y4) * Float64(Float64(y1 * y2) - Float64(y * b)));
	elseif (y1 <= -5.7e+47)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (y1 <= -5.6e-14)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y1 <= -2.25e-234)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y1 <= 4.9e-293)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 6.6e-261)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 4.2e-84)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(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)
	tmp = 0.0;
	if (y1 <= -2.1e+224)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y1 <= -1.55e+104)
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	elseif (y1 <= -5.7e+47)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (y1 <= -5.6e-14)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (y1 <= -2.25e-234)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y1 <= 4.9e-293)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 6.6e-261)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 4.2e-84)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = ((z * i) - (y2 * y4)) * (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_] := If[LessEqual[y1, -2.1e+224], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.55e+104], N[(N[(k * y4), $MachinePrecision] * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.7e+47], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -5.6e-14], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.25e-234], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.9e-293], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6.6e-261], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.2e-84], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y1 < -2.1000000000000002e224

   1. Initial program 27.8%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in k around inf 44.4%

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

   6. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   if -2.1000000000000002e224 < y1 < -1.55000000000000008e104

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   5. Taylor expanded in k around inf 38.4%

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

   6. Taylor expanded in y4 around inf 56.2%

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

      1. associate-*r* 56.2%

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

      2. +-commutative 56.2%

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

      3. mul-1-neg 56.2%

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

      4. unsub-neg 56.2%

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

      5. *-commutative 56.2%

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

   8. Simplified 56.2%

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

   if -1.55000000000000008e104 < y1 < -5.6999999999999997e47

   1. Initial program 39.9%

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

   3. Simplified 39.9%

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

   5. Taylor expanded in y0 around inf 40.6%

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

   6. Taylor expanded in y3 around -inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-rgt-neg-in 60.9%

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

      3. +-commutative 60.9%

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

      4. mul-1-neg 60.9%

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

      5. unsub-neg 60.9%

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

      6. *-commutative 60.9%

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

      7. *-commutative 60.9%

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

   8. Simplified 60.9%

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

   if -5.6999999999999997e47 < y1 < -5.6000000000000001e-14

   1. Initial program 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y0 around inf 42.0%

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

   6. Taylor expanded in y5 around inf 49.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 49.0%

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

   8. Simplified 49.0%

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

   if -5.6000000000000001e-14 < y1 < -2.25000000000000005e-234

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in y0 around inf 40.7%

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

   6. Taylor expanded in j around inf 40.8%

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

      1. *-commutative 40.8%

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

   8. Simplified 40.8%

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

   if -2.25000000000000005e-234 < y1 < 4.9e-293

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in b around inf 33.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 67.1%

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

      1. mul-1-neg 67.1%

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

      2. distribute-lft-neg-out 67.1%

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

      3. +-commutative 67.1%

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

      4. *-commutative 67.1%

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

      5. cancel-sign-sub-inv 67.1%

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

      6. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   if 4.9e-293 < y1 < 6.5999999999999996e-261

   1. Initial program 49.8%

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

   3. Simplified 49.8%

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

   5. Taylor expanded in b around inf 31.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 61.1%

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

   if 6.5999999999999996e-261 < y1 < 4.19999999999999996e-84

   1. Initial program 44.7%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in b around inf 56.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 48.9%

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

   if 4.19999999999999996e-84 < y1

   1. Initial program 33.9%

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

   3. Taylor expanded in c around inf 51.5%

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

   4. Taylor expanded in x around 0 50.3%

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

      1. *-commutative 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in t around inf 41.1%

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

      1. *-commutative 41.1%

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

      2. associate-*r* 39.8%

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

      3. *-commutative 39.8%

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

      4. associate-*l* 38.6%

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

   9. Simplified 38.6%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.1 \cdot 10^{+224}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.55 \cdot 10^{+104}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -5.7 \cdot 10^{+47}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;y1 \leq -5.6 \cdot 10^{-14}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.9 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 6.6 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 4.2 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.78 \cdot 10^{+227}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -2.7:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.42 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 8.5 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.78e+227)
   (* k (* z (- (* b y0) (* i y1))))
   (if (<= y1 -3.3e+59)
     (* (* k y4) (- (* y1 y2) (* y b)))
     (if (<= y1 -2.7)
       (* y0 (* y5 (- (* j y3) (* k y2))))
       (if (<= y1 -7.5e-14)
         (* c (* y0 (- (* x y2) (* z y3))))
         (if (<= y1 -2.42e-234)
           (* j (* y0 (- (* y3 y5) (* x b))))
           (if (<= y1 3.2e-299)
             (* a (* b (- (* x y) (* z t))))
             (if (<= y1 8.5e-260)
               (* b (* j (- (* t y4) (* x y0))))
               (if (<= y1 1.1e-83)
                 (* b (* y0 (- (* z k) (* x j))))
                 (* (- (* z i) (* y2 y4)) (* 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 tmp;
	if (y1 <= -1.78e+227) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -3.3e+59) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -2.7) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (y1 <= -7.5e-14) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y1 <= -2.42e-234) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 3.2e-299) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 8.5e-260) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 1.1e-83) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = ((z * i) - (y2 * y4)) * (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) :: tmp
    if (y1 <= (-1.78d+227)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y1 <= (-3.3d+59)) then
        tmp = (k * y4) * ((y1 * y2) - (y * b))
    else if (y1 <= (-2.7d0)) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (y1 <= (-7.5d-14)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y1 <= (-2.42d-234)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y1 <= 3.2d-299) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 8.5d-260) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 1.1d-83) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = ((z * i) - (y2 * y4)) * (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 tmp;
	if (y1 <= -1.78e+227) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -3.3e+59) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -2.7) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (y1 <= -7.5e-14) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y1 <= -2.42e-234) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 3.2e-299) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 8.5e-260) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 1.1e-83) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.78e+227:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y1 <= -3.3e+59:
		tmp = (k * y4) * ((y1 * y2) - (y * b))
	elif y1 <= -2.7:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif y1 <= -7.5e-14:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y1 <= -2.42e-234:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y1 <= 3.2e-299:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 8.5e-260:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 1.1e-83:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.78e+227)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y1 <= -3.3e+59)
		tmp = Float64(Float64(k * y4) * Float64(Float64(y1 * y2) - Float64(y * b)));
	elseif (y1 <= -2.7)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (y1 <= -7.5e-14)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y1 <= -2.42e-234)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y1 <= 3.2e-299)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 8.5e-260)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 1.1e-83)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(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)
	tmp = 0.0;
	if (y1 <= -1.78e+227)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y1 <= -3.3e+59)
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	elseif (y1 <= -2.7)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (y1 <= -7.5e-14)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y1 <= -2.42e-234)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y1 <= 3.2e-299)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 8.5e-260)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 1.1e-83)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = ((z * i) - (y2 * y4)) * (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_] := If[LessEqual[y1, -1.78e+227], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.3e+59], N[(N[(k * y4), $MachinePrecision] * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.7], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -7.5e-14], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.42e-234], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.2e-299], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 8.5e-260], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.1e-83], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y1 < -1.77999999999999995e227

   1. Initial program 27.8%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in k around inf 44.4%

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

   6. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   if -1.77999999999999995e227 < y1 < -3.2999999999999999e59

   1. Initial program 22.6%

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

   3. Simplified 22.6%

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

   5. Taylor expanded in k around inf 38.1%

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

   6. Taylor expanded in y4 around inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. +-commutative 50.9%

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

      3. mul-1-neg 50.9%

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

      4. unsub-neg 50.9%

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

      5. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if -3.2999999999999999e59 < y1 < -2.7000000000000002

   1. Initial program 43.8%

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

   3. Simplified 43.8%

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

   5. Taylor expanded in y0 around inf 38.4%

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

   6. Taylor expanded in y5 around inf 57.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 57.9%

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

   8. Simplified 57.9%

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

   if -2.7000000000000002 < y1 < -7.4999999999999996e-14

   1. Initial program 61.2%

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

   3. Simplified 61.2%

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

   5. Taylor expanded in y0 around inf 61.9%

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

   6. Taylor expanded in c around inf 80.5%

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

      1. *-commutative 80.5%

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

      2. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   if -7.4999999999999996e-14 < y1 < -2.4200000000000001e-234

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   5. Taylor expanded in y0 around inf 40.7%

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

   6. Taylor expanded in j around inf 40.8%

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

      1. *-commutative 40.8%

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

   8. Simplified 40.8%

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

   if -2.4200000000000001e-234 < y1 < 3.20000000000000008e-299

   1. Initial program 37.5%

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

   3. Simplified 37.5%

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

   5. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-lft-neg-out 69.2%

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

      3. +-commutative 69.2%

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

      4. *-commutative 69.2%

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

      5. cancel-sign-sub-inv 69.2%

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

      6. *-commutative 69.2%

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

   8. Simplified 69.2%

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

   if 3.20000000000000008e-299 < y1 < 8.5000000000000003e-260

   1. Initial program 41.5%

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

   3. Simplified 41.5%

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

   5. Taylor expanded in b around inf 25.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 59.2%

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

   if 8.5000000000000003e-260 < y1 < 1.10000000000000004e-83

   1. Initial program 44.7%

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

   3. Simplified 44.7%

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

   5. Taylor expanded in b around inf 56.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 48.9%

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

   if 1.10000000000000004e-83 < y1

   1. Initial program 33.9%

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

   3. Taylor expanded in c around inf 51.5%

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

   4. Taylor expanded in x around 0 50.3%

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

      1. *-commutative 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in t around inf 41.1%

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

      1. *-commutative 41.1%

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

      2. associate-*r* 39.8%

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

      3. *-commutative 39.8%

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

      4. associate-*l* 38.6%

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

   9. Simplified 38.6%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.78 \cdot 10^{+227}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -2.7:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.42 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 8.5 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 1.1 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y1 \leq -1 \cdot 10^{+227}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.35 \cdot 10^{+56}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -7 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 2.25 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.3 \cdot 10^{+63}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y1 -1e+227)
     (* k (* z (- (* b y0) (* i y1))))
     (if (<= y1 -3.35e+56)
       (* (* k y4) (- (* y1 y2) (* y b)))
       (if (<= y1 -7e-236)
         (* j (* y0 (- (* y3 y5) (* x b))))
         (if (<= y1 2.7e-299)
           t_1
           (if (<= y1 1.95e-262)
             (* b (* j (- (* t y4) (* x y0))))
             (if (<= y1 2.6e-171)
               t_1
               (if (<= y1 2.25e-85)
                 (* b (* y0 (- (* z k) (* x j))))
                 (if (<= y1 3.3e+63)
                   (* c (* i (* z t)))
                   (* k (* y1 (- (* y2 y4) (* z i))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y1 <= -1e+227) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -3.35e+56) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -7e-236) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 2.7e-299) {
		tmp = t_1;
	} else if (y1 <= 1.95e-262) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 2.6e-171) {
		tmp = t_1;
	} else if (y1 <= 2.25e-85) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 3.3e+63) {
		tmp = c * (i * (z * t));
	} else {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y1 <= (-1d+227)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y1 <= (-3.35d+56)) then
        tmp = (k * y4) * ((y1 * y2) - (y * b))
    else if (y1 <= (-7d-236)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y1 <= 2.7d-299) then
        tmp = t_1
    else if (y1 <= 1.95d-262) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 2.6d-171) then
        tmp = t_1
    else if (y1 <= 2.25d-85) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y1 <= 3.3d+63) then
        tmp = c * (i * (z * t))
    else
        tmp = k * (y1 * ((y2 * y4) - (z * i)))
    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 * (b * ((x * y) - (z * t)));
	double tmp;
	if (y1 <= -1e+227) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -3.35e+56) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -7e-236) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 2.7e-299) {
		tmp = t_1;
	} else if (y1 <= 1.95e-262) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 2.6e-171) {
		tmp = t_1;
	} else if (y1 <= 2.25e-85) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 3.3e+63) {
		tmp = c * (i * (z * t));
	} else {
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y1 <= -1e+227:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y1 <= -3.35e+56:
		tmp = (k * y4) * ((y1 * y2) - (y * b))
	elif y1 <= -7e-236:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y1 <= 2.7e-299:
		tmp = t_1
	elif y1 <= 1.95e-262:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 2.6e-171:
		tmp = t_1
	elif y1 <= 2.25e-85:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y1 <= 3.3e+63:
		tmp = c * (i * (z * t))
	else:
		tmp = k * (y1 * ((y2 * y4) - (z * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y1 <= -1e+227)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y1 <= -3.35e+56)
		tmp = Float64(Float64(k * y4) * Float64(Float64(y1 * y2) - Float64(y * b)));
	elseif (y1 <= -7e-236)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y1 <= 2.7e-299)
		tmp = t_1;
	elseif (y1 <= 1.95e-262)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 2.6e-171)
		tmp = t_1;
	elseif (y1 <= 2.25e-85)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y1 <= 3.3e+63)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	else
		tmp = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))));
	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 * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y1 <= -1e+227)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y1 <= -3.35e+56)
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	elseif (y1 <= -7e-236)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y1 <= 2.7e-299)
		tmp = t_1;
	elseif (y1 <= 1.95e-262)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 2.6e-171)
		tmp = t_1;
	elseif (y1 <= 2.25e-85)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y1 <= 3.3e+63)
		tmp = c * (i * (z * t));
	else
		tmp = k * (y1 * ((y2 * y4) - (z * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1e+227], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.35e+56], N[(N[(k * y4), $MachinePrecision] * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -7e-236], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.7e-299], t$95$1, If[LessEqual[y1, 1.95e-262], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.6e-171], t$95$1, If[LessEqual[y1, 2.25e-85], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.3e+63], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y1 < -1.0000000000000001e227

   1. Initial program 27.8%

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

   3. Simplified 27.8%

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

   5. Taylor expanded in k around inf 44.4%

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

   6. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   if -1.0000000000000001e227 < y1 < -3.35e56

   1. Initial program 22.6%

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

   3. Simplified 22.6%

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

   5. Taylor expanded in k around inf 38.1%

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

   6. Taylor expanded in y4 around inf 50.9%

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

      1. associate-*r* 50.9%

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

      2. +-commutative 50.9%

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

      3. mul-1-neg 50.9%

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

      4. unsub-neg 50.9%

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

      5. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if -3.35e56 < y1 < -6.99999999999999988e-236

   1. Initial program 37.9%

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

   3. Simplified 37.9%

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

   5. Taylor expanded in y0 around inf 41.7%

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

   6. Taylor expanded in j around inf 38.9%

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

      1. *-commutative 38.9%

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

   8. Simplified 38.9%

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

   if -6.99999999999999988e-236 < y1 < 2.70000000000000002e-299 or 1.94999999999999992e-262 < y1 < 2.60000000000000005e-171

   1. Initial program 38.2%

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

   3. Simplified 38.2%

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

   5. Taylor expanded in b around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-lft-neg-out 62.9%

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

      3. +-commutative 62.9%

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

      4. *-commutative 62.9%

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

      5. cancel-sign-sub-inv 62.9%

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

      6. *-commutative 62.9%

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

   8. Simplified 62.9%

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

   if 2.70000000000000002e-299 < y1 < 1.94999999999999992e-262

   1. Initial program 41.5%

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

   3. Simplified 41.5%

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

   5. Taylor expanded in b around inf 25.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 59.2%

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

   if 2.60000000000000005e-171 < y1 < 2.25000000000000002e-85

   1. Initial program 46.0%

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

   3. Simplified 46.0%

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

   5. Taylor expanded in b around inf 69.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 54.7%

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

   if 2.25000000000000002e-85 < y1 < 3.3000000000000002e63

   1. Initial program 48.3%

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

   3. Taylor expanded in c around inf 64.0%

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

   4. Taylor expanded in x around 0 54.5%

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

      1. *-commutative 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in i around inf 35.3%

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

   if 3.3000000000000002e63 < y1

   1. Initial program 25.3%

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

   3. Simplified 25.3%

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

   5. Taylor expanded in k around inf 34.5%

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

   6. Taylor expanded in y1 around inf 46.1%

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

      1. *-commutative 46.1%

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

   8. Simplified 46.1%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1 \cdot 10^{+227}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -3.35 \cdot 10^{+56}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -7 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 2.7 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 1.95 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 2.6 \cdot 10^{-171}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 2.25 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 3.3 \cdot 10^{+63}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 31.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y2 \cdot \left(c \cdot \left(t \cdot \frac{z \cdot i}{y2}\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{if}\;y5 \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{-35}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -9.8 \cdot 10^{-178}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y2 (- (* c (* t (/ (* z i) y2))) (* c (* t y4))))))
   (if (<= y5 -5.8e+85)
     (* t (* y5 (- (* a y2) (* i j))))
     (if (<= y5 -1.25e-35)
       (* k (* y (- (* i y5) (* b y4))))
       (if (<= y5 -9.8e-178)
         (* c (* y0 (- (* x y2) (* z y3))))
         (if (<= y5 1.15e-145)
           t_1
           (if (<= y5 9e-88)
             (* b (* y4 (- (* t j) (* y k))))
             (if (<= y5 8e-18)
               t_1
               (if (<= y5 2.7e+55)
                 (* k (* z (- (* b y0) (* i y1))))
                 (* (* j y5) (- (* y0 y3) (* 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) {
	double t_1 = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)));
	double tmp;
	if (y5 <= -5.8e+85) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (y5 <= -1.25e-35) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y5 <= -9.8e-178) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y5 <= 1.15e-145) {
		tmp = t_1;
	} else if (y5 <= 9e-88) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y5 <= 8e-18) {
		tmp = t_1;
	} else if (y5 <= 2.7e+55) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)))
    if (y5 <= (-5.8d+85)) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (y5 <= (-1.25d-35)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y5 <= (-9.8d-178)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (y5 <= 1.15d-145) then
        tmp = t_1
    else if (y5 <= 9d-88) then
        tmp = b * (y4 * ((t * j) - (y * k)))
    else if (y5 <= 8d-18) then
        tmp = t_1
    else if (y5 <= 2.7d+55) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else
        tmp = (j * y5) * ((y0 * y3) - (t * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)));
	double tmp;
	if (y5 <= -5.8e+85) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (y5 <= -1.25e-35) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y5 <= -9.8e-178) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (y5 <= 1.15e-145) {
		tmp = t_1;
	} else if (y5 <= 9e-88) {
		tmp = b * (y4 * ((t * j) - (y * k)));
	} else if (y5 <= 8e-18) {
		tmp = t_1;
	} else if (y5 <= 2.7e+55) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else {
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)))
	tmp = 0
	if y5 <= -5.8e+85:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif y5 <= -1.25e-35:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y5 <= -9.8e-178:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif y5 <= 1.15e-145:
		tmp = t_1
	elif y5 <= 9e-88:
		tmp = b * (y4 * ((t * j) - (y * k)))
	elif y5 <= 8e-18:
		tmp = t_1
	elif y5 <= 2.7e+55:
		tmp = k * (z * ((b * y0) - (i * y1)))
	else:
		tmp = (j * y5) * ((y0 * y3) - (t * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y2 * Float64(Float64(c * Float64(t * Float64(Float64(z * i) / y2))) - Float64(c * Float64(t * y4))))
	tmp = 0.0
	if (y5 <= -5.8e+85)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (y5 <= -1.25e-35)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y5 <= -9.8e-178)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y5 <= 1.15e-145)
		tmp = t_1;
	elseif (y5 <= 9e-88)
		tmp = Float64(b * Float64(y4 * Float64(Float64(t * j) - Float64(y * k))));
	elseif (y5 <= 8e-18)
		tmp = t_1;
	elseif (y5 <= 2.7e+55)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	else
		tmp = Float64(Float64(j * y5) * Float64(Float64(y0 * y3) - Float64(t * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y2 * ((c * (t * ((z * i) / y2))) - (c * (t * y4)));
	tmp = 0.0;
	if (y5 <= -5.8e+85)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (y5 <= -1.25e-35)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y5 <= -9.8e-178)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (y5 <= 1.15e-145)
		tmp = t_1;
	elseif (y5 <= 9e-88)
		tmp = b * (y4 * ((t * j) - (y * k)));
	elseif (y5 <= 8e-18)
		tmp = t_1;
	elseif (y5 <= 2.7e+55)
		tmp = k * (z * ((b * y0) - (i * y1)));
	else
		tmp = (j * y5) * ((y0 * y3) - (t * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y2 * N[(N[(c * N[(t * N[(N[(z * i), $MachinePrecision] / y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.8e+85], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.25e-35], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -9.8e-178], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.15e-145], t$95$1, If[LessEqual[y5, 9e-88], N[(b * N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 8e-18], t$95$1, If[LessEqual[y5, 2.7e+55], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * y5), $MachinePrecision] * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y5 < -5.79999999999999995e85

   1. Initial program 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in y5 around -inf 55.8%

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

   6. Taylor expanded in t around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(y5 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right)\right) \]

   8. Simplified 55.7%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y5 \cdot \left(j \cdot i - y2 \cdot a\right)\right)\right)} \]

   if -5.79999999999999995e85 < y5 < -1.24999999999999991e-35

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in k around inf 46.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in y around inf 37.3%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.3%

         \[\leadsto \color{blue}{-k \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

      2. distribute-rgt-neg-in 37.3%

         \[\leadsto \color{blue}{k \cdot \left(-y \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

      3. *-commutative 37.3%

         \[\leadsto k \cdot \left(-\color{blue}{\left(b \cdot y4 - i \cdot y5\right) \cdot y}\right) \]

      4. distribute-rgt-neg-in 37.3%

         \[\leadsto k \cdot \color{blue}{\left(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(-y\right)\right)} \]

      5. *-commutative 37.3%

         \[\leadsto k \cdot \left(\left(\color{blue}{y4 \cdot b} - i \cdot y5\right) \cdot \left(-y\right)\right) \]

      6. *-commutative 37.3%

         \[\leadsto k \cdot \left(\left(y4 \cdot b - \color{blue}{y5 \cdot i}\right) \cdot \left(-y\right)\right) \]

   8. Simplified 37.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(y4 \cdot b - y5 \cdot i\right) \cdot \left(-y\right)\right)} \]

   if -1.24999999999999991e-35 < y5 < -9.80000000000000041e-178

   1. Initial program 65.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 65.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 42.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in c around inf 42.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

      2. *-commutative 42.3%

         \[\leadsto c \cdot \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right)\right)} \]

   if -9.80000000000000041e-178 < y5 < 1.15000000000000004e-145 or 8.99999999999999982e-88 < y5 < 8.0000000000000006e-18

   1. Initial program 35.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 57.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 54.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 54.9%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 54.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot t\right)} \]

      2. associate-*r* 43.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right) \cdot t} \]

      3. *-commutative 43.9%

         \[\leadsto \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot c\right)} \cdot t \]

      4. associate-*l* 41.4%

         \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   9. Simplified 41.4%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   10. Taylor expanded in y2 around -inf 45.9%

       \[\leadsto \color{blue}{-1 \cdot \left(y2 \cdot \left(-1 \cdot \frac{c \cdot \left(i \cdot \left(t \cdot z\right)\right)}{y2} + c \cdot \left(t \cdot y4\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 45.9%

          \[\leadsto \color{blue}{-y2 \cdot \left(-1 \cdot \frac{c \cdot \left(i \cdot \left(t \cdot z\right)\right)}{y2} + c \cdot \left(t \cdot y4\right)\right)} \]

       2. *-commutative 45.9%

          \[\leadsto -\color{blue}{\left(-1 \cdot \frac{c \cdot \left(i \cdot \left(t \cdot z\right)\right)}{y2} + c \cdot \left(t \cdot y4\right)\right) \cdot y2} \]

       3. distribute-rgt-neg-in 45.9%

          \[\leadsto \color{blue}{\left(-1 \cdot \frac{c \cdot \left(i \cdot \left(t \cdot z\right)\right)}{y2} + c \cdot \left(t \cdot y4\right)\right) \cdot \left(-y2\right)} \]

       4. +-commutative 45.9%

          \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot y4\right) + -1 \cdot \frac{c \cdot \left(i \cdot \left(t \cdot z\right)\right)}{y2}\right)} \cdot \left(-y2\right) \]

       5. mul-1-neg 45.9%

          \[\leadsto \left(c \cdot \left(t \cdot y4\right) + \color{blue}{\left(-\frac{c \cdot \left(i \cdot \left(t \cdot z\right)\right)}{y2}\right)}\right) \cdot \left(-y2\right) \]

       6. unsub-neg 45.9%

          \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot y4\right) - \frac{c \cdot \left(i \cdot \left(t \cdot z\right)\right)}{y2}\right)} \cdot \left(-y2\right) \]

       7. associate-/l* 48.3%

          \[\leadsto \left(c \cdot \left(t \cdot y4\right) - \color{blue}{c \cdot \frac{i \cdot \left(t \cdot z\right)}{y2}}\right) \cdot \left(-y2\right) \]

       8. associate-*r* 49.5%

          \[\leadsto \left(c \cdot \left(t \cdot y4\right) - c \cdot \frac{\color{blue}{\left(i \cdot t\right) \cdot z}}{y2}\right) \cdot \left(-y2\right) \]

       9. *-commutative 49.5%

          \[\leadsto \left(c \cdot \left(t \cdot y4\right) - c \cdot \frac{\color{blue}{\left(t \cdot i\right)} \cdot z}{y2}\right) \cdot \left(-y2\right) \]

       10. associate-*l* 48.3%

           \[\leadsto \left(c \cdot \left(t \cdot y4\right) - c \cdot \frac{\color{blue}{t \cdot \left(i \cdot z\right)}}{y2}\right) \cdot \left(-y2\right) \]

       11. associate-/l* 49.5%

           \[\leadsto \left(c \cdot \left(t \cdot y4\right) - c \cdot \color{blue}{\left(t \cdot \frac{i \cdot z}{y2}\right)}\right) \cdot \left(-y2\right) \]

   12. Simplified 49.5%

       \[\leadsto \color{blue}{\left(c \cdot \left(t \cdot y4\right) - c \cdot \left(t \cdot \frac{i \cdot z}{y2}\right)\right) \cdot \left(-y2\right)} \]

   if 1.15000000000000004e-145 < y5 < 8.99999999999999982e-88

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 41.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y4 around inf 58.9%

      \[\leadsto \color{blue}{b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)} \]

   if 8.0000000000000006e-18 < y5 < 2.69999999999999977e55

   1. Initial program 50.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in k around inf 38.8%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in z around inf 64.6%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto k \cdot \left(z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 64.6%

         \[\leadsto k \cdot \left(z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if 2.69999999999999977e55 < y5

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y5 around -inf 54.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in j around inf 54.2%

      \[\leadsto -1 \cdot \color{blue}{\left(j \cdot \left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right) \cdot j\right)} \]

      2. *-commutative 54.2%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right) \cdot y5\right)} \cdot j\right) \]

      3. associate-*l* 53.5%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right) \cdot \left(y5 \cdot j\right)\right)} \]

      4. +-commutative 53.5%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(i \cdot t + -1 \cdot \left(y0 \cdot y3\right)\right)} \cdot \left(y5 \cdot j\right)\right) \]

      5. mul-1-neg 53.5%

         \[\leadsto -1 \cdot \left(\left(i \cdot t + \color{blue}{\left(-y0 \cdot y3\right)}\right) \cdot \left(y5 \cdot j\right)\right) \]

      6. unsub-neg 53.5%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(i \cdot t - y0 \cdot y3\right)} \cdot \left(y5 \cdot j\right)\right) \]

      7. *-commutative 53.5%

         \[\leadsto -1 \cdot \left(\left(\color{blue}{t \cdot i} - y0 \cdot y3\right) \cdot \left(y5 \cdot j\right)\right) \]

   8. Simplified 53.5%

      \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot i - y0 \cdot y3\right) \cdot \left(y5 \cdot j\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -1.25 \cdot 10^{-35}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -9.8 \cdot 10^{-178}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.15 \cdot 10^{-145}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(t \cdot \frac{z \cdot i}{y2}\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{-18}:\\ \;\;\;\;y2 \cdot \left(c \cdot \left(t \cdot \frac{z \cdot i}{y2}\right) - c \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot y5\right) \cdot \left(y0 \cdot y3 - t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y1 \leq -9.4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -5.4 \cdot 10^{-235}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.04 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (- (* y2 y4) (* z i)))))
        (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= y1 -9.4e+30)
     t_1
     (if (<= y1 -5.4e-235)
       (* j (* y0 (- (* y3 y5) (* x b))))
       (if (<= y1 4.8e-298)
         t_2
         (if (<= y1 7.6e-263)
           (* b (* j (- (* t y4) (* x y0))))
           (if (<= y1 3.5e-171)
             t_2
             (if (<= y1 3.7e-86)
               (* b (* y0 (- (* z k) (* x j))))
               (if (<= y1 1.04e+65) (* c (* i (* z t))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y1 <= -9.4e+30) {
		tmp = t_1;
	} else if (y1 <= -5.4e-235) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 4.8e-298) {
		tmp = t_2;
	} else if (y1 <= 7.6e-263) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 3.5e-171) {
		tmp = t_2;
	} else if (y1 <= 3.7e-86) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 1.04e+65) {
		tmp = c * (i * (z * t));
	} 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 = k * (y1 * ((y2 * y4) - (z * i)))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (y1 <= (-9.4d+30)) then
        tmp = t_1
    else if (y1 <= (-5.4d-235)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y1 <= 4.8d-298) then
        tmp = t_2
    else if (y1 <= 7.6d-263) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 3.5d-171) then
        tmp = t_2
    else if (y1 <= 3.7d-86) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (y1 <= 1.04d+65) then
        tmp = c * (i * (z * t))
    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 = k * (y1 * ((y2 * y4) - (z * i)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y1 <= -9.4e+30) {
		tmp = t_1;
	} else if (y1 <= -5.4e-235) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 4.8e-298) {
		tmp = t_2;
	} else if (y1 <= 7.6e-263) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 3.5e-171) {
		tmp = t_2;
	} else if (y1 <= 3.7e-86) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (y1 <= 1.04e+65) {
		tmp = c * (i * (z * t));
	} 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 = k * (y1 * ((y2 * y4) - (z * i)))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y1 <= -9.4e+30:
		tmp = t_1
	elif y1 <= -5.4e-235:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y1 <= 4.8e-298:
		tmp = t_2
	elif y1 <= 7.6e-263:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 3.5e-171:
		tmp = t_2
	elif y1 <= 3.7e-86:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif y1 <= 1.04e+65:
		tmp = c * (i * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y1 <= -9.4e+30)
		tmp = t_1;
	elseif (y1 <= -5.4e-235)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y1 <= 4.8e-298)
		tmp = t_2;
	elseif (y1 <= 7.6e-263)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 3.5e-171)
		tmp = t_2;
	elseif (y1 <= 3.7e-86)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y1 <= 1.04e+65)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	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 = k * (y1 * ((y2 * y4) - (z * i)));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y1 <= -9.4e+30)
		tmp = t_1;
	elseif (y1 <= -5.4e-235)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y1 <= 4.8e-298)
		tmp = t_2;
	elseif (y1 <= 7.6e-263)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 3.5e-171)
		tmp = t_2;
	elseif (y1 <= 3.7e-86)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (y1 <= 1.04e+65)
		tmp = c * (i * (z * t));
	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[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -9.4e+30], t$95$1, If[LessEqual[y1, -5.4e-235], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.8e-298], t$95$2, If[LessEqual[y1, 7.6e-263], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.5e-171], t$95$2, If[LessEqual[y1, 3.7e-86], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.04e+65], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -9.39999999999999979e30 or 1.03999999999999999e65 < y1

   1. Initial program 26.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in k around inf 37.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 44.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto k \cdot \left(y1 \cdot \left(y2 \cdot y4 - \color{blue}{z \cdot i}\right)\right) \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)} \]

   if -9.39999999999999979e30 < y1 < -5.4000000000000003e-235

   1. Initial program 37.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 41.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 39.4%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.4%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3 - b \cdot x\right)\right)} \]

   if -5.4000000000000003e-235 < y1 < 4.79999999999999975e-298 or 7.60000000000000009e-263 < y1 < 3.49999999999999994e-171

   1. Initial program 38.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 62.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 62.9%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 62.9%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 62.9%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 62.9%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 62.9%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 62.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   if 4.79999999999999975e-298 < y1 < 7.60000000000000009e-263

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 25.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 59.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 3.49999999999999994e-171 < y1 < 3.6999999999999998e-86

   1. Initial program 46.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 69.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 54.7%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 3.6999999999999998e-86 < y1 < 1.03999999999999999e65

   1. Initial program 48.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 64.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 54.5%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 54.5%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 54.5%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 35.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -9.4 \cdot 10^{+30}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;y1 \leq -5.4 \cdot 10^{-235}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.8 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 7.6 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.5 \cdot 10^{-171}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y1 \leq 1.04 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 1.6 \cdot 10^{-129}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.95 \cdot 10^{+59}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{+98}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(j \cdot \left(y0 \cdot \left(y3 \cdot \frac{y5}{y2}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -1.2e+86)
   (* t (* y5 (- (* a y2) (* i j))))
   (if (<= y5 1.6e-129)
     (*
      c
      (+
       (- (* y0 (- (* x y2) (* z y3))) (* (* x y) i))
       (* y4 (- (* y y3) (* t y2)))))
     (if (<= y5 4.6e+33)
       (* c (* z (- (* t i) (* y0 y3))))
       (if (<= y5 1.95e+59)
         (* k (* z (- (* b y0) (* i y1))))
         (if (<= y5 1e+98)
           (* b (* j (- (* t y4) (* x y0))))
           (if (<= y5 3.9e+113)
             (* b (* z (- (* k y0) (* t a))))
             (* y2 (* j (* y0 (* y3 (/ y5 y2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.2e+86) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (y5 <= 1.6e-129) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - ((x * y) * i)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 4.6e+33) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y5 <= 1.95e+59) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y5 <= 1e+98) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 3.9e+113) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else {
		tmp = y2 * (j * (y0 * (y3 * (y5 / y2))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-1.2d+86)) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else if (y5 <= 1.6d-129) then
        tmp = c * (((y0 * ((x * y2) - (z * y3))) - ((x * y) * i)) + (y4 * ((y * y3) - (t * y2))))
    else if (y5 <= 4.6d+33) then
        tmp = c * (z * ((t * i) - (y0 * y3)))
    else if (y5 <= 1.95d+59) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y5 <= 1d+98) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y5 <= 3.9d+113) then
        tmp = b * (z * ((k * y0) - (t * a)))
    else
        tmp = y2 * (j * (y0 * (y3 * (y5 / y2))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -1.2e+86) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else if (y5 <= 1.6e-129) {
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - ((x * y) * i)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y5 <= 4.6e+33) {
		tmp = c * (z * ((t * i) - (y0 * y3)));
	} else if (y5 <= 1.95e+59) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y5 <= 1e+98) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 3.9e+113) {
		tmp = b * (z * ((k * y0) - (t * a)));
	} else {
		tmp = y2 * (j * (y0 * (y3 * (y5 / y2))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -1.2e+86:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	elif y5 <= 1.6e-129:
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - ((x * y) * i)) + (y4 * ((y * y3) - (t * y2))))
	elif y5 <= 4.6e+33:
		tmp = c * (z * ((t * i) - (y0 * y3)))
	elif y5 <= 1.95e+59:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y5 <= 1e+98:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y5 <= 3.9e+113:
		tmp = b * (z * ((k * y0) - (t * a)))
	else:
		tmp = y2 * (j * (y0 * (y3 * (y5 / y2))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -1.2e+86)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	elseif (y5 <= 1.6e-129)
		tmp = Float64(c * Float64(Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) - Float64(Float64(x * y) * i)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y5 <= 4.6e+33)
		tmp = Float64(c * Float64(z * Float64(Float64(t * i) - Float64(y0 * y3))));
	elseif (y5 <= 1.95e+59)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y5 <= 1e+98)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y5 <= 3.9e+113)
		tmp = Float64(b * Float64(z * Float64(Float64(k * y0) - Float64(t * a))));
	else
		tmp = Float64(y2 * Float64(j * Float64(y0 * Float64(y3 * Float64(y5 / y2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -1.2e+86)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	elseif (y5 <= 1.6e-129)
		tmp = c * (((y0 * ((x * y2) - (z * y3))) - ((x * y) * i)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y5 <= 4.6e+33)
		tmp = c * (z * ((t * i) - (y0 * y3)));
	elseif (y5 <= 1.95e+59)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y5 <= 1e+98)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y5 <= 3.9e+113)
		tmp = b * (z * ((k * y0) - (t * a)));
	else
		tmp = y2 * (j * (y0 * (y3 * (y5 / y2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -1.2e+86], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.6e-129], N[(c * N[(N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * y), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.6e+33], N[(c * N[(z * N[(N[(t * i), $MachinePrecision] - N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.95e+59], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e+98], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.9e+113], N[(b * N[(z * N[(N[(k * y0), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(j * N[(y0 * N[(y3 * N[(y5 / y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y5 < -1.2e86

   1. Initial program 23.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y5 around -inf 55.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in t around inf 55.7%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y5 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(y5 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right)\right) \]

      2. *-commutative 55.7%

         \[\leadsto -1 \cdot \left(t \cdot \left(y5 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right)\right) \]

   8. Simplified 55.7%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y5 \cdot \left(j \cdot i - y2 \cdot a\right)\right)\right)} \]

   if -1.2e86 < y5 < 1.6000000000000001e-129

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 51.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around inf 48.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{-1 \cdot \left(i \cdot \left(x \cdot y\right)\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 48.9%

         \[\leadsto c \cdot \left(\left(\color{blue}{\left(-i \cdot \left(x \cdot y\right)\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      2. *-commutative 48.9%

         \[\leadsto c \cdot \left(\left(\left(-i \cdot \color{blue}{\left(y \cdot x\right)}\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      3. distribute-rgt-neg-in 48.9%

         \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(-y \cdot x\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      4. distribute-rgt-neg-in 48.9%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(y \cdot \left(-x\right)\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 48.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(y \cdot \left(-x\right)\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   if 1.6000000000000001e-129 < y5 < 4.60000000000000021e33

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 49.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 55.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 55.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 55.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]

   if 4.60000000000000021e33 < y5 < 1.95000000000000011e59

   1. Initial program 33.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in k around inf 33.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto k \cdot \left(z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 100.0%

         \[\leadsto k \cdot \left(z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if 1.95000000000000011e59 < y5 < 9.99999999999999998e97

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 62.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 9.99999999999999998e97 < y5 < 3.9000000000000002e113

   1. Initial program 0.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 0.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 71.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in z around inf 72.1%

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(-1 \cdot \left(a \cdot t\right) - -1 \cdot \left(k \cdot y0\right)\right)\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-out-- 72.1%

         \[\leadsto b \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]

      2. *-commutative 72.1%

         \[\leadsto b \cdot \left(z \cdot \left(-1 \cdot \left(\color{blue}{t \cdot a} - k \cdot y0\right)\right)\right) \]

   8. Simplified 72.1%

      \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(-1 \cdot \left(t \cdot a - k \cdot y0\right)\right)\right)} \]

   if 3.9000000000000002e113 < y5

   1. Initial program 31.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 40.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 42.2%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 43.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in j around inf 45.4%

       \[\leadsto y2 \cdot \color{blue}{\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2}} \]
   11. Step-by-step derivation

       1. associate-*r/ 47.5%

          \[\leadsto y2 \cdot \color{blue}{\left(j \cdot \frac{y0 \cdot \left(y3 \cdot y5\right)}{y2}\right)} \]

       2. associate-/l* 51.6%

          \[\leadsto y2 \cdot \left(j \cdot \color{blue}{\left(y0 \cdot \frac{y3 \cdot y5}{y2}\right)}\right) \]

       3. associate-/l* 58.7%

          \[\leadsto y2 \cdot \left(j \cdot \left(y0 \cdot \color{blue}{\left(y3 \cdot \frac{y5}{y2}\right)}\right)\right) \]

   12. Simplified 58.7%

       \[\leadsto y2 \cdot \color{blue}{\left(j \cdot \left(y0 \cdot \left(y3 \cdot \frac{y5}{y2}\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.2 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 1.6 \cdot 10^{-129}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) - \left(x \cdot y\right) \cdot i\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y5 \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(z \cdot \left(t \cdot i - y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 1.95 \cdot 10^{+59}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{+98}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.9 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(z \cdot \left(k \cdot y0 - t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(j \cdot \left(y0 \cdot \left(y3 \cdot \frac{y5}{y2}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -75000000000:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (- (* y2 y4) (* z i))))))
   (if (<= b -1.9e+138)
     (* b (* y0 (- (* z k) (* x j))))
     (if (<= b -75000000000.0)
       (* a (* b (- (* x y) (* z t))))
       (if (<= b -8.2e-225)
         t_1
         (if (<= b 2.2e-116)
           (* y0 (* y3 (- (* j y5) (* z c))))
           (if (<= b 6.4e-90)
             t_1
             (if (<= b 1.26e+17)
               (* t (* y5 (- (* a y2) (* i j))))
               (* b (* j (- (* t y4) (* x y0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * ((y2 * y4) - (z * i)));
	double tmp;
	if (b <= -1.9e+138) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -75000000000.0) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -8.2e-225) {
		tmp = t_1;
	} else if (b <= 2.2e-116) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 6.4e-90) {
		tmp = t_1;
	} else if (b <= 1.26e+17) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else {
		tmp = b * (j * ((t * y4) - (x * 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) :: tmp
    t_1 = k * (y1 * ((y2 * y4) - (z * i)))
    if (b <= (-1.9d+138)) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (b <= (-75000000000.0d0)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (b <= (-8.2d-225)) then
        tmp = t_1
    else if (b <= 2.2d-116) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (b <= 6.4d-90) then
        tmp = t_1
    else if (b <= 1.26d+17) then
        tmp = t * (y5 * ((a * y2) - (i * j)))
    else
        tmp = b * (j * ((t * y4) - (x * 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 = k * (y1 * ((y2 * y4) - (z * i)));
	double tmp;
	if (b <= -1.9e+138) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (b <= -75000000000.0) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (b <= -8.2e-225) {
		tmp = t_1;
	} else if (b <= 2.2e-116) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (b <= 6.4e-90) {
		tmp = t_1;
	} else if (b <= 1.26e+17) {
		tmp = t * (y5 * ((a * y2) - (i * j)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * ((y2 * y4) - (z * i)))
	tmp = 0
	if b <= -1.9e+138:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif b <= -75000000000.0:
		tmp = a * (b * ((x * y) - (z * t)))
	elif b <= -8.2e-225:
		tmp = t_1
	elif b <= 2.2e-116:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif b <= 6.4e-90:
		tmp = t_1
	elif b <= 1.26e+17:
		tmp = t * (y5 * ((a * y2) - (i * j)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(Float64(y2 * y4) - Float64(z * i))))
	tmp = 0.0
	if (b <= -1.9e+138)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (b <= -75000000000.0)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (b <= -8.2e-225)
		tmp = t_1;
	elseif (b <= 2.2e-116)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (b <= 6.4e-90)
		tmp = t_1;
	elseif (b <= 1.26e+17)
		tmp = Float64(t * Float64(y5 * Float64(Float64(a * y2) - Float64(i * j))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * 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 = k * (y1 * ((y2 * y4) - (z * i)));
	tmp = 0.0;
	if (b <= -1.9e+138)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (b <= -75000000000.0)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (b <= -8.2e-225)
		tmp = t_1;
	elseif (b <= 2.2e-116)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (b <= 6.4e-90)
		tmp = t_1;
	elseif (b <= 1.26e+17)
		tmp = t * (y5 * ((a * y2) - (i * j)));
	else
		tmp = b * (j * ((t * y4) - (x * 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[(k * N[(y1 * N[(N[(y2 * y4), $MachinePrecision] - N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+138], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -75000000000.0], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.2e-225], t$95$1, If[LessEqual[b, 2.2e-116], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e-90], t$95$1, If[LessEqual[b, 1.26e+17], N[(t * N[(y5 * N[(N[(a * y2), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.90000000000000006e138

   1. Initial program 35.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 68.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 61.1%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if -1.90000000000000006e138 < b < -7.5e10

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 36.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 51.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 51.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 51.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 51.7%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 51.7%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 51.7%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 51.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   if -7.5e10 < b < -8.20000000000000044e-225 or 2.2000000000000001e-116 < b < 6.40000000000000014e-90

   1. Initial program 38.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in k around inf 50.3%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in y1 around inf 43.3%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - i \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.3%

         \[\leadsto k \cdot \left(y1 \cdot \left(y2 \cdot y4 - \color{blue}{z \cdot i}\right)\right) \]

   8. Simplified 43.3%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)} \]

   if -8.20000000000000044e-225 < b < 2.2000000000000001e-116

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 43.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y3 around -inf 50.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 50.3%

         \[\leadsto \color{blue}{-y0 \cdot \left(y3 \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      2. distribute-rgt-neg-in 50.3%

         \[\leadsto \color{blue}{y0 \cdot \left(-y3 \cdot \left(-1 \cdot \left(j \cdot y5\right) + c \cdot z\right)\right)} \]

      3. +-commutative 50.3%

         \[\leadsto y0 \cdot \left(-y3 \cdot \color{blue}{\left(c \cdot z + -1 \cdot \left(j \cdot y5\right)\right)}\right) \]

      4. mul-1-neg 50.3%

         \[\leadsto y0 \cdot \left(-y3 \cdot \left(c \cdot z + \color{blue}{\left(-j \cdot y5\right)}\right)\right) \]

      5. unsub-neg 50.3%

         \[\leadsto y0 \cdot \left(-y3 \cdot \color{blue}{\left(c \cdot z - j \cdot y5\right)}\right) \]

      6. *-commutative 50.3%

         \[\leadsto y0 \cdot \left(-y3 \cdot \left(\color{blue}{z \cdot c} - j \cdot y5\right)\right) \]

      7. *-commutative 50.3%

         \[\leadsto y0 \cdot \left(-y3 \cdot \left(z \cdot c - \color{blue}{y5 \cdot j}\right)\right) \]

   8. Simplified 50.3%

      \[\leadsto \color{blue}{y0 \cdot \left(-y3 \cdot \left(z \cdot c - y5 \cdot j\right)\right)} \]

   if 6.40000000000000014e-90 < b < 1.26e17

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.3%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y5 around -inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in t around inf 51.0%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y5 \cdot \left(i \cdot j - a \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto -1 \cdot \left(t \cdot \left(y5 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right)\right) \]

      2. *-commutative 51.0%

         \[\leadsto -1 \cdot \left(t \cdot \left(y5 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right)\right) \]

   8. Simplified 51.0%

      \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \left(y5 \cdot \left(j \cdot i - y2 \cdot a\right)\right)\right)} \]

   if 1.26e17 < b

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 43.5%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -75000000000:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-225}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-90}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4 - z \cdot i\right)\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(a \cdot y2 - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 27.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -1.55 \cdot 10^{+226}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{+58}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-235}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -1.55e+226)
   (* k (* z (- (* b y0) (* i y1))))
   (if (<= y1 -9e+58)
     (* (* k y4) (- (* y1 y2) (* y b)))
     (if (<= y1 -4.4e-235)
       (* j (* y0 (- (* y3 y5) (* x b))))
       (if (<= y1 4.7e-299)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y1 3.8e-261)
           (* b (* j (- (* t y4) (* x y0))))
           (if (<= y1 5.5e-84)
             (* b (* y0 (- (* z k) (* x j))))
             (* (- (* z i) (* y2 y4)) (* 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 tmp;
	if (y1 <= -1.55e+226) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -9e+58) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -4.4e-235) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 4.7e-299) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 3.8e-261) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 5.5e-84) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = ((z * i) - (y2 * y4)) * (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) :: tmp
    if (y1 <= (-1.55d+226)) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else if (y1 <= (-9d+58)) then
        tmp = (k * y4) * ((y1 * y2) - (y * b))
    else if (y1 <= (-4.4d-235)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y1 <= 4.7d-299) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 3.8d-261) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y1 <= 5.5d-84) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else
        tmp = ((z * i) - (y2 * y4)) * (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 tmp;
	if (y1 <= -1.55e+226) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else if (y1 <= -9e+58) {
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	} else if (y1 <= -4.4e-235) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y1 <= 4.7e-299) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 3.8e-261) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y1 <= 5.5e-84) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else {
		tmp = ((z * i) - (y2 * y4)) * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.55e+226:
		tmp = k * (z * ((b * y0) - (i * y1)))
	elif y1 <= -9e+58:
		tmp = (k * y4) * ((y1 * y2) - (y * b))
	elif y1 <= -4.4e-235:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y1 <= 4.7e-299:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 3.8e-261:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y1 <= 5.5e-84:
		tmp = b * (y0 * ((z * k) - (x * j)))
	else:
		tmp = ((z * i) - (y2 * y4)) * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -1.55e+226)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	elseif (y1 <= -9e+58)
		tmp = Float64(Float64(k * y4) * Float64(Float64(y1 * y2) - Float64(y * b)));
	elseif (y1 <= -4.4e-235)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y1 <= 4.7e-299)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 3.8e-261)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y1 <= 5.5e-84)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(Float64(Float64(z * i) - Float64(y2 * y4)) * Float64(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)
	tmp = 0.0;
	if (y1 <= -1.55e+226)
		tmp = k * (z * ((b * y0) - (i * y1)));
	elseif (y1 <= -9e+58)
		tmp = (k * y4) * ((y1 * y2) - (y * b));
	elseif (y1 <= -4.4e-235)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y1 <= 4.7e-299)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 3.8e-261)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y1 <= 5.5e-84)
		tmp = b * (y0 * ((z * k) - (x * j)));
	else
		tmp = ((z * i) - (y2 * y4)) * (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_] := If[LessEqual[y1, -1.55e+226], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -9e+58], N[(N[(k * y4), $MachinePrecision] * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.4e-235], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.7e-299], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.8e-261], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.5e-84], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision] * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y1 < -1.54999999999999988e226

   1. Initial program 27.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in k around inf 44.4%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto k \cdot \left(z \cdot \left(\color{blue}{y0 \cdot b} - i \cdot y1\right)\right) \]

      2. *-commutative 56.3%

         \[\leadsto k \cdot \left(z \cdot \left(y0 \cdot b - \color{blue}{y1 \cdot i}\right)\right) \]

   8. Simplified 56.3%

      \[\leadsto \color{blue}{k \cdot \left(z \cdot \left(y0 \cdot b - y1 \cdot i\right)\right)} \]

   if -1.54999999999999988e226 < y1 < -8.9999999999999996e58

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in k around inf 38.1%

      \[\leadsto \color{blue}{k \cdot \left(\left(-1 \cdot \left(y \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) - -1 \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   6. Taylor expanded in y4 around inf 50.9%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.9%

         \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(-1 \cdot \left(b \cdot y\right) + y1 \cdot y2\right)} \]

      2. +-commutative 50.9%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(b \cdot y\right)\right)} \]

      3. mul-1-neg 50.9%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(y1 \cdot y2 + \color{blue}{\left(-b \cdot y\right)}\right) \]

      4. unsub-neg 50.9%

         \[\leadsto \left(k \cdot y4\right) \cdot \color{blue}{\left(y1 \cdot y2 - b \cdot y\right)} \]

      5. *-commutative 50.9%

         \[\leadsto \left(k \cdot y4\right) \cdot \left(\color{blue}{y2 \cdot y1} - b \cdot y\right) \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{\left(k \cdot y4\right) \cdot \left(y2 \cdot y1 - b \cdot y\right)} \]

   if -8.9999999999999996e58 < y1 < -4.39999999999999968e-235

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 41.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 38.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto j \cdot \left(y0 \cdot \left(\color{blue}{y5 \cdot y3} - b \cdot x\right)\right) \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3 - b \cdot x\right)\right)} \]

   if -4.39999999999999968e-235 < y1 < 4.6999999999999997e-299

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 69.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 69.2%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 69.2%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 69.2%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 69.2%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 69.2%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 69.2%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 69.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   if 4.6999999999999997e-299 < y1 < 3.8e-261

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 25.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 59.2%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 3.8e-261 < y1 < 5.50000000000000019e-84

   1. Initial program 44.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 56.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 48.9%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 5.50000000000000019e-84 < y1

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 50.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 50.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in t around inf 41.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot t\right)} \]

      2. associate-*r* 39.8%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right) \cdot t} \]

      3. *-commutative 39.8%

         \[\leadsto \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot c\right)} \cdot t \]

      4. associate-*l* 38.6%

         \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   9. Simplified 38.6%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.55 \cdot 10^{+226}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -9 \cdot 10^{+58}:\\ \;\;\;\;\left(k \cdot y4\right) \cdot \left(y1 \cdot y2 - y \cdot b\right)\\ \mathbf{elif}\;y1 \leq -4.4 \cdot 10^{-235}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 3.8 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 5.5 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot i - y2 \cdot y4\right) \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 27.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-270}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= i -3.5e+104)
     (* c (* i (* z t)))
     (if (<= i -1.6e-201)
       t_1
       (if (<= i -2.85e-270)
         (* c (* x (* y0 y2)))
         (if (<= i -6.8e-301)
           t_1
           (if (<= i 3.6e-54)
             (* b (* y0 (- (* z k) (* x j))))
             (if (<= i 1.05e+175)
               (* b (* j (- (* t y4) (* x y0))))
               (* t (* c (* z i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (i <= -3.5e+104) {
		tmp = c * (i * (z * t));
	} else if (i <= -1.6e-201) {
		tmp = t_1;
	} else if (i <= -2.85e-270) {
		tmp = c * (x * (y0 * y2));
	} else if (i <= -6.8e-301) {
		tmp = t_1;
	} else if (i <= 3.6e-54) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 1.05e+175) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (c * (z * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (i <= (-3.5d+104)) then
        tmp = c * (i * (z * t))
    else if (i <= (-1.6d-201)) then
        tmp = t_1
    else if (i <= (-2.85d-270)) then
        tmp = c * (x * (y0 * y2))
    else if (i <= (-6.8d-301)) then
        tmp = t_1
    else if (i <= 3.6d-54) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (i <= 1.05d+175) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t * (c * (z * i))
    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 * (b * ((x * y) - (z * t)));
	double tmp;
	if (i <= -3.5e+104) {
		tmp = c * (i * (z * t));
	} else if (i <= -1.6e-201) {
		tmp = t_1;
	} else if (i <= -2.85e-270) {
		tmp = c * (x * (y0 * y2));
	} else if (i <= -6.8e-301) {
		tmp = t_1;
	} else if (i <= 3.6e-54) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 1.05e+175) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (c * (z * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if i <= -3.5e+104:
		tmp = c * (i * (z * t))
	elif i <= -1.6e-201:
		tmp = t_1
	elif i <= -2.85e-270:
		tmp = c * (x * (y0 * y2))
	elif i <= -6.8e-301:
		tmp = t_1
	elif i <= 3.6e-54:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif i <= 1.05e+175:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t * (c * (z * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (i <= -3.5e+104)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (i <= -1.6e-201)
		tmp = t_1;
	elseif (i <= -2.85e-270)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (i <= -6.8e-301)
		tmp = t_1;
	elseif (i <= 3.6e-54)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (i <= 1.05e+175)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(t * Float64(c * Float64(z * i)));
	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 * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (i <= -3.5e+104)
		tmp = c * (i * (z * t));
	elseif (i <= -1.6e-201)
		tmp = t_1;
	elseif (i <= -2.85e-270)
		tmp = c * (x * (y0 * y2));
	elseif (i <= -6.8e-301)
		tmp = t_1;
	elseif (i <= 3.6e-54)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (i <= 1.05e+175)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t * (c * (z * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.5e+104], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.6e-201], t$95$1, If[LessEqual[i, -2.85e-270], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.8e-301], t$95$1, If[LessEqual[i, 3.6e-54], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e+175], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.5000000000000002e104

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 45.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 38.5%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 38.5%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 38.5%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 46.1%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -3.5000000000000002e104 < i < -1.6000000000000001e-201 or -2.8500000000000001e-270 < i < -6.8000000000000004e-301

   1. Initial program 41.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 40.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 36.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 36.8%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 36.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   if -1.6000000000000001e-201 < i < -2.8500000000000001e-270

   1. Initial program 38.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 45.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 45.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 45.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 34.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.7%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   9. Simplified 34.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   if -6.8000000000000004e-301 < i < 3.59999999999999976e-54

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 43.4%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 3.59999999999999976e-54 < i < 1.05e175

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 1.05e175 < i

   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. Add Preprocessing

   3. Taylor expanded in c around inf 70.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 67.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 67.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in t around inf 60.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot t\right)} \]

      2. associate-*r* 57.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right) \cdot t} \]

      3. *-commutative 57.4%

         \[\leadsto \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot c\right)} \cdot t \]

      4. associate-*l* 54.0%

         \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   9. Simplified 54.0%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   10. Taylor expanded in i around inf 47.9%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 51.0%

          \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \]

       2. *-commutative 51.0%

          \[\leadsto c \cdot \left(\color{blue}{\left(t \cdot i\right)} \cdot z\right) \]

       3. associate-*l* 54.3%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z\right)\right)} \]

       4. associate-*l* 47.9%

          \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot \left(i \cdot z\right)} \]

       5. *-commutative 47.9%

          \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot \left(i \cdot z\right) \]

       6. associate-*l* 51.3%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot \left(i \cdot z\right)\right)} \]

   12. Simplified 51.3%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot \left(i \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.5 \cdot 10^{+104}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -2.85 \cdot 10^{-270}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y5 \leq -1.15 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 5.1 \cdot 10^{-272}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 1.16 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(t \cdot \left(-y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{+68}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y3 (* y0 y5)))) (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= y5 -1.15e+193)
     t_1
     (if (<= y5 -3.7e-190)
       t_2
       (if (<= y5 5.1e-272)
         (* (* y0 y2) (* x c))
         (if (<= y5 8e-186)
           t_2
           (if (<= y5 1.16e-82)
             (* c (* t (- (* y2 y4))))
             (if (<= y5 7.5e+68) (* (* t i) (* z c)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y3 * (y0 * y5));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y5 <= -1.15e+193) {
		tmp = t_1;
	} else if (y5 <= -3.7e-190) {
		tmp = t_2;
	} else if (y5 <= 5.1e-272) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 8e-186) {
		tmp = t_2;
	} else if (y5 <= 1.16e-82) {
		tmp = c * (t * -(y2 * y4));
	} else if (y5 <= 7.5e+68) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y3 * (y0 * y5))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (y5 <= (-1.15d+193)) then
        tmp = t_1
    else if (y5 <= (-3.7d-190)) then
        tmp = t_2
    else if (y5 <= 5.1d-272) then
        tmp = (y0 * y2) * (x * c)
    else if (y5 <= 8d-186) then
        tmp = t_2
    else if (y5 <= 1.16d-82) then
        tmp = c * (t * -(y2 * y4))
    else if (y5 <= 7.5d+68) then
        tmp = (t * i) * (z * c)
    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 = j * (y3 * (y0 * y5));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y5 <= -1.15e+193) {
		tmp = t_1;
	} else if (y5 <= -3.7e-190) {
		tmp = t_2;
	} else if (y5 <= 5.1e-272) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 8e-186) {
		tmp = t_2;
	} else if (y5 <= 1.16e-82) {
		tmp = c * (t * -(y2 * y4));
	} else if (y5 <= 7.5e+68) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y3 * (y0 * y5))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y5 <= -1.15e+193:
		tmp = t_1
	elif y5 <= -3.7e-190:
		tmp = t_2
	elif y5 <= 5.1e-272:
		tmp = (y0 * y2) * (x * c)
	elif y5 <= 8e-186:
		tmp = t_2
	elif y5 <= 1.16e-82:
		tmp = c * (t * -(y2 * y4))
	elif y5 <= 7.5e+68:
		tmp = (t * i) * (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y3 * Float64(y0 * y5)))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y5 <= -1.15e+193)
		tmp = t_1;
	elseif (y5 <= -3.7e-190)
		tmp = t_2;
	elseif (y5 <= 5.1e-272)
		tmp = Float64(Float64(y0 * y2) * Float64(x * c));
	elseif (y5 <= 8e-186)
		tmp = t_2;
	elseif (y5 <= 1.16e-82)
		tmp = Float64(c * Float64(t * Float64(-Float64(y2 * y4))));
	elseif (y5 <= 7.5e+68)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	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 = j * (y3 * (y0 * y5));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y5 <= -1.15e+193)
		tmp = t_1;
	elseif (y5 <= -3.7e-190)
		tmp = t_2;
	elseif (y5 <= 5.1e-272)
		tmp = (y0 * y2) * (x * c);
	elseif (y5 <= 8e-186)
		tmp = t_2;
	elseif (y5 <= 1.16e-82)
		tmp = c * (t * -(y2 * y4));
	elseif (y5 <= 7.5e+68)
		tmp = (t * i) * (z * c);
	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[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.15e+193], t$95$1, If[LessEqual[y5, -3.7e-190], t$95$2, If[LessEqual[y5, 5.1e-272], N[(N[(y0 * y2), $MachinePrecision] * N[(x * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 8e-186], t$95$2, If[LessEqual[y5, 1.16e-82], N[(c * N[(t * (-N[(y2 * y4), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.5e+68], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -1.15000000000000007e193 or 7.49999999999999959e68 < y5

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 38.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 43.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 43.8%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 42.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 39.9%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 39.9%

          \[\leadsto j \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y0\right)} \]

       2. associate-*l* 44.4%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0\right)\right)} \]

       3. *-commutative 44.4%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]

   12. Simplified 44.4%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if -1.15000000000000007e193 < y5 < -3.7000000000000002e-190 or 5.0999999999999998e-272 < y5 < 7.9999999999999993e-186

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 37.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 37.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 37.8%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 37.8%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 37.8%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   if -3.7000000000000002e-190 < y5 < 5.0999999999999998e-272

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 57.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 52.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 52.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 52.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 32.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

      2. associate-*r* 32.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right) \cdot x} \]

      3. *-commutative 32.9%

         \[\leadsto \color{blue}{\left(\left(y0 \cdot y2\right) \cdot c\right)} \cdot x \]

      4. associate-*l* 38.2%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   9. Simplified 38.2%

      \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   if 7.9999999999999993e-186 < y5 < 1.16e-82

   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. Add Preprocessing

   3. Taylor expanded in c around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 48.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 48.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in t around inf 57.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 57.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot t\right)} \]

      2. associate-*r* 57.7%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right) \cdot t} \]

      3. *-commutative 57.7%

         \[\leadsto \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot c\right)} \cdot t \]

      4. associate-*l* 49.1%

         \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   9. Simplified 49.1%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   10. Taylor expanded in i around 0 44.9%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]

   if 1.16e-82 < y5 < 7.49999999999999959e68

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 49.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 51.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 51.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.4%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*r* 36.4%

         \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \cdot c \]

      3. associate-*l* 39.7%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot \left(z \cdot c\right)} \]

      4. *-commutative 39.7%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot \left(z \cdot c\right) \]

   9. Simplified 39.7%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot \left(z \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.15 \cdot 10^{+193}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 5.1 \cdot 10^{-272}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 8 \cdot 10^{-186}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 1.16 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(t \cdot \left(-y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{+68}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.5 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq -6.4 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(\left(t \cdot b\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{-208}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(t \cdot \left(-y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y3 (* y0 y5)))))
   (if (<= y5 -1.5e+188)
     t_1
     (if (<= y5 -2.8e-184)
       (* a (* (* x y) b))
       (if (<= y5 -6.4e-304)
         (* a (* (* t b) (- z)))
         (if (<= y5 4e-208)
           (* (* y0 y2) (* x c))
           (if (<= y5 3.5e-84)
             (* c (* t (- (* y2 y4))))
             (if (<= y5 2e+70) (* (* t i) (* z c)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y3 * (y0 * y5));
	double tmp;
	if (y5 <= -1.5e+188) {
		tmp = t_1;
	} else if (y5 <= -2.8e-184) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= -6.4e-304) {
		tmp = a * ((t * b) * -z);
	} else if (y5 <= 4e-208) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 3.5e-84) {
		tmp = c * (t * -(y2 * y4));
	} else if (y5 <= 2e+70) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y3 * (y0 * y5))
    if (y5 <= (-1.5d+188)) then
        tmp = t_1
    else if (y5 <= (-2.8d-184)) then
        tmp = a * ((x * y) * b)
    else if (y5 <= (-6.4d-304)) then
        tmp = a * ((t * b) * -z)
    else if (y5 <= 4d-208) then
        tmp = (y0 * y2) * (x * c)
    else if (y5 <= 3.5d-84) then
        tmp = c * (t * -(y2 * y4))
    else if (y5 <= 2d+70) then
        tmp = (t * i) * (z * c)
    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 = j * (y3 * (y0 * y5));
	double tmp;
	if (y5 <= -1.5e+188) {
		tmp = t_1;
	} else if (y5 <= -2.8e-184) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= -6.4e-304) {
		tmp = a * ((t * b) * -z);
	} else if (y5 <= 4e-208) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 3.5e-84) {
		tmp = c * (t * -(y2 * y4));
	} else if (y5 <= 2e+70) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y3 * (y0 * y5))
	tmp = 0
	if y5 <= -1.5e+188:
		tmp = t_1
	elif y5 <= -2.8e-184:
		tmp = a * ((x * y) * b)
	elif y5 <= -6.4e-304:
		tmp = a * ((t * b) * -z)
	elif y5 <= 4e-208:
		tmp = (y0 * y2) * (x * c)
	elif y5 <= 3.5e-84:
		tmp = c * (t * -(y2 * y4))
	elif y5 <= 2e+70:
		tmp = (t * i) * (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y3 * Float64(y0 * y5)))
	tmp = 0.0
	if (y5 <= -1.5e+188)
		tmp = t_1;
	elseif (y5 <= -2.8e-184)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= -6.4e-304)
		tmp = Float64(a * Float64(Float64(t * b) * Float64(-z)));
	elseif (y5 <= 4e-208)
		tmp = Float64(Float64(y0 * y2) * Float64(x * c));
	elseif (y5 <= 3.5e-84)
		tmp = Float64(c * Float64(t * Float64(-Float64(y2 * y4))));
	elseif (y5 <= 2e+70)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	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 = j * (y3 * (y0 * y5));
	tmp = 0.0;
	if (y5 <= -1.5e+188)
		tmp = t_1;
	elseif (y5 <= -2.8e-184)
		tmp = a * ((x * y) * b);
	elseif (y5 <= -6.4e-304)
		tmp = a * ((t * b) * -z);
	elseif (y5 <= 4e-208)
		tmp = (y0 * y2) * (x * c);
	elseif (y5 <= 3.5e-84)
		tmp = c * (t * -(y2 * y4));
	elseif (y5 <= 2e+70)
		tmp = (t * i) * (z * c);
	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[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.5e+188], t$95$1, If[LessEqual[y5, -2.8e-184], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -6.4e-304], N[(a * N[(N[(t * b), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4e-208], N[(N[(y0 * y2), $MachinePrecision] * N[(x * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 3.5e-84], N[(c * N[(t * (-N[(y2 * y4), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2e+70], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.5e188 or 2.00000000000000015e70 < y5

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 38.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 43.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 43.8%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 42.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 39.9%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 39.9%

          \[\leadsto j \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y0\right)} \]

       2. associate-*l* 44.4%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0\right)\right)} \]

       3. *-commutative 44.4%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]

   12. Simplified 44.4%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if -1.5e188 < y5 < -2.7999999999999998e-184

   1. Initial program 43.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 31.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 31.5%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 31.5%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 31.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   9. Taylor expanded in y around inf 24.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 24.8%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   11. Simplified 24.8%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(y \cdot x\right)\right)} \]

   if -2.7999999999999998e-184 < y5 < -6.39999999999999998e-304

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 31.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 31.1%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 31.1%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 31.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   9. Taylor expanded in y around 0 27.7%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.7%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. associate-*r* 38.2%

          \[\leadsto a \cdot \left(-\color{blue}{\left(b \cdot t\right) \cdot z}\right) \]

       3. distribute-rgt-neg-in 38.2%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot \left(-z\right)\right)} \]

       4. *-commutative 38.2%

          \[\leadsto a \cdot \left(\color{blue}{\left(t \cdot b\right)} \cdot \left(-z\right)\right) \]

   11. Simplified 38.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot b\right) \cdot \left(-z\right)\right)} \]

   if -6.39999999999999998e-304 < y5 < 4.0000000000000004e-208

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 50.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 39.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 39.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 38.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

      2. associate-*r* 38.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right) \cdot x} \]

      3. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(\left(y0 \cdot y2\right) \cdot c\right)} \cdot x \]

      4. associate-*l* 41.5%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   9. Simplified 41.5%

      \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   if 4.0000000000000004e-208 < y5 < 3.5000000000000001e-84

   1. Initial program 42.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 50.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 50.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 50.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in t around inf 55.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot t\right)} \]

      2. associate-*r* 55.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right) \cdot t} \]

      3. *-commutative 55.0%

         \[\leadsto \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot c\right)} \cdot t \]

      4. associate-*l* 47.5%

         \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   9. Simplified 47.5%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   10. Taylor expanded in i around 0 43.7%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]

   if 3.5000000000000001e-84 < y5 < 2.00000000000000015e70

   1. Initial program 45.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 49.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 51.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 51.9%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 51.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 33.4%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.4%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*r* 36.4%

         \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \cdot c \]

      3. associate-*l* 39.7%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot \left(z \cdot c\right)} \]

      4. *-commutative 39.7%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot \left(z \cdot c\right) \]

   9. Simplified 39.7%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot \left(z \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.5 \cdot 10^{+188}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq -6.4 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(\left(t \cdot b\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y5 \leq 4 \cdot 10^{-208}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 3.5 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(t \cdot \left(-y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -1.36 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq -1.6 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(\left(t \cdot b\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-207}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 9.2 \cdot 10^{-133}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(t \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y5 \leq 9.2 \cdot 10^{+70}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y3 (* y0 y5)))))
   (if (<= y5 -1.36e+188)
     t_1
     (if (<= y5 -2.8e-184)
       (* a (* (* x y) b))
       (if (<= y5 -1.6e-308)
         (* a (* (* t b) (- z)))
         (if (<= y5 1e-207)
           (* (* y0 y2) (* x c))
           (if (<= y5 9.2e-133)
             (* (* y2 y4) (* t (- c)))
             (if (<= y5 9.2e+70) (* (* t i) (* z c)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y3 * (y0 * y5));
	double tmp;
	if (y5 <= -1.36e+188) {
		tmp = t_1;
	} else if (y5 <= -2.8e-184) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= -1.6e-308) {
		tmp = a * ((t * b) * -z);
	} else if (y5 <= 1e-207) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 9.2e-133) {
		tmp = (y2 * y4) * (t * -c);
	} else if (y5 <= 9.2e+70) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y3 * (y0 * y5))
    if (y5 <= (-1.36d+188)) then
        tmp = t_1
    else if (y5 <= (-2.8d-184)) then
        tmp = a * ((x * y) * b)
    else if (y5 <= (-1.6d-308)) then
        tmp = a * ((t * b) * -z)
    else if (y5 <= 1d-207) then
        tmp = (y0 * y2) * (x * c)
    else if (y5 <= 9.2d-133) then
        tmp = (y2 * y4) * (t * -c)
    else if (y5 <= 9.2d+70) then
        tmp = (t * i) * (z * c)
    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 = j * (y3 * (y0 * y5));
	double tmp;
	if (y5 <= -1.36e+188) {
		tmp = t_1;
	} else if (y5 <= -2.8e-184) {
		tmp = a * ((x * y) * b);
	} else if (y5 <= -1.6e-308) {
		tmp = a * ((t * b) * -z);
	} else if (y5 <= 1e-207) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 9.2e-133) {
		tmp = (y2 * y4) * (t * -c);
	} else if (y5 <= 9.2e+70) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y3 * (y0 * y5))
	tmp = 0
	if y5 <= -1.36e+188:
		tmp = t_1
	elif y5 <= -2.8e-184:
		tmp = a * ((x * y) * b)
	elif y5 <= -1.6e-308:
		tmp = a * ((t * b) * -z)
	elif y5 <= 1e-207:
		tmp = (y0 * y2) * (x * c)
	elif y5 <= 9.2e-133:
		tmp = (y2 * y4) * (t * -c)
	elif y5 <= 9.2e+70:
		tmp = (t * i) * (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y3 * Float64(y0 * y5)))
	tmp = 0.0
	if (y5 <= -1.36e+188)
		tmp = t_1;
	elseif (y5 <= -2.8e-184)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y5 <= -1.6e-308)
		tmp = Float64(a * Float64(Float64(t * b) * Float64(-z)));
	elseif (y5 <= 1e-207)
		tmp = Float64(Float64(y0 * y2) * Float64(x * c));
	elseif (y5 <= 9.2e-133)
		tmp = Float64(Float64(y2 * y4) * Float64(t * Float64(-c)));
	elseif (y5 <= 9.2e+70)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	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 = j * (y3 * (y0 * y5));
	tmp = 0.0;
	if (y5 <= -1.36e+188)
		tmp = t_1;
	elseif (y5 <= -2.8e-184)
		tmp = a * ((x * y) * b);
	elseif (y5 <= -1.6e-308)
		tmp = a * ((t * b) * -z);
	elseif (y5 <= 1e-207)
		tmp = (y0 * y2) * (x * c);
	elseif (y5 <= 9.2e-133)
		tmp = (y2 * y4) * (t * -c);
	elseif (y5 <= 9.2e+70)
		tmp = (t * i) * (z * c);
	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[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.36e+188], t$95$1, If[LessEqual[y5, -2.8e-184], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.6e-308], N[(a * N[(N[(t * b), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1e-207], N[(N[(y0 * y2), $MachinePrecision] * N[(x * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9.2e-133], N[(N[(y2 * y4), $MachinePrecision] * N[(t * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9.2e+70], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y5 < -1.36e188 or 9.19999999999999975e70 < y5

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 38.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 43.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 43.8%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 42.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 39.9%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 39.9%

          \[\leadsto j \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y0\right)} \]

       2. associate-*l* 44.4%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0\right)\right)} \]

       3. *-commutative 44.4%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]

   12. Simplified 44.4%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if -1.36e188 < y5 < -2.7999999999999998e-184

   1. Initial program 43.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 31.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 31.5%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 31.5%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 31.5%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 31.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   9. Taylor expanded in y around inf 24.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 24.8%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   11. Simplified 24.8%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(y \cdot x\right)\right)} \]

   if -2.7999999999999998e-184 < y5 < -1.6000000000000001e-308

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.9%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 31.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 31.1%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 31.1%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 31.1%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 31.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   9. Taylor expanded in y around 0 27.7%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(b \cdot \left(t \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 27.7%

          \[\leadsto a \cdot \color{blue}{\left(-b \cdot \left(t \cdot z\right)\right)} \]

       2. associate-*r* 38.2%

          \[\leadsto a \cdot \left(-\color{blue}{\left(b \cdot t\right) \cdot z}\right) \]

       3. distribute-rgt-neg-in 38.2%

          \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot t\right) \cdot \left(-z\right)\right)} \]

       4. *-commutative 38.2%

          \[\leadsto a \cdot \left(\color{blue}{\left(t \cdot b\right)} \cdot \left(-z\right)\right) \]

   11. Simplified 38.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(t \cdot b\right) \cdot \left(-z\right)\right)} \]

   if -1.6000000000000001e-308 < y5 < 9.99999999999999925e-208

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 50.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 39.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 39.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 38.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

      2. associate-*r* 38.0%

         \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right) \cdot x} \]

      3. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(\left(y0 \cdot y2\right) \cdot c\right)} \cdot x \]

      4. associate-*l* 41.5%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   9. Simplified 41.5%

      \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   if 9.99999999999999925e-208 < y5 < 9.2000000000000001e-133

   1. Initial program 47.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 60.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 60.1%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 60.1%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 60.1%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in t around inf 54.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot t\right)} \]

      2. associate-*r* 54.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right) \cdot t} \]

      3. *-commutative 54.5%

         \[\leadsto \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot c\right)} \cdot t \]

      4. associate-*l* 54.6%

         \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   9. Simplified 54.6%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   10. Taylor expanded in i around 0 54.5%

       \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 54.5%

          \[\leadsto \color{blue}{-c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)} \]

       2. associate-*r* 54.5%

          \[\leadsto -\color{blue}{\left(c \cdot t\right) \cdot \left(y2 \cdot y4\right)} \]

       3. distribute-rgt-neg-out 54.5%

          \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot \left(-y2 \cdot y4\right)} \]

       4. *-commutative 54.5%

          \[\leadsto \color{blue}{\left(-y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

       5. distribute-rgt-neg-in 54.5%

          \[\leadsto \color{blue}{\left(y2 \cdot \left(-y4\right)\right)} \cdot \left(c \cdot t\right) \]

   12. Simplified 54.5%

       \[\leadsto \color{blue}{\left(y2 \cdot \left(-y4\right)\right) \cdot \left(c \cdot t\right)} \]

   if 9.2000000000000001e-133 < y5 < 9.19999999999999975e70

   1. Initial program 42.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 48.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 48.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 32.0%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.0%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*r* 34.2%

         \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \cdot c \]

      3. associate-*l* 36.6%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot \left(z \cdot c\right)} \]

      4. *-commutative 36.6%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot \left(z \cdot c\right) \]

   9. Simplified 36.6%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot \left(z \cdot c\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.36 \cdot 10^{+188}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y5 \leq -1.6 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(\left(t \cdot b\right) \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y5 \leq 10^{-207}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 9.2 \cdot 10^{-133}:\\ \;\;\;\;\left(y2 \cdot y4\right) \cdot \left(t \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y5 \leq 9.2 \cdot 10^{+70}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 28.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y5 \leq -2.05 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1.05 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 3.6 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y3 (* y0 y5)))) (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= y5 -2.05e+200)
     t_1
     (if (<= y5 -1.05e-205)
       t_2
       (if (<= y5 3.6e-271)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y5 4.9e-157)
           t_2
           (if (<= y5 5.4e+75) (* b (* j (- (* t y4) (* x y0)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y3 * (y0 * y5));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y5 <= -2.05e+200) {
		tmp = t_1;
	} else if (y5 <= -1.05e-205) {
		tmp = t_2;
	} else if (y5 <= 3.6e-271) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y5 <= 4.9e-157) {
		tmp = t_2;
	} else if (y5 <= 5.4e+75) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (y3 * (y0 * y5))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (y5 <= (-2.05d+200)) then
        tmp = t_1
    else if (y5 <= (-1.05d-205)) then
        tmp = t_2
    else if (y5 <= 3.6d-271) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y5 <= 4.9d-157) then
        tmp = t_2
    else if (y5 <= 5.4d+75) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y3 * (y0 * y5));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y5 <= -2.05e+200) {
		tmp = t_1;
	} else if (y5 <= -1.05e-205) {
		tmp = t_2;
	} else if (y5 <= 3.6e-271) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y5 <= 4.9e-157) {
		tmp = t_2;
	} else if (y5 <= 5.4e+75) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y3 * (y0 * y5))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y5 <= -2.05e+200:
		tmp = t_1
	elif y5 <= -1.05e-205:
		tmp = t_2
	elif y5 <= 3.6e-271:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y5 <= 4.9e-157:
		tmp = t_2
	elif y5 <= 5.4e+75:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y3 * Float64(y0 * y5)))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y5 <= -2.05e+200)
		tmp = t_1;
	elseif (y5 <= -1.05e-205)
		tmp = t_2;
	elseif (y5 <= 3.6e-271)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y5 <= 4.9e-157)
		tmp = t_2;
	elseif (y5 <= 5.4e+75)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y3 * (y0 * y5));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y5 <= -2.05e+200)
		tmp = t_1;
	elseif (y5 <= -1.05e-205)
		tmp = t_2;
	elseif (y5 <= 3.6e-271)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y5 <= 4.9e-157)
		tmp = t_2;
	elseif (y5 <= 5.4e+75)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -2.05e+200], t$95$1, If[LessEqual[y5, -1.05e-205], t$95$2, If[LessEqual[y5, 3.6e-271], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.9e-157], t$95$2, If[LessEqual[y5, 5.4e+75], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -2.0500000000000001e200 or 5.39999999999999996e75 < y5

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 38.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 43.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 41.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 39.7%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 39.7%

          \[\leadsto j \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y0\right)} \]

       2. associate-*l* 44.3%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0\right)\right)} \]

       3. *-commutative 44.3%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]

   12. Simplified 44.3%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if -2.0500000000000001e200 < y5 < -1.04999999999999991e-205 or 3.5999999999999998e-271 < y5 < 4.8999999999999998e-157

   1. Initial program 43.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 37.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 38.3%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 38.3%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 38.3%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 38.3%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 38.3%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   if -1.04999999999999991e-205 < y5 < 3.5999999999999998e-271

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in x around inf 43.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto b \cdot \left(x \cdot \left(\color{blue}{y \cdot a} - j \cdot y0\right)\right) \]

      2. *-commutative 43.4%

         \[\leadsto b \cdot \left(x \cdot \left(y \cdot a - \color{blue}{y0 \cdot j}\right)\right) \]

   8. Simplified 43.4%

      \[\leadsto \color{blue}{b \cdot \left(x \cdot \left(y \cdot a - y0 \cdot j\right)\right)} \]

   if 4.8999999999999998e-157 < y5 < 5.39999999999999996e75

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 38.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -2.05 \cdot 10^{+200}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.05 \cdot 10^{-205}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 3.6 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 4.9 \cdot 10^{-157}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 27.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y5 \leq -5.9 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -1.2 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 4.2 \cdot 10^{-272}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 1.76 \cdot 10^{-158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y3 (* y0 y5)))) (t_2 (* a (* b (- (* x y) (* z t))))))
   (if (<= y5 -5.9e+190)
     t_1
     (if (<= y5 -1.2e-190)
       t_2
       (if (<= y5 4.2e-272)
         (* (* y0 y2) (* x c))
         (if (<= y5 1.76e-158)
           t_2
           (if (<= y5 2.7e+76) (* b (* j (- (* t y4) (* x y0)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y3 * (y0 * y5));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y5 <= -5.9e+190) {
		tmp = t_1;
	} else if (y5 <= -1.2e-190) {
		tmp = t_2;
	} else if (y5 <= 4.2e-272) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 1.76e-158) {
		tmp = t_2;
	} else if (y5 <= 2.7e+76) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (y3 * (y0 * y5))
    t_2 = a * (b * ((x * y) - (z * t)))
    if (y5 <= (-5.9d+190)) then
        tmp = t_1
    else if (y5 <= (-1.2d-190)) then
        tmp = t_2
    else if (y5 <= 4.2d-272) then
        tmp = (y0 * y2) * (x * c)
    else if (y5 <= 1.76d-158) then
        tmp = t_2
    else if (y5 <= 2.7d+76) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y3 * (y0 * y5));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y5 <= -5.9e+190) {
		tmp = t_1;
	} else if (y5 <= -1.2e-190) {
		tmp = t_2;
	} else if (y5 <= 4.2e-272) {
		tmp = (y0 * y2) * (x * c);
	} else if (y5 <= 1.76e-158) {
		tmp = t_2;
	} else if (y5 <= 2.7e+76) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y3 * (y0 * y5))
	t_2 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y5 <= -5.9e+190:
		tmp = t_1
	elif y5 <= -1.2e-190:
		tmp = t_2
	elif y5 <= 4.2e-272:
		tmp = (y0 * y2) * (x * c)
	elif y5 <= 1.76e-158:
		tmp = t_2
	elif y5 <= 2.7e+76:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y3 * Float64(y0 * y5)))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y5 <= -5.9e+190)
		tmp = t_1;
	elseif (y5 <= -1.2e-190)
		tmp = t_2;
	elseif (y5 <= 4.2e-272)
		tmp = Float64(Float64(y0 * y2) * Float64(x * c));
	elseif (y5 <= 1.76e-158)
		tmp = t_2;
	elseif (y5 <= 2.7e+76)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y3 * (y0 * y5));
	t_2 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y5 <= -5.9e+190)
		tmp = t_1;
	elseif (y5 <= -1.2e-190)
		tmp = t_2;
	elseif (y5 <= 4.2e-272)
		tmp = (y0 * y2) * (x * c);
	elseif (y5 <= 1.76e-158)
		tmp = t_2;
	elseif (y5 <= 2.7e+76)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -5.9e+190], t$95$1, If[LessEqual[y5, -1.2e-190], t$95$2, If[LessEqual[y5, 4.2e-272], N[(N[(y0 * y2), $MachinePrecision] * N[(x * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.76e-158], t$95$2, If[LessEqual[y5, 2.7e+76], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y5 < -5.89999999999999972e190 or 2.6999999999999999e76 < y5

   1. Initial program 26.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 38.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 43.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.6%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 41.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 39.7%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 39.7%

          \[\leadsto j \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y0\right)} \]

       2. associate-*l* 44.3%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0\right)\right)} \]

       3. *-commutative 44.3%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]

   12. Simplified 44.3%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if -5.89999999999999972e190 < y5 < -1.2e-190 or 4.19999999999999974e-272 < y5 < 1.76e-158

   1. Initial program 41.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.7%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 38.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 38.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 38.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 38.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 38.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 38.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 38.0%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 38.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   if -1.2e-190 < y5 < 4.19999999999999974e-272

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 57.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 52.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 52.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 52.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 32.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

      2. associate-*r* 32.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right) \cdot x} \]

      3. *-commutative 32.9%

         \[\leadsto \color{blue}{\left(\left(y0 \cdot y2\right) \cdot c\right)} \cdot x \]

      4. associate-*l* 38.2%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   9. Simplified 38.2%

      \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   if 1.76e-158 < y5 < 2.6999999999999999e76

   1. Initial program 39.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 35.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 38.3%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -5.9 \cdot 10^{+190}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -1.2 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 4.2 \cdot 10^{-272}:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{elif}\;y5 \leq 1.76 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq 2.7 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{if}\;y0 \leq -1 \cdot 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -0.00044:\\ \;\;\;\;y2 \cdot \left(y5 \cdot \left(y0 \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.95 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 6.6 \cdot 10^{+189}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y5 (* y0 y3)))))
   (if (<= y0 -1e+261)
     t_1
     (if (<= y0 -1.35e+61)
       (* c (* x (* y0 y2)))
       (if (<= y0 -0.00044)
         (* y2 (* y5 (* y0 (- k))))
         (if (<= y0 2.95e-245)
           (* y (* c (* y3 y4)))
           (if (<= y0 6.6e+189) (* (* t i) (* z c)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y5 * (y0 * y3));
	double tmp;
	if (y0 <= -1e+261) {
		tmp = t_1;
	} else if (y0 <= -1.35e+61) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= -0.00044) {
		tmp = y2 * (y5 * (y0 * -k));
	} else if (y0 <= 2.95e-245) {
		tmp = y * (c * (y3 * y4));
	} else if (y0 <= 6.6e+189) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y5 * (y0 * y3))
    if (y0 <= (-1d+261)) then
        tmp = t_1
    else if (y0 <= (-1.35d+61)) then
        tmp = c * (x * (y0 * y2))
    else if (y0 <= (-0.00044d0)) then
        tmp = y2 * (y5 * (y0 * -k))
    else if (y0 <= 2.95d-245) then
        tmp = y * (c * (y3 * y4))
    else if (y0 <= 6.6d+189) then
        tmp = (t * i) * (z * c)
    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 = j * (y5 * (y0 * y3));
	double tmp;
	if (y0 <= -1e+261) {
		tmp = t_1;
	} else if (y0 <= -1.35e+61) {
		tmp = c * (x * (y0 * y2));
	} else if (y0 <= -0.00044) {
		tmp = y2 * (y5 * (y0 * -k));
	} else if (y0 <= 2.95e-245) {
		tmp = y * (c * (y3 * y4));
	} else if (y0 <= 6.6e+189) {
		tmp = (t * i) * (z * c);
	} 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 = j * (y5 * (y0 * y3))
	tmp = 0
	if y0 <= -1e+261:
		tmp = t_1
	elif y0 <= -1.35e+61:
		tmp = c * (x * (y0 * y2))
	elif y0 <= -0.00044:
		tmp = y2 * (y5 * (y0 * -k))
	elif y0 <= 2.95e-245:
		tmp = y * (c * (y3 * y4))
	elif y0 <= 6.6e+189:
		tmp = (t * i) * (z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y5 * Float64(y0 * y3)))
	tmp = 0.0
	if (y0 <= -1e+261)
		tmp = t_1;
	elseif (y0 <= -1.35e+61)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y0 <= -0.00044)
		tmp = Float64(y2 * Float64(y5 * Float64(y0 * Float64(-k))));
	elseif (y0 <= 2.95e-245)
		tmp = Float64(y * Float64(c * Float64(y3 * y4)));
	elseif (y0 <= 6.6e+189)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	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 = j * (y5 * (y0 * y3));
	tmp = 0.0;
	if (y0 <= -1e+261)
		tmp = t_1;
	elseif (y0 <= -1.35e+61)
		tmp = c * (x * (y0 * y2));
	elseif (y0 <= -0.00044)
		tmp = y2 * (y5 * (y0 * -k));
	elseif (y0 <= 2.95e-245)
		tmp = y * (c * (y3 * y4));
	elseif (y0 <= 6.6e+189)
		tmp = (t * i) * (z * c);
	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[(j * N[(y5 * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1e+261], t$95$1, If[LessEqual[y0, -1.35e+61], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -0.00044], N[(y2 * N[(y5 * N[(y0 * (-k)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.95e-245], N[(y * N[(c * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.6e+189], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -9.9999999999999993e260 or 6.6000000000000004e189 < y0

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 59.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 40.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 40.2%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 52.0%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 49.4%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 55.5%

          \[\leadsto j \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   12. Simplified 55.5%

       \[\leadsto \color{blue}{j \cdot \left(\left(y0 \cdot y3\right) \cdot y5\right)} \]

   if -9.9999999999999993e260 < y0 < -1.3500000000000001e61

   1. Initial program 28.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 47.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 43.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 43.9%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 43.9%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 35.3%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   9. Simplified 35.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   if -1.3500000000000001e61 < y0 < -4.40000000000000016e-4

   1. Initial program 40.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 40.6%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 44.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 35.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.9%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 35.9%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 46.9%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in j around 0 39.3%

       \[\leadsto y2 \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 39.3%

          \[\leadsto y2 \cdot \left(-1 \cdot \color{blue}{\left(\left(k \cdot y0\right) \cdot y5\right)}\right) \]

       2. *-commutative 39.3%

          \[\leadsto y2 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y0\right)\right)}\right) \]

       3. neg-mul-1 39.3%

          \[\leadsto y2 \cdot \color{blue}{\left(-y5 \cdot \left(k \cdot y0\right)\right)} \]

       4. distribute-rgt-neg-in 39.3%

          \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \left(-k \cdot y0\right)\right)} \]

       5. *-commutative 39.3%

          \[\leadsto y2 \cdot \left(y5 \cdot \left(-\color{blue}{y0 \cdot k}\right)\right) \]

       6. distribute-rgt-neg-in 39.3%

          \[\leadsto y2 \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot \left(-k\right)\right)}\right) \]

   12. Simplified 39.3%

       \[\leadsto y2 \cdot \color{blue}{\left(y5 \cdot \left(y0 \cdot \left(-k\right)\right)\right)} \]

   if -4.40000000000000016e-4 < y0 < 2.9499999999999999e-245

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 39.5%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 38.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 38.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 38.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in y around inf 25.4%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 25.4%

         \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right) \cdot c} \]

      2. associate-*r* 27.9%

         \[\leadsto \color{blue}{y \cdot \left(\left(y3 \cdot y4\right) \cdot c\right)} \]

      3. *-commutative 27.9%

         \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]

   9. Simplified 27.9%

      \[\leadsto \color{blue}{y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)} \]

   if 2.9499999999999999e-245 < y0 < 6.6000000000000004e189

   1. Initial program 35.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 49.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 44.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 44.6%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 33.9%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.9%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*r* 33.8%

         \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \cdot c \]

      3. associate-*l* 36.4%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot \left(z \cdot c\right)} \]

      4. *-commutative 36.4%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot \left(z \cdot c\right) \]

   9. Simplified 36.4%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot \left(z \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1 \cdot 10^{+261}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -0.00044:\\ \;\;\;\;y2 \cdot \left(y5 \cdot \left(y0 \cdot \left(-k\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.95 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 6.6 \cdot 10^{+189}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-69}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-284}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-251}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -1.4e-69)
   (* (* t i) (* z c))
   (if (<= z -3.4e-284)
     (* c (* y (* y3 y4)))
     (if (<= z 5.8e-251)
       (* j (* y0 (* y3 y5)))
       (if (<= z 1.45e-104)
         (* y (* c (* y3 y4)))
         (if (<= z 3800000.0) (* (* y0 y2) (* x c)) (* c (* i (* z t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -1.4e-69) {
		tmp = (t * i) * (z * c);
	} else if (z <= -3.4e-284) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 5.8e-251) {
		tmp = j * (y0 * (y3 * y5));
	} else if (z <= 1.45e-104) {
		tmp = y * (c * (y3 * y4));
	} else if (z <= 3800000.0) {
		tmp = (y0 * y2) * (x * c);
	} else {
		tmp = c * (i * (z * t));
	}
	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 <= (-1.4d-69)) then
        tmp = (t * i) * (z * c)
    else if (z <= (-3.4d-284)) then
        tmp = c * (y * (y3 * y4))
    else if (z <= 5.8d-251) then
        tmp = j * (y0 * (y3 * y5))
    else if (z <= 1.45d-104) then
        tmp = y * (c * (y3 * y4))
    else if (z <= 3800000.0d0) then
        tmp = (y0 * y2) * (x * c)
    else
        tmp = c * (i * (z * t))
    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 <= -1.4e-69) {
		tmp = (t * i) * (z * c);
	} else if (z <= -3.4e-284) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 5.8e-251) {
		tmp = j * (y0 * (y3 * y5));
	} else if (z <= 1.45e-104) {
		tmp = y * (c * (y3 * y4));
	} else if (z <= 3800000.0) {
		tmp = (y0 * y2) * (x * c);
	} else {
		tmp = c * (i * (z * t));
	}
	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 <= -1.4e-69:
		tmp = (t * i) * (z * c)
	elif z <= -3.4e-284:
		tmp = c * (y * (y3 * y4))
	elif z <= 5.8e-251:
		tmp = j * (y0 * (y3 * y5))
	elif z <= 1.45e-104:
		tmp = y * (c * (y3 * y4))
	elif z <= 3800000.0:
		tmp = (y0 * y2) * (x * c)
	else:
		tmp = c * (i * (z * t))
	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 <= -1.4e-69)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	elseif (z <= -3.4e-284)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (z <= 5.8e-251)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (z <= 1.45e-104)
		tmp = Float64(y * Float64(c * Float64(y3 * y4)));
	elseif (z <= 3800000.0)
		tmp = Float64(Float64(y0 * y2) * Float64(x * c));
	else
		tmp = Float64(c * Float64(i * Float64(z * t)));
	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 <= -1.4e-69)
		tmp = (t * i) * (z * c);
	elseif (z <= -3.4e-284)
		tmp = c * (y * (y3 * y4));
	elseif (z <= 5.8e-251)
		tmp = j * (y0 * (y3 * y5));
	elseif (z <= 1.45e-104)
		tmp = y * (c * (y3 * y4));
	elseif (z <= 3800000.0)
		tmp = (y0 * y2) * (x * c);
	else
		tmp = c * (i * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -1.4e-69], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-284], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-251], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-104], N[(y * N[(c * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3800000.0], N[(N[(y0 * y2), $MachinePrecision] * N[(x * c), $MachinePrecision]), $MachinePrecision], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.3999999999999999e-69

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 41.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 38.5%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 38.5%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 38.5%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 36.2%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.2%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*r* 33.6%

         \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \cdot c \]

      3. associate-*l* 36.3%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot \left(z \cdot c\right)} \]

      4. *-commutative 36.3%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot \left(z \cdot c\right) \]

   9. Simplified 36.3%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot \left(z \cdot c\right)} \]

   if -1.3999999999999999e-69 < z < -3.39999999999999991e-284

   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. Add Preprocessing

   3. Taylor expanded in c around inf 49.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 52.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 52.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in y around inf 32.5%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -3.39999999999999991e-284 < z < 5.8000000000000001e-251

   1. Initial program 45.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 50.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 38.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 38.0%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 38.0%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in k around 0 33.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.9%

          \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \]

   11. Simplified 33.9%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3\right)\right)} \]

   if 5.8000000000000001e-251 < z < 1.4500000000000001e-104

   1. Initial program 21.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 48.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 44.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 44.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 44.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in y around inf 31.5%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.5%

         \[\leadsto \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right) \cdot c} \]

      2. associate-*r* 31.6%

         \[\leadsto \color{blue}{y \cdot \left(\left(y3 \cdot y4\right) \cdot c\right)} \]

      3. *-commutative 31.6%

         \[\leadsto y \cdot \color{blue}{\left(c \cdot \left(y3 \cdot y4\right)\right)} \]

   9. Simplified 31.6%

      \[\leadsto \color{blue}{y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)} \]

   if 1.4500000000000001e-104 < z < 3.8e6

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 41.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 41.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 41.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 29.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

      2. associate-*r* 35.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2\right)\right) \cdot x} \]

      3. *-commutative 35.6%

         \[\leadsto \color{blue}{\left(\left(y0 \cdot y2\right) \cdot c\right)} \cdot x \]

      4. associate-*l* 32.9%

         \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   9. Simplified 32.9%

      \[\leadsto \color{blue}{\left(y0 \cdot y2\right) \cdot \left(c \cdot x\right)} \]

   if 3.8e6 < z

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 51.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 46.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 41.7%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-69}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-284}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-251}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(c \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;\left(y0 \cdot y2\right) \cdot \left(x \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 23.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ t_2 := c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-284}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4000000:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* i (* z t)))) (t_2 (* c (* y (* y3 y4)))))
   (if (<= z -2.5e-69)
     t_1
     (if (<= z -1.28e-284)
       t_2
       (if (<= z 1.4e-241)
         (* j (* y0 (* y3 y5)))
         (if (<= z 9.6e-105)
           t_2
           (if (<= z 4000000.0) (* c (* x (* y0 y2))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * (z * t));
	double t_2 = c * (y * (y3 * y4));
	double tmp;
	if (z <= -2.5e-69) {
		tmp = t_1;
	} else if (z <= -1.28e-284) {
		tmp = t_2;
	} else if (z <= 1.4e-241) {
		tmp = j * (y0 * (y3 * y5));
	} else if (z <= 9.6e-105) {
		tmp = t_2;
	} else if (z <= 4000000.0) {
		tmp = c * (x * (y0 * 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 = c * (i * (z * t))
    t_2 = c * (y * (y3 * y4))
    if (z <= (-2.5d-69)) then
        tmp = t_1
    else if (z <= (-1.28d-284)) then
        tmp = t_2
    else if (z <= 1.4d-241) then
        tmp = j * (y0 * (y3 * y5))
    else if (z <= 9.6d-105) then
        tmp = t_2
    else if (z <= 4000000.0d0) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * (z * t));
	double t_2 = c * (y * (y3 * y4));
	double tmp;
	if (z <= -2.5e-69) {
		tmp = t_1;
	} else if (z <= -1.28e-284) {
		tmp = t_2;
	} else if (z <= 1.4e-241) {
		tmp = j * (y0 * (y3 * y5));
	} else if (z <= 9.6e-105) {
		tmp = t_2;
	} else if (z <= 4000000.0) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (i * (z * t))
	t_2 = c * (y * (y3 * y4))
	tmp = 0
	if z <= -2.5e-69:
		tmp = t_1
	elif z <= -1.28e-284:
		tmp = t_2
	elif z <= 1.4e-241:
		tmp = j * (y0 * (y3 * y5))
	elif z <= 9.6e-105:
		tmp = t_2
	elif z <= 4000000.0:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(i * Float64(z * t)))
	t_2 = Float64(c * Float64(y * Float64(y3 * y4)))
	tmp = 0.0
	if (z <= -2.5e-69)
		tmp = t_1;
	elseif (z <= -1.28e-284)
		tmp = t_2;
	elseif (z <= 1.4e-241)
		tmp = Float64(j * Float64(y0 * Float64(y3 * y5)));
	elseif (z <= 9.6e-105)
		tmp = t_2;
	elseif (z <= 4000000.0)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (i * (z * t));
	t_2 = c * (y * (y3 * y4));
	tmp = 0.0;
	if (z <= -2.5e-69)
		tmp = t_1;
	elseif (z <= -1.28e-284)
		tmp = t_2;
	elseif (z <= 1.4e-241)
		tmp = j * (y0 * (y3 * y5));
	elseif (z <= 9.6e-105)
		tmp = t_2;
	elseif (z <= 4000000.0)
		tmp = c * (x * (y0 * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-69], t$95$1, If[LessEqual[z, -1.28e-284], t$95$2, If[LessEqual[z, 1.4e-241], N[(j * N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-105], t$95$2, If[LessEqual[z, 4000000.0], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.50000000000000017e-69 or 4e6 < z

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 45.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 42.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 42.0%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 42.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 38.7%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -2.50000000000000017e-69 < z < -1.28000000000000006e-284 or 1.4e-241 < z < 9.6000000000000006e-105

   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. Add Preprocessing

   3. Taylor expanded in c around inf 49.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 49.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 49.3%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 49.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in y around inf 32.2%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -1.28000000000000006e-284 < z < 1.4e-241

   1. Initial program 45.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 50.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 38.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 38.0%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 38.0%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in k around 0 33.9%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.9%

          \[\leadsto j \cdot \left(y0 \cdot \color{blue}{\left(y5 \cdot y3\right)}\right) \]

   11. Simplified 33.9%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y5 \cdot y3\right)\right)} \]

   if 9.6000000000000006e-105 < z < 4e6

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 41.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 41.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 41.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 29.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   9. Simplified 29.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-69}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-284}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-241}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 4000000:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 27.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -5.1 \cdot 10^{-275}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= i -3.2e+23)
   (* c (* i (* z t)))
   (if (<= i -5.1e-275)
     (* c (* y0 (- (* x y2) (* z y3))))
     (if (<= i 1.55e-53)
       (* b (* y0 (- (* z k) (* x j))))
       (if (<= i 3e+175)
         (* b (* j (- (* t y4) (* x y0))))
         (* t (* c (* z i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (i <= -3.2e+23) {
		tmp = c * (i * (z * t));
	} else if (i <= -5.1e-275) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (i <= 1.55e-53) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 3e+175) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (c * (z * i));
	}
	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 (i <= (-3.2d+23)) then
        tmp = c * (i * (z * t))
    else if (i <= (-5.1d-275)) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (i <= 1.55d-53) then
        tmp = b * (y0 * ((z * k) - (x * j)))
    else if (i <= 3d+175) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t * (c * (z * i))
    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 (i <= -3.2e+23) {
		tmp = c * (i * (z * t));
	} else if (i <= -5.1e-275) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (i <= 1.55e-53) {
		tmp = b * (y0 * ((z * k) - (x * j)));
	} else if (i <= 3e+175) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t * (c * (z * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if i <= -3.2e+23:
		tmp = c * (i * (z * t))
	elif i <= -5.1e-275:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif i <= 1.55e-53:
		tmp = b * (y0 * ((z * k) - (x * j)))
	elif i <= 3e+175:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t * (c * (z * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (i <= -3.2e+23)
		tmp = Float64(c * Float64(i * Float64(z * t)));
	elseif (i <= -5.1e-275)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (i <= 1.55e-53)
		tmp = Float64(b * Float64(y0 * Float64(Float64(z * k) - Float64(x * j))));
	elseif (i <= 3e+175)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(t * Float64(c * Float64(z * i)));
	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 (i <= -3.2e+23)
		tmp = c * (i * (z * t));
	elseif (i <= -5.1e-275)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (i <= 1.55e-53)
		tmp = b * (y0 * ((z * k) - (x * j)));
	elseif (i <= 3e+175)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t * (c * (z * i));
	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[i, -3.2e+23], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.1e-275], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.55e-53], N[(b * N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e+175], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * N[(z * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.2e23

   1. Initial program 30.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 47.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 42.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 42.3%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 42.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 42.5%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -3.2e23 < i < -5.09999999999999984e-275

   1. Initial program 39.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 34.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in c around inf 35.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.5%

         \[\leadsto c \cdot \left(y0 \cdot \left(\color{blue}{y2 \cdot x} - y3 \cdot z\right)\right) \]

      2. *-commutative 35.5%

         \[\leadsto c \cdot \left(y0 \cdot \left(y2 \cdot x - \color{blue}{z \cdot y3}\right)\right) \]

   8. Simplified 35.5%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x - z \cdot y3\right)\right)} \]

   if -5.09999999999999984e-275 < i < 1.55000000000000008e-53

   1. Initial program 34.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 45.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y0 around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(y0 \cdot \left(k \cdot z - j \cdot x\right)\right)} \]

   if 1.55000000000000008e-53 < i < 3.0000000000000002e175

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.1%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 39.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in j around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

   if 3.0000000000000002e175 < i

   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. Add Preprocessing

   3. Taylor expanded in c around inf 70.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 67.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 67.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in t around inf 60.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot \left(i \cdot z - y2 \cdot y4\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot t\right)} \]

      2. associate-*r* 57.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(i \cdot z - y2 \cdot y4\right)\right) \cdot t} \]

      3. *-commutative 57.4%

         \[\leadsto \color{blue}{\left(\left(i \cdot z - y2 \cdot y4\right) \cdot c\right)} \cdot t \]

      4. associate-*l* 54.0%

         \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   9. Simplified 54.0%

      \[\leadsto \color{blue}{\left(i \cdot z - y2 \cdot y4\right) \cdot \left(c \cdot t\right)} \]

   10. Taylor expanded in i around inf 47.9%

       \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 51.0%

          \[\leadsto c \cdot \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \]

       2. *-commutative 51.0%

          \[\leadsto c \cdot \left(\color{blue}{\left(t \cdot i\right)} \cdot z\right) \]

       3. associate-*l* 54.3%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot \left(i \cdot z\right)\right)} \]

       4. associate-*l* 47.9%

          \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot \left(i \cdot z\right)} \]

       5. *-commutative 47.9%

          \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot \left(i \cdot z\right) \]

       6. associate-*l* 51.3%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot \left(i \cdot z\right)\right)} \]

   12. Simplified 51.3%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot \left(i \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -5.1 \cdot 10^{-275}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot \left(z \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 23.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2000000:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* i (* z t)))))
   (if (<= z -4.8e-71)
     t_1
     (if (<= z 1.7e-104)
       (* c (* y (* y3 y4)))
       (if (<= z 2000000.0) (* c (* x (* y0 y2))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * (z * t));
	double tmp;
	if (z <= -4.8e-71) {
		tmp = t_1;
	} else if (z <= 1.7e-104) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 2000000.0) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (i * (z * t))
    if (z <= (-4.8d-71)) then
        tmp = t_1
    else if (z <= 1.7d-104) then
        tmp = c * (y * (y3 * y4))
    else if (z <= 2000000.0d0) then
        tmp = c * (x * (y0 * y2))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * (z * t));
	double tmp;
	if (z <= -4.8e-71) {
		tmp = t_1;
	} else if (z <= 1.7e-104) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 2000000.0) {
		tmp = c * (x * (y0 * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (i * (z * t))
	tmp = 0
	if z <= -4.8e-71:
		tmp = t_1
	elif z <= 1.7e-104:
		tmp = c * (y * (y3 * y4))
	elif z <= 2000000.0:
		tmp = c * (x * (y0 * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(i * Float64(z * t)))
	tmp = 0.0
	if (z <= -4.8e-71)
		tmp = t_1;
	elseif (z <= 1.7e-104)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (z <= 2000000.0)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (i * (z * t));
	tmp = 0.0;
	if (z <= -4.8e-71)
		tmp = t_1;
	elseif (z <= 1.7e-104)
		tmp = c * (y * (y3 * y4));
	elseif (z <= 2000000.0)
		tmp = c * (x * (y0 * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-71], t$95$1, If[LessEqual[z, 1.7e-104], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2000000.0], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e-71 or 2e6 < z

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 45.8%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 42.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 42.0%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 42.0%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 38.7%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -4.8e-71 < z < 1.70000000000000008e-104

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 43.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 43.3%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 43.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in y around inf 25.8%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 1.70000000000000008e-104 < z < 2e6

   1. Initial program 34.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 41.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 41.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 41.6%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in x around inf 29.9%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot y2\right) \cdot x\right)} \]

   9. Simplified 29.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot y2\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2000000:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 22.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* i (* z t)))))
   (if (<= z -3.5e-75)
     t_1
     (if (<= z 1.8e-104)
       (* c (* y (* y3 y4)))
       (if (<= z 6.6e-61) (* a (* (* x y) b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * (z * t));
	double tmp;
	if (z <= -3.5e-75) {
		tmp = t_1;
	} else if (z <= 1.8e-104) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 6.6e-61) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (i * (z * t))
    if (z <= (-3.5d-75)) then
        tmp = t_1
    else if (z <= 1.8d-104) then
        tmp = c * (y * (y3 * y4))
    else if (z <= 6.6d-61) then
        tmp = a * ((x * y) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (i * (z * t));
	double tmp;
	if (z <= -3.5e-75) {
		tmp = t_1;
	} else if (z <= 1.8e-104) {
		tmp = c * (y * (y3 * y4));
	} else if (z <= 6.6e-61) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (i * (z * t))
	tmp = 0
	if z <= -3.5e-75:
		tmp = t_1
	elif z <= 1.8e-104:
		tmp = c * (y * (y3 * y4))
	elif z <= 6.6e-61:
		tmp = a * ((x * y) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(i * Float64(z * t)))
	tmp = 0.0
	if (z <= -3.5e-75)
		tmp = t_1;
	elseif (z <= 1.8e-104)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (z <= 6.6e-61)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (i * (z * t));
	tmp = 0.0;
	if (z <= -3.5e-75)
		tmp = t_1;
	elseif (z <= 1.8e-104)
		tmp = c * (y * (y3 * y4));
	elseif (z <= 6.6e-61)
		tmp = a * ((x * y) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-75], t$95$1, If[LessEqual[z, 1.8e-104], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-61], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999985e-75 or 6.59999999999999992e-61 < z

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 47.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 43.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 43.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 35.8%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -3.49999999999999985e-75 < z < 1.7999999999999999e-104

   1. Initial program 39.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 43.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 43.3%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 43.3%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in y around inf 25.8%

      \[\leadsto \color{blue}{c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 1.7999999999999999e-104 < z < 6.59999999999999992e-61

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 42.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 51.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 51.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 51.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 51.0%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 51.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 51.0%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 51.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   9. Taylor expanded in y around inf 50.7%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 50.7%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   11. Simplified 50.7%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(y \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-104}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 22.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -1.9 \cdot 10^{+125} \lor \neg \left(y5 \leq 2.3 \cdot 10^{+69}\right):\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y5 -1.9e+125) (not (<= y5 2.3e+69)))
   (* j (* y3 (* y0 y5)))
   (* (* t i) (* z 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 tmp;
	if ((y5 <= -1.9e+125) || !(y5 <= 2.3e+69)) {
		tmp = j * (y3 * (y0 * y5));
	} else {
		tmp = (t * i) * (z * 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) :: tmp
    if ((y5 <= (-1.9d+125)) .or. (.not. (y5 <= 2.3d+69))) then
        tmp = j * (y3 * (y0 * y5))
    else
        tmp = (t * i) * (z * 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 tmp;
	if ((y5 <= -1.9e+125) || !(y5 <= 2.3e+69)) {
		tmp = j * (y3 * (y0 * y5));
	} else {
		tmp = (t * i) * (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y5 <= -1.9e+125) or not (y5 <= 2.3e+69):
		tmp = j * (y3 * (y0 * y5))
	else:
		tmp = (t * i) * (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y5 <= -1.9e+125) || !(y5 <= 2.3e+69))
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	else
		tmp = Float64(Float64(t * i) * Float64(z * 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)
	tmp = 0.0;
	if ((y5 <= -1.9e+125) || ~((y5 <= 2.3e+69)))
		tmp = j * (y3 * (y0 * y5));
	else
		tmp = (t * i) * (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y5, -1.9e+125], N[Not[LessEqual[y5, 2.3e+69]], $MachinePrecision]], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y5 < -1.90000000000000001e125 or 2.30000000000000017e69 < y5

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 38.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 42.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.4%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 42.4%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 39.8%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 38.9%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 38.9%

          \[\leadsto j \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y0\right)} \]

       2. associate-*l* 43.0%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0\right)\right)} \]

       3. *-commutative 43.0%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]

   12. Simplified 43.0%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if -1.90000000000000001e125 < y5 < 2.30000000000000017e69

   1. Initial program 38.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 50.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 45.7%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 45.7%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 25.3%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 25.3%

         \[\leadsto \color{blue}{\left(i \cdot \left(t \cdot z\right)\right) \cdot c} \]

      2. associate-*r* 25.9%

         \[\leadsto \color{blue}{\left(\left(i \cdot t\right) \cdot z\right)} \cdot c \]

      3. associate-*l* 27.1%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot \left(z \cdot c\right)} \]

      4. *-commutative 27.1%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot \left(z \cdot c\right) \]

   9. Simplified 27.1%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot \left(z \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.9 \cdot 10^{+125} \lor \neg \left(y5 \leq 2.3 \cdot 10^{+69}\right):\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 22.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -3.4 \cdot 10^{+139} \lor \neg \left(y5 \leq 9.5 \cdot 10^{+70}\right):\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y5 -3.4e+139) (not (<= y5 9.5e+70)))
   (* j (* y3 (* y0 y5)))
   (* c (* i (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -3.4e+139) || !(y5 <= 9.5e+70)) {
		tmp = j * (y3 * (y0 * y5));
	} else {
		tmp = c * (i * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y5 <= (-3.4d+139)) .or. (.not. (y5 <= 9.5d+70))) then
        tmp = j * (y3 * (y0 * y5))
    else
        tmp = c * (i * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y5 <= -3.4e+139) || !(y5 <= 9.5e+70)) {
		tmp = j * (y3 * (y0 * y5));
	} else {
		tmp = c * (i * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y5 <= -3.4e+139) or not (y5 <= 9.5e+70):
		tmp = j * (y3 * (y0 * y5))
	else:
		tmp = c * (i * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y5 <= -3.4e+139) || !(y5 <= 9.5e+70))
		tmp = Float64(j * Float64(y3 * Float64(y0 * y5)));
	else
		tmp = Float64(c * Float64(i * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y5 <= -3.4e+139) || ~((y5 <= 9.5e+70)))
		tmp = j * (y3 * (y0 * y5));
	else
		tmp = c * (i * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y5, -3.4e+139], N[Not[LessEqual[y5, 9.5e+70]], $MachinePrecision]], N[(j * N[(y3 * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y5 < -3.4000000000000002e139 or 9.5000000000000002e70 < y5

   1. Initial program 27.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y0 around inf 37.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in y5 around inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 42.5%

         \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   8. Simplified 42.5%

      \[\leadsto \color{blue}{-y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   9. Taylor expanded in y2 around inf 39.7%

      \[\leadsto \color{blue}{y2 \cdot \left(\frac{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)}{y2} - k \cdot \left(y0 \cdot y5\right)\right)} \]

   10. Taylor expanded in y2 around 0 38.9%

       \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 38.9%

          \[\leadsto j \cdot \color{blue}{\left(\left(y3 \cdot y5\right) \cdot y0\right)} \]

       2. associate-*l* 43.1%

          \[\leadsto j \cdot \color{blue}{\left(y3 \cdot \left(y5 \cdot y0\right)\right)} \]

       3. *-commutative 43.1%

          \[\leadsto j \cdot \left(y3 \cdot \color{blue}{\left(y0 \cdot y5\right)}\right) \]

   12. Simplified 43.1%

       \[\leadsto \color{blue}{j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)} \]

   if -3.4000000000000002e139 < y5 < 9.5000000000000002e70

   1. Initial program 38.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 50.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 46.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 46.2%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 25.8%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.4 \cdot 10^{+139} \lor \neg \left(y5 \leq 9.5 \cdot 10^{+70}\right):\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 22.6% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-75} \lor \neg \left(z \leq 1.2 \cdot 10^{-60}\right):\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= z -1.3e-75) (not (<= z 1.2e-60)))
   (* c (* i (* z t)))
   (* 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 ((z <= -1.3e-75) || !(z <= 1.2e-60)) {
		tmp = c * (i * (z * t));
	} 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 ((z <= (-1.3d-75)) .or. (.not. (z <= 1.2d-60))) then
        tmp = c * (i * (z * t))
    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 ((z <= -1.3e-75) || !(z <= 1.2e-60)) {
		tmp = c * (i * (z * t));
	} 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 (z <= -1.3e-75) or not (z <= 1.2e-60):
		tmp = c * (i * (z * t))
	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 ((z <= -1.3e-75) || !(z <= 1.2e-60))
		tmp = Float64(c * Float64(i * Float64(z * t)));
	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 ((z <= -1.3e-75) || ~((z <= 1.2e-60)))
		tmp = c * (i * (z * t));
	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[Or[LessEqual[z, -1.3e-75], N[Not[LessEqual[z, 1.2e-60]], $MachinePrecision]], N[(c * N[(i * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-75 or 1.20000000000000005e-60 < z

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 47.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   4. Taylor expanded in x around 0 43.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(t \cdot z\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto c \cdot \left(\left(i \cdot \color{blue}{\left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   6. Simplified 43.8%

      \[\leadsto c \cdot \left(\left(\color{blue}{i \cdot \left(z \cdot t\right)} + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Taylor expanded in i around inf 35.8%

      \[\leadsto \color{blue}{c \cdot \left(i \cdot \left(t \cdot z\right)\right)} \]

   if -1.3e-75 < z < 1.20000000000000005e-60

   1. Initial program 38.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.4%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 38.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   6. Taylor expanded in a around inf 20.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 20.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

      2. distribute-lft-neg-out 20.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

      3. +-commutative 20.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

      4. *-commutative 20.4%

         \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

      5. cancel-sign-sub-inv 20.4%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

      6. *-commutative 20.4%

         \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

   8. Simplified 20.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

   9. Taylor expanded in y around inf 19.2%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 19.2%

          \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

   11. Simplified 19.2%

       \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(y \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-75} \lor \neg \left(z \leq 1.2 \cdot 10^{-60}\right):\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 17.2% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 34.5%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 34.9%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 36.2%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

6. Taylor expanded in a around inf 26.8%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right)} \]
7. Step-by-step derivation

   1. mul-1-neg 26.8%

      \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + x \cdot y\right)\right) \]

   2. distribute-lft-neg-out 26.8%

      \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{\left(-t\right) \cdot z} + x \cdot y\right)\right) \]

   3. +-commutative 26.8%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(x \cdot y + \left(-t\right) \cdot z\right)}\right) \]

   4. *-commutative 26.8%

      \[\leadsto a \cdot \left(b \cdot \left(\color{blue}{y \cdot x} + \left(-t\right) \cdot z\right)\right) \]

   5. cancel-sign-sub-inv 26.8%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x - t \cdot z\right)}\right) \]

   6. *-commutative 26.8%

      \[\leadsto a \cdot \left(b \cdot \left(y \cdot x - \color{blue}{z \cdot t}\right)\right) \]

8. Simplified 26.8%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - z \cdot t\right)\right)} \]

9. Taylor expanded in y around inf 14.8%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
10. Step-by-step derivation

    1. *-commutative 14.8%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(y \cdot x\right)}\right) \]

11. Simplified 14.8%

    \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(y \cdot x\right)\right)} \]

12. Final simplification 14.8%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
13. Add Preprocessing

Developer target: 27.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t\_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t\_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t\_9\\ t_11 := t\_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t\_4 \cdot t\_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t\_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t\_3 \cdot t\_1 - t\_14\right)\right) + \left(t\_8 - \left(t\_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t\_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t\_13\right)\right) + \left(t\_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t\_10 - \left(y \cdot x - z \cdot t\right) \cdot t\_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t\_8 - \left(t\_11 - t\_6\right)\right) - \left(\frac{t\_3}{\frac{1}{t\_1}} - t\_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t\_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t\_2 - \left(t\_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t\_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t\_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t\_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t\_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t\_5\right) - t\_17 \cdot t\_1\right) + t\_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))