Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.7% → 43.0%

Time: 54.5s

Alternatives: 39

Speedup: 4.5×

• 88.8% 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: 29.7% 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: 43.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y4 - a \cdot y5\\ t_2 := i \cdot y5 - b \cdot y4\\ t_3 := t \cdot y2 - y \cdot y3\\ t_4 := a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot t\_3\right)\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := t\_5 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+172}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - \left(\frac{b \cdot \left(x \cdot y0\right) + \left(t \cdot t\_2 - y0 \cdot \left(y3 \cdot y5\right)\right)}{y1} + y3 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-197}:\\ \;\;\;\;t\_6 + \left(i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - t\_3 \cdot t\_1\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-289}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t\_5\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-212}:\\ \;\;\;\;t\_6 + y \cdot \left(\left(k \cdot t\_2 + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot t\_1\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+44}:\\ \;\;\;\;t\_6 + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y4) (* a y5)))
        (t_2 (- (* i y5) (* b y4)))
        (t_3 (- (* t y2) (* y y3)))
        (t_4
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 t_3))))
        (t_5 (- (* k y2) (* j y3)))
        (t_6 (* t_5 (- (* y1 y4) (* y0 y5)))))
   (if (<= a -4.7e+172)
     t_4
     (if (<= a -2.65e-132)
       (*
        j
        (*
         y1
         (-
          (* x i)
          (+
           (/ (+ (* b (* x y0)) (- (* t t_2) (* y0 (* y3 y5)))) y1)
           (* y3 y4)))))
       (if (<= a -2.35e-197)
         (+ t_6 (- (* i (* y5 (- (* y k) (* t j)))) (* t_3 t_1)))
         (if (<= a -2.9e-289)
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 t_5))
             (* c (- (* y y3) (* t y2)))))
           (if (<= a 2.7e-212)
             (+
              t_6
              (* y (+ (+ (* k t_2) (* x (- (* a b) (* c i)))) (* y3 t_1))))
             (if (<= a 1.75e-109)
               (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))
               (if (<= a 5.2e+44)
                 (+
                  t_6
                  (*
                   t
                   (+
                    (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
                    (* y2 (- (* a y5) (* c y4))))))
                 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 = (c * y4) - (a * y5);
	double t_2 = (i * y5) - (b * y4);
	double t_3 = (t * y2) - (y * y3);
	double t_4 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_3));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = t_5 * ((y1 * y4) - (y0 * y5));
	double tmp;
	if (a <= -4.7e+172) {
		tmp = t_4;
	} else if (a <= -2.65e-132) {
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * t_2) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	} else if (a <= -2.35e-197) {
		tmp = t_6 + ((i * (y5 * ((y * k) - (t * j)))) - (t_3 * t_1));
	} else if (a <= -2.9e-289) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 2.7e-212) {
		tmp = t_6 + (y * (((k * t_2) + (x * ((a * b) - (c * i)))) + (y3 * t_1)));
	} else if (a <= 1.75e-109) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 5.2e+44) {
		tmp = t_6 + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	} 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) :: tmp
    t_1 = (c * y4) - (a * y5)
    t_2 = (i * y5) - (b * y4)
    t_3 = (t * y2) - (y * y3)
    t_4 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_3))
    t_5 = (k * y2) - (j * y3)
    t_6 = t_5 * ((y1 * y4) - (y0 * y5))
    if (a <= (-4.7d+172)) then
        tmp = t_4
    else if (a <= (-2.65d-132)) then
        tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * t_2) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))))
    else if (a <= (-2.35d-197)) then
        tmp = t_6 + ((i * (y5 * ((y * k) - (t * j)))) - (t_3 * t_1))
    else if (a <= (-2.9d-289)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))))
    else if (a <= 2.7d-212) then
        tmp = t_6 + (y * (((k * t_2) + (x * ((a * b) - (c * i)))) + (y3 * t_1)))
    else if (a <= 1.75d-109) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    else if (a <= 5.2d+44) then
        tmp = t_6 + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))))
    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 = (c * y4) - (a * y5);
	double t_2 = (i * y5) - (b * y4);
	double t_3 = (t * y2) - (y * y3);
	double t_4 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_3));
	double t_5 = (k * y2) - (j * y3);
	double t_6 = t_5 * ((y1 * y4) - (y0 * y5));
	double tmp;
	if (a <= -4.7e+172) {
		tmp = t_4;
	} else if (a <= -2.65e-132) {
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * t_2) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	} else if (a <= -2.35e-197) {
		tmp = t_6 + ((i * (y5 * ((y * k) - (t * j)))) - (t_3 * t_1));
	} else if (a <= -2.9e-289) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 2.7e-212) {
		tmp = t_6 + (y * (((k * t_2) + (x * ((a * b) - (c * i)))) + (y3 * t_1)));
	} else if (a <= 1.75e-109) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 5.2e+44) {
		tmp = t_6 + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	} 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 = (c * y4) - (a * y5)
	t_2 = (i * y5) - (b * y4)
	t_3 = (t * y2) - (y * y3)
	t_4 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_3))
	t_5 = (k * y2) - (j * y3)
	t_6 = t_5 * ((y1 * y4) - (y0 * y5))
	tmp = 0
	if a <= -4.7e+172:
		tmp = t_4
	elif a <= -2.65e-132:
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * t_2) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))))
	elif a <= -2.35e-197:
		tmp = t_6 + ((i * (y5 * ((y * k) - (t * j)))) - (t_3 * t_1))
	elif a <= -2.9e-289:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))))
	elif a <= 2.7e-212:
		tmp = t_6 + (y * (((k * t_2) + (x * ((a * b) - (c * i)))) + (y3 * t_1)))
	elif a <= 1.75e-109:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	elif a <= 5.2e+44:
		tmp = t_6 + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))))
	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(c * y4) - Float64(a * y5))
	t_2 = Float64(Float64(i * y5) - Float64(b * y4))
	t_3 = Float64(Float64(t * y2) - Float64(y * y3))
	t_4 = 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_3)))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(t_5 * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	tmp = 0.0
	if (a <= -4.7e+172)
		tmp = t_4;
	elseif (a <= -2.65e-132)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(Float64(Float64(Float64(b * Float64(x * y0)) + Float64(Float64(t * t_2) - Float64(y0 * Float64(y3 * y5)))) / y1) + Float64(y3 * y4)))));
	elseif (a <= -2.35e-197)
		tmp = Float64(t_6 + Float64(Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))) - Float64(t_3 * t_1)));
	elseif (a <= -2.9e-289)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_5)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (a <= 2.7e-212)
		tmp = Float64(t_6 + Float64(y * Float64(Float64(Float64(k * t_2) + Float64(x * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y3 * t_1))));
	elseif (a <= 1.75e-109)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))));
	elseif (a <= 5.2e+44)
		tmp = Float64(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 * Float64(Float64(a * y5) - Float64(c * y4))))));
	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 = (c * y4) - (a * y5);
	t_2 = (i * y5) - (b * y4);
	t_3 = (t * y2) - (y * y3);
	t_4 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * t_3));
	t_5 = (k * y2) - (j * y3);
	t_6 = t_5 * ((y1 * y4) - (y0 * y5));
	tmp = 0.0;
	if (a <= -4.7e+172)
		tmp = t_4;
	elseif (a <= -2.65e-132)
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * t_2) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	elseif (a <= -2.35e-197)
		tmp = t_6 + ((i * (y5 * ((y * k) - (t * j)))) - (t_3 * t_1));
	elseif (a <= -2.9e-289)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_5)) + (c * ((y * y3) - (t * y2))));
	elseif (a <= 2.7e-212)
		tmp = t_6 + (y * (((k * t_2) + (x * ((a * b) - (c * i)))) + (y3 * t_1)));
	elseif (a <= 1.75e-109)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	elseif (a <= 5.2e+44)
		tmp = t_6 + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	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[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = 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$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$5 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e+172], t$95$4, If[LessEqual[a, -2.65e-132], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(N[(N[(N[(b * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t$95$2), $MachinePrecision] - N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y1), $MachinePrecision] + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.35e-197], N[(t$95$6 + N[(N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.9e-289], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-212], N[(t$95$6 + N[(y * N[(N[(N[(k * t$95$2), $MachinePrecision] + N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-109], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+44], N[(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 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -4.7000000000000001e172 or 5.1999999999999998e44 < a

   1. Initial program 22.4%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in a around inf 65.5%

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

   if -4.7000000000000001e172 < a < -2.65000000000000015e-132

   1. Initial program 27.6%

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

   3. Taylor expanded in j around inf 48.6%

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

   4. Taylor expanded in y1 around -inf 62.1%

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

   if -2.65000000000000015e-132 < a < -2.3500000000000001e-197

   1. Initial program 26.7%

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

   3. Taylor expanded in y5 around inf 60.7%

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

      1. mul-1-neg 60.7%

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

   5. Simplified 60.7%

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

   if -2.3500000000000001e-197 < a < -2.90000000000000006e-289

   1. Initial program 15.9%

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

   3. Taylor expanded in y4 around inf 64.5%

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

   if -2.90000000000000006e-289 < a < 2.69999999999999981e-212

   1. Initial program 52.7%

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

   3. Taylor expanded in y around inf 68.3%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if 2.69999999999999981e-212 < a < 1.75e-109

   1. Initial program 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 56.3%

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

   if 1.75e-109 < a < 5.1999999999999998e44

   1. Initial program 23.0%

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

   3. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+172}:\\ \;\;\;\;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}\;a \leq -2.65 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - \left(\frac{b \cdot \left(x \cdot y0\right) + \left(t \cdot \left(i \cdot y5 - b \cdot y4\right) - y0 \cdot \left(y3 \cdot y5\right)\right)}{y1} + y3 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-197}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + \left(i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-289}:\\ \;\;\;\;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}\;a \leq 2.7 \cdot 10^{-212}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+44}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + 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}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * t_2) + Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(i * y1) - Float64(b * y0)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))) + Float64(t_1 * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * t_2)) + Float64(y5 * 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 = (t * y2) - (y * y3);
	t_2 = (x * y) - (z * t);
	t_3 = (((((((a * b) - (c * i)) * t_2) + (((x * j) - (z * k)) * ((i * y1) - (b * y0)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (t_1 * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = a * (((y1 * ((z * y3) - (x * y2))) + (b * t_2)) + (y5 * 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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(a * N[(N[(N[(y1 * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y5 * 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 84.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in a around inf 42.4%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.2%

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

Alternative 3: 42.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - \left(\frac{b \cdot \left(x \cdot y0\right) + \left(t \cdot \left(i \cdot y5 - b \cdot y4\right) - y0 \cdot \left(y3 \cdot y5\right)\right)}{y1} + y3 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-207}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+40}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 (- (* t y2) (* y y3)))))))
   (if (<= a -3.5e+173)
     t_1
     (if (<= a -1.7e-132)
       (*
        j
        (*
         y1
         (-
          (* x i)
          (+
           (/
            (+ (* b (* x y0)) (- (* t (- (* i y5) (* b y4))) (* y0 (* y3 y5))))
            y1)
           (* y3 y4)))))
       (if (<= a 2.55e-207)
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= a 1.38e-109)
           (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))
           (if (<= a 6.2e+40)
             (+
              (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))
              (*
               t
               (+
                (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
                (* y2 (- (* a y5) (* c y4))))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (a <= -3.5e+173) {
		tmp = t_1;
	} else if (a <= -1.7e-132) {
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	} else if (a <= 2.55e-207) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (a <= 1.38e-109) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 6.2e+40) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
    if (a <= (-3.5d+173)) then
        tmp = t_1
    else if (a <= (-1.7d-132)) then
        tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))))
    else if (a <= 2.55d-207) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (a <= 1.38d-109) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    else if (a <= 6.2d+40) then
        tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (a <= -3.5e+173) {
		tmp = t_1;
	} else if (a <= -1.7e-132) {
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	} else if (a <= 2.55e-207) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (a <= 1.38e-109) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 6.2e+40) {
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
	tmp = 0
	if a <= -3.5e+173:
		tmp = t_1
	elif a <= -1.7e-132:
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))))
	elif a <= 2.55e-207:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif a <= 1.38e-109:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	elif a <= 6.2e+40:
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (a <= -3.5e+173)
		tmp = t_1;
	elseif (a <= -1.7e-132)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(Float64(Float64(Float64(b * Float64(x * y0)) + Float64(Float64(t * Float64(Float64(i * y5) - Float64(b * y4))) - Float64(y0 * Float64(y3 * y5)))) / y1) + Float64(y3 * y4)))));
	elseif (a <= 2.55e-207)
		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 (a <= 1.38e-109)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))));
	elseif (a <= 6.2e+40)
		tmp = Float64(Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))) + Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	tmp = 0.0;
	if (a <= -3.5e+173)
		tmp = t_1;
	elseif (a <= -1.7e-132)
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	elseif (a <= 2.55e-207)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (a <= 1.38e-109)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	elseif (a <= 6.2e+40)
		tmp = (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))) + (t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(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 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+173], t$95$1, If[LessEqual[a, -1.7e-132], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(N[(N[(N[(b * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y1), $MachinePrecision] + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e-207], 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[a, 1.38e-109], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+40], N[(N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.4999999999999999e173 or 6.1999999999999995e40 < a

   1. Initial program 22.4%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in a around inf 65.5%

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

   if -3.4999999999999999e173 < a < -1.69999999999999991e-132

   1. Initial program 28.8%

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

   3. Taylor expanded in j around inf 49.4%

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

   4. Taylor expanded in y1 around -inf 62.7%

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

   if -1.69999999999999991e-132 < a < 2.5500000000000002e-207

   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 c around inf 45.7%

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

   if 2.5500000000000002e-207 < a < 1.3800000000000001e-109

   1. Initial program 15.2%

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

   3. Simplified 15.2%

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

   5. Taylor expanded in y2 around inf 36.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 58.2%

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

   if 1.3800000000000001e-109 < a < 6.1999999999999995e40

   1. Initial program 23.0%

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

   3. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - \left(\frac{b \cdot \left(x \cdot y0\right) + \left(t \cdot \left(i \cdot y5 - b \cdot y4\right) - y0 \cdot \left(y3 \cdot y5\right)\right)}{y1} + y3 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-207}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+40}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := j \cdot y3 - k \cdot y2\\ t_3 := z \cdot y3 - x \cdot y2\\ t_4 := t \cdot y2 - y \cdot y3\\ t_5 := a \cdot \left(\left(y1 \cdot t\_3 + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot t\_4\right)\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+126}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-41}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot t\_3 + y4 \cdot t\_1\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-196}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_4 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t\_2\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-214}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t\_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-110}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot t\_2 + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* j y3) (* k y2)))
        (t_3 (- (* z y3) (* x y2)))
        (t_4 (- (* t y2) (* y y3)))
        (t_5 (* a (+ (+ (* y1 t_3) (* b (- (* x y) (* z t)))) (* y5 t_4)))))
   (if (<= a -2.4e+126)
     t_5
     (if (<= a -1.7e-41)
       (* y1 (+ (+ (* a t_3) (* y4 t_1)) (* i (- (* x j) (* z k)))))
       (if (<= a -1.02e-196)
         (* y5 (+ (* a t_4) (+ (* i (- (* y k) (* t j))) (* y0 t_2))))
         (if (<= a 9.5e-214)
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 t_1))
             (* c (- (* y y3) (* t y2)))))
           (if (<= a 4.2e-110)
             (* y0 (+ (* y5 t_2) (* c (* x y2))))
             (if (<= a 3.4e+43)
               (*
                t
                (+
                 (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
                 (* y2 (- (* a y5) (* c y4)))))
               t_5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (z * y3) - (x * y2);
	double t_4 = (t * y2) - (y * y3);
	double t_5 = a * (((y1 * t_3) + (b * ((x * y) - (z * t)))) + (y5 * t_4));
	double tmp;
	if (a <= -2.4e+126) {
		tmp = t_5;
	} else if (a <= -1.7e-41) {
		tmp = y1 * (((a * t_3) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	} else if (a <= -1.02e-196) {
		tmp = y5 * ((a * t_4) + ((i * ((y * k) - (t * j))) + (y0 * t_2)));
	} else if (a <= 9.5e-214) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 4.2e-110) {
		tmp = y0 * ((y5 * t_2) + (c * (x * y2)));
	} else if (a <= 3.4e+43) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (j * y3) - (k * y2)
    t_3 = (z * y3) - (x * y2)
    t_4 = (t * y2) - (y * y3)
    t_5 = a * (((y1 * t_3) + (b * ((x * y) - (z * t)))) + (y5 * t_4))
    if (a <= (-2.4d+126)) then
        tmp = t_5
    else if (a <= (-1.7d-41)) then
        tmp = y1 * (((a * t_3) + (y4 * t_1)) + (i * ((x * j) - (z * k))))
    else if (a <= (-1.02d-196)) then
        tmp = y5 * ((a * t_4) + ((i * ((y * k) - (t * j))) + (y0 * t_2)))
    else if (a <= 9.5d-214) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
    else if (a <= 4.2d-110) then
        tmp = y0 * ((y5 * t_2) + (c * (x * y2)))
    else if (a <= 3.4d+43) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (z * y3) - (x * y2);
	double t_4 = (t * y2) - (y * y3);
	double t_5 = a * (((y1 * t_3) + (b * ((x * y) - (z * t)))) + (y5 * t_4));
	double tmp;
	if (a <= -2.4e+126) {
		tmp = t_5;
	} else if (a <= -1.7e-41) {
		tmp = y1 * (((a * t_3) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	} else if (a <= -1.02e-196) {
		tmp = y5 * ((a * t_4) + ((i * ((y * k) - (t * j))) + (y0 * t_2)));
	} else if (a <= 9.5e-214) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 4.2e-110) {
		tmp = y0 * ((y5 * t_2) + (c * (x * y2)));
	} else if (a <= 3.4e+43) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = (j * y3) - (k * y2)
	t_3 = (z * y3) - (x * y2)
	t_4 = (t * y2) - (y * y3)
	t_5 = a * (((y1 * t_3) + (b * ((x * y) - (z * t)))) + (y5 * t_4))
	tmp = 0
	if a <= -2.4e+126:
		tmp = t_5
	elif a <= -1.7e-41:
		tmp = y1 * (((a * t_3) + (y4 * t_1)) + (i * ((x * j) - (z * k))))
	elif a <= -1.02e-196:
		tmp = y5 * ((a * t_4) + ((i * ((y * k) - (t * j))) + (y0 * t_2)))
	elif a <= 9.5e-214:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
	elif a <= 4.2e-110:
		tmp = y0 * ((y5 * t_2) + (c * (x * y2)))
	elif a <= 3.4e+43:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(j * y3) - Float64(k * y2))
	t_3 = Float64(Float64(z * y3) - Float64(x * y2))
	t_4 = Float64(Float64(t * y2) - Float64(y * y3))
	t_5 = Float64(a * Float64(Float64(Float64(y1 * t_3) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * t_4)))
	tmp = 0.0
	if (a <= -2.4e+126)
		tmp = t_5;
	elseif (a <= -1.7e-41)
		tmp = Float64(y1 * Float64(Float64(Float64(a * t_3) + Float64(y4 * t_1)) + Float64(i * Float64(Float64(x * j) - Float64(z * k)))));
	elseif (a <= -1.02e-196)
		tmp = Float64(y5 * Float64(Float64(a * t_4) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_2))));
	elseif (a <= 9.5e-214)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_1)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (a <= 4.2e-110)
		tmp = Float64(y0 * Float64(Float64(y5 * t_2) + Float64(c * Float64(x * y2))));
	elseif (a <= 3.4e+43)
		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 * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (j * y3) - (k * y2);
	t_3 = (z * y3) - (x * y2);
	t_4 = (t * y2) - (y * y3);
	t_5 = a * (((y1 * t_3) + (b * ((x * y) - (z * t)))) + (y5 * t_4));
	tmp = 0.0;
	if (a <= -2.4e+126)
		tmp = t_5;
	elseif (a <= -1.7e-41)
		tmp = y1 * (((a * t_3) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	elseif (a <= -1.02e-196)
		tmp = y5 * ((a * t_4) + ((i * ((y * k) - (t * j))) + (y0 * t_2)));
	elseif (a <= 9.5e-214)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	elseif (a <= 4.2e-110)
		tmp = y0 * ((y5 * t_2) + (c * (x * y2)));
	elseif (a <= 3.4e+43)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(a * N[(N[(N[(y1 * t$95$3), $MachinePrecision] + N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+126], t$95$5, If[LessEqual[a, -1.7e-41], N[(y1 * N[(N[(N[(a * t$95$3), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.02e-196], N[(y5 * N[(N[(a * t$95$4), $MachinePrecision] + N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-214], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-110], N[(y0 * N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+43], 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 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.40000000000000012e126 or 3.40000000000000012e43 < a

   1. Initial program 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in a around inf 64.5%

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

   if -2.40000000000000012e126 < a < -1.6999999999999999e-41

   1. Initial program 38.4%

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

   3. Taylor expanded in y1 around inf 62.5%

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

   if -1.6999999999999999e-41 < a < -1.0200000000000001e-196

   1. Initial program 18.3%

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

   3. Taylor expanded in y5 around -inf 50.5%

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

   if -1.0200000000000001e-196 < a < 9.4999999999999999e-214

   1. Initial program 39.5%

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

   3. Taylor expanded in y4 around inf 51.5%

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

   if 9.4999999999999999e-214 < a < 4.20000000000000004e-110

   1. Initial program 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 56.3%

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

   if 4.20000000000000004e-110 < a < 3.40000000000000012e43

   1. Initial program 23.0%

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

   3. Taylor expanded in t around inf 42.7%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-41}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-196}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-214}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-110}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-133}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - \left(\frac{b \cdot \left(x \cdot y0\right) + \left(t \cdot \left(i \cdot y5 - b \cdot y4\right) - y0 \cdot \left(y3 \cdot y5\right)\right)}{y1} + y3 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-207}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-110}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          a
          (+
           (+ (* y1 (- (* z y3) (* x y2))) (* b (- (* x y) (* z t))))
           (* y5 (- (* t y2) (* y y3)))))))
   (if (<= a -3.6e+173)
     t_1
     (if (<= a -6.1e-133)
       (*
        j
        (*
         y1
         (-
          (* x i)
          (+
           (/
            (+ (* b (* x y0)) (- (* t (- (* i y5) (* b y4))) (* y0 (* y3 y5))))
            y1)
           (* y3 y4)))))
       (if (<= a 2.5e-207)
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))
         (if (<= a 5.8e-110)
           (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))
           (if (<= a 5.8e+43)
             (*
              t
              (+
               (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
               (* y2 (- (* a y5) (* c y4)))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (a <= -3.6e+173) {
		tmp = t_1;
	} else if (a <= -6.1e-133) {
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	} else if (a <= 2.5e-207) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (a <= 5.8e-110) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 5.8e+43) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
    if (a <= (-3.6d+173)) then
        tmp = t_1
    else if (a <= (-6.1d-133)) then
        tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))))
    else if (a <= 2.5d-207) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (a <= 5.8d-110) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    else if (a <= 5.8d+43) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	double tmp;
	if (a <= -3.6e+173) {
		tmp = t_1;
	} else if (a <= -6.1e-133) {
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	} else if (a <= 2.5e-207) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (a <= 5.8e-110) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 5.8e+43) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))))
	tmp = 0
	if a <= -3.6e+173:
		tmp = t_1
	elif a <= -6.1e-133:
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))))
	elif a <= 2.5e-207:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif a <= 5.8e-110:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	elif a <= 5.8e+43:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(Float64(Float64(y1 * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(b * Float64(Float64(x * y) - Float64(z * t)))) + Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (a <= -3.6e+173)
		tmp = t_1;
	elseif (a <= -6.1e-133)
		tmp = Float64(j * Float64(y1 * Float64(Float64(x * i) - Float64(Float64(Float64(Float64(b * Float64(x * y0)) + Float64(Float64(t * Float64(Float64(i * y5) - Float64(b * y4))) - Float64(y0 * Float64(y3 * y5)))) / y1) + Float64(y3 * y4)))));
	elseif (a <= 2.5e-207)
		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 (a <= 5.8e-110)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))));
	elseif (a <= 5.8e+43)
		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 * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (((y1 * ((z * y3) - (x * y2))) + (b * ((x * y) - (z * t)))) + (y5 * ((t * y2) - (y * y3))));
	tmp = 0.0;
	if (a <= -3.6e+173)
		tmp = t_1;
	elseif (a <= -6.1e-133)
		tmp = j * (y1 * ((x * i) - ((((b * (x * y0)) + ((t * ((i * y5) - (b * y4))) - (y0 * (y3 * y5)))) / y1) + (y3 * y4))));
	elseif (a <= 2.5e-207)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (a <= 5.8e-110)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	elseif (a <= 5.8e+43)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(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 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+173], t$95$1, If[LessEqual[a, -6.1e-133], N[(j * N[(y1 * N[(N[(x * i), $MachinePrecision] - N[(N[(N[(N[(b * N[(x * y0), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y1), $MachinePrecision] + N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-207], 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[a, 5.8e-110], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+43], 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 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.6000000000000002e173 or 5.8000000000000004e43 < a

   1. Initial program 22.4%

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

   3. Simplified 22.4%

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

   5. Taylor expanded in a around inf 65.5%

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

   if -3.6000000000000002e173 < a < -6.1000000000000004e-133

   1. Initial program 28.8%

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

   3. Taylor expanded in j around inf 49.4%

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

   4. Taylor expanded in y1 around -inf 62.7%

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

   if -6.1000000000000004e-133 < a < 2.50000000000000007e-207

   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 c around inf 45.7%

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

   if 2.50000000000000007e-207 < a < 5.8000000000000005e-110

   1. Initial program 15.2%

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

   3. Simplified 15.2%

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

   5. Taylor expanded in y2 around inf 36.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 58.2%

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

   if 5.8000000000000005e-110 < a < 5.8000000000000004e43

   1. Initial program 23.0%

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

   3. Taylor expanded in t around inf 42.7%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 58.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-133}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(x \cdot i - \left(\frac{b \cdot \left(x \cdot y0\right) + \left(t \cdot \left(i \cdot y5 - b \cdot y4\right) - y0 \cdot \left(y3 \cdot y5\right)\right)}{y1} + y3 \cdot y4\right)\right)\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-207}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-110}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(y1 \cdot \left(z \cdot y3 - x \cdot y2\right) + b \cdot \left(x \cdot y - z \cdot t\right)\right) + y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y4 - i \cdot y5\\ t_2 := y0 \cdot y5 - y1 \cdot y4\\ t_3 := a \cdot y5 - c \cdot y4\\ t_4 := t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t\_1\right) + y2 \cdot t\_3\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+45}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-70}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t\_2 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_1 + y3 \cdot t\_2\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-103}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+83}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y4) (* i y5)))
        (t_2 (- (* y0 y5) (* y1 y4)))
        (t_3 (- (* a y5) (* c y4)))
        (t_4 (* t (+ (+ (* z (- (* c i) (* a b))) (* j t_1)) (* y2 t_3)))))
   (if (<= t -5.4e+45)
     t_4
     (if (<= t -8e-70)
       (*
        y3
        (+
         (* y (- (* c y4) (* a y5)))
         (+ (* j t_2) (* z (- (* a y1) (* c y0))))))
       (if (<= t 2.9e-291)
         (* j (+ (+ (* t t_1) (* y3 t_2)) (* x (- (* i y1) (* b y0)))))
         (if (<= t 5e-103)
           (*
            c
            (+
             (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
             (* y4 (- (* y y3) (* t y2)))))
           (if (<= t 8.5e+83)
             (*
              y2
              (+
               (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
               (* t t_3)))
             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 = (b * y4) - (i * y5);
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3));
	double tmp;
	if (t <= -5.4e+45) {
		tmp = t_4;
	} else if (t <= -8e-70) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))));
	} else if (t <= 2.9e-291) {
		tmp = j * (((t * t_1) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))));
	} else if (t <= 5e-103) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (t <= 8.5e+83) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3));
	} 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) :: tmp
    t_1 = (b * y4) - (i * y5)
    t_2 = (y0 * y5) - (y1 * y4)
    t_3 = (a * y5) - (c * y4)
    t_4 = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3))
    if (t <= (-5.4d+45)) then
        tmp = t_4
    else if (t <= (-8d-70)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))))
    else if (t <= 2.9d-291) then
        tmp = j * (((t * t_1) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))))
    else if (t <= 5d-103) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (t <= 8.5d+83) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3))
    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 = (b * y4) - (i * y5);
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = (a * y5) - (c * y4);
	double t_4 = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3));
	double tmp;
	if (t <= -5.4e+45) {
		tmp = t_4;
	} else if (t <= -8e-70) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))));
	} else if (t <= 2.9e-291) {
		tmp = j * (((t * t_1) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))));
	} else if (t <= 5e-103) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (t <= 8.5e+83) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3));
	} 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 = (b * y4) - (i * y5)
	t_2 = (y0 * y5) - (y1 * y4)
	t_3 = (a * y5) - (c * y4)
	t_4 = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3))
	tmp = 0
	if t <= -5.4e+45:
		tmp = t_4
	elif t <= -8e-70:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))))
	elif t <= 2.9e-291:
		tmp = j * (((t * t_1) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))))
	elif t <= 5e-103:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif t <= 8.5e+83:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3))
	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(b * y4) - Float64(i * y5))
	t_2 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_3 = Float64(Float64(a * y5) - Float64(c * y4))
	t_4 = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_1)) + Float64(y2 * t_3)))
	tmp = 0.0
	if (t <= -5.4e+45)
		tmp = t_4;
	elseif (t <= -8e-70)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_2) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))));
	elseif (t <= 2.9e-291)
		tmp = Float64(j * Float64(Float64(Float64(t * t_1) + Float64(y3 * t_2)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (t <= 5e-103)
		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 (t <= 8.5e+83)
		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)));
	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 = (b * y4) - (i * y5);
	t_2 = (y0 * y5) - (y1 * y4);
	t_3 = (a * y5) - (c * y4);
	t_4 = t * (((z * ((c * i) - (a * b))) + (j * t_1)) + (y2 * t_3));
	tmp = 0.0;
	if (t <= -5.4e+45)
		tmp = t_4;
	elseif (t <= -8e-70)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_2) + (z * ((a * y1) - (c * y0)))));
	elseif (t <= 2.9e-291)
		tmp = j * (((t * t_1) + (y3 * t_2)) + (x * ((i * y1) - (b * y0))));
	elseif (t <= 5e-103)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (t <= 8.5e+83)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_3));
	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[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+45], t$95$4, If[LessEqual[t, -8e-70], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$2), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-291], N[(j * N[(N[(N[(t * t$95$1), $MachinePrecision] + N[(y3 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-103], 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[t, 8.5e+83], 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], t$95$4]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.39999999999999968e45 or 8.4999999999999995e83 < t

   1. Initial program 21.8%

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

   3. Taylor expanded in t around inf 47.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 55.3%

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

   if -5.39999999999999968e45 < t < -7.99999999999999997e-70

   1. Initial program 15.6%

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

   3. Taylor expanded in y3 around -inf 62.0%

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

   if -7.99999999999999997e-70 < t < 2.90000000000000002e-291

   1. Initial program 36.3%

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

   3. Taylor expanded in j around inf 54.6%

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

   if 2.90000000000000002e-291 < t < 4.99999999999999966e-103

   1. Initial program 21.0%

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

   3. Simplified 21.0%

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

   5. Taylor expanded in c around inf 56.7%

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

   if 4.99999999999999966e-103 < t < 8.4999999999999995e83

   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 y2 around inf 48.1%

      \[\leadsto \color{blue}{y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-70}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-291}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-103}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+83}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;y1 \leq -1.4 \cdot 10^{+214}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + y4 \cdot t\_1\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -4.35 \cdot 10^{+43}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq -8.4 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \left(y2 \cdot t\_2\right) + t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-206}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t\_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3))) (t_2 (- (* a y5) (* c y4))))
   (if (<= y1 -1.4e+214)
     (*
      y1
      (+ (+ (* a (- (* z y3) (* x y2))) (* y4 t_1)) (* i (- (* x j) (* z k)))))
     (if (<= y1 -4.35e+43)
       (*
        y2
        (+
         (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
         (* t t_2)))
       (if (<= y1 -8.4e-262)
         (+
          (* t (* y2 t_2))
          (* t (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))))
         (if (<= y1 5.2e-206)
           (* j (* y0 (- (* y3 y5) (* x b))))
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 t_1))
             (* c (- (* y y3) (* t y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (a * y5) - (c * y4);
	double tmp;
	if (y1 <= -1.4e+214) {
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	} else if (y1 <= -4.35e+43) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (y1 <= -8.4e-262) {
		tmp = (t * (y2 * t_2)) + (t * ((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))));
	} else if (y1 <= 5.2e-206) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (a * y5) - (c * y4)
    if (y1 <= (-1.4d+214)) then
        tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))))
    else if (y1 <= (-4.35d+43)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
    else if (y1 <= (-8.4d-262)) then
        tmp = (t * (y2 * t_2)) + (t * ((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))))
    else if (y1 <= 5.2d-206) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (a * y5) - (c * y4);
	double tmp;
	if (y1 <= -1.4e+214) {
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	} else if (y1 <= -4.35e+43) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (y1 <= -8.4e-262) {
		tmp = (t * (y2 * t_2)) + (t * ((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))));
	} else if (y1 <= 5.2e-206) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = (a * y5) - (c * y4)
	tmp = 0
	if y1 <= -1.4e+214:
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))))
	elif y1 <= -4.35e+43:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
	elif y1 <= -8.4e-262:
		tmp = (t * (y2 * t_2)) + (t * ((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))))
	elif y1 <= 5.2e-206:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (y1 <= -1.4e+214)
		tmp = Float64(y1 * Float64(Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(y4 * t_1)) + Float64(i * Float64(Float64(x * j) - Float64(z * k)))));
	elseif (y1 <= -4.35e+43)
		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_2)));
	elseif (y1 <= -8.4e-262)
		tmp = Float64(Float64(t * Float64(y2 * t_2)) + Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5))))));
	elseif (y1 <= 5.2e-206)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_1)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (y1 <= -1.4e+214)
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	elseif (y1 <= -4.35e+43)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	elseif (y1 <= -8.4e-262)
		tmp = (t * (y2 * t_2)) + (t * ((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))));
	elseif (y1 <= 5.2e-206)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.4e+214], N[(y1 * N[(N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -4.35e+43], 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$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8.4e-262], N[(N[(t * N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t * 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]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e-206], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -1.3999999999999999e214

   1. Initial program 22.2%

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

   3. Taylor expanded in y1 around inf 83.3%

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

   if -1.3999999999999999e214 < y1 < -4.34999999999999977e43

   1. Initial program 16.0%

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

   3. Taylor expanded in y2 around inf 56.8%

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

   if -4.34999999999999977e43 < y1 < -8.3999999999999998e-262

   1. Initial program 27.9%

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

   3. Taylor expanded in t around inf 48.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 50.5%

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

   5. Taylor expanded in y2 around 0 50.5%

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

   if -8.3999999999999998e-262 < y1 < 5.2000000000000001e-206

   1. Initial program 18.7%

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

   3. Taylor expanded in j around inf 39.6%

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

   4. Taylor expanded in y0 around inf 52.1%

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

   if 5.2000000000000001e-206 < y1

   1. Initial program 30.5%

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

   3. Taylor expanded in y4 around inf 50.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -1.4 \cdot 10^{+214}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -4.35 \cdot 10^{+43}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -8.4 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-206}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;y1 \leq -2.8 \cdot 10^{+215}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + y4 \cdot t\_1\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{+43}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq -1.95 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot t\_2\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-206}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t\_1\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3))) (t_2 (- (* a y5) (* c y4))))
   (if (<= y1 -2.8e+215)
     (*
      y1
      (+ (+ (* a (- (* z y3) (* x y2))) (* y4 t_1)) (* i (- (* x j) (* z k)))))
     (if (<= y1 -3.8e+43)
       (*
        y2
        (+
         (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
         (* t t_2)))
       (if (<= y1 -1.95e-260)
         (*
          t
          (+
           (+ (* z (- (* c i) (* a b))) (* j (- (* b y4) (* i y5))))
           (* y2 t_2)))
         (if (<= y1 6e-206)
           (* j (* y0 (- (* y3 y5) (* x b))))
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 t_1))
             (* c (- (* y y3) (* t y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (a * y5) - (c * y4);
	double tmp;
	if (y1 <= -2.8e+215) {
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	} else if (y1 <= -3.8e+43) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (y1 <= -1.95e-260) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_2));
	} else if (y1 <= 6e-206) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (a * y5) - (c * y4)
    if (y1 <= (-2.8d+215)) then
        tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))))
    else if (y1 <= (-3.8d+43)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
    else if (y1 <= (-1.95d-260)) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_2))
    else if (y1 <= 6d-206) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (a * y5) - (c * y4);
	double tmp;
	if (y1 <= -2.8e+215) {
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	} else if (y1 <= -3.8e+43) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (y1 <= -1.95e-260) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_2));
	} else if (y1 <= 6e-206) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = (a * y5) - (c * y4)
	tmp = 0
	if y1 <= -2.8e+215:
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))))
	elif y1 <= -3.8e+43:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
	elif y1 <= -1.95e-260:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_2))
	elif y1 <= 6e-206:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (y1 <= -2.8e+215)
		tmp = Float64(y1 * Float64(Float64(Float64(a * Float64(Float64(z * y3) - Float64(x * y2))) + Float64(y4 * t_1)) + Float64(i * Float64(Float64(x * j) - Float64(z * k)))));
	elseif (y1 <= -3.8e+43)
		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_2)));
	elseif (y1 <= -1.95e-260)
		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_2)));
	elseif (y1 <= 6e-206)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_1)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (y1 <= -2.8e+215)
		tmp = y1 * (((a * ((z * y3) - (x * y2))) + (y4 * t_1)) + (i * ((x * j) - (z * k))));
	elseif (y1 <= -3.8e+43)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	elseif (y1 <= -1.95e-260)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * ((b * y4) - (i * y5)))) + (y2 * t_2));
	elseif (y1 <= 6e-206)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_1)) + (c * ((y * y3) - (t * y2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -2.8e+215], N[(y1 * N[(N[(N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -3.8e+43], 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$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.95e-260], 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$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 6e-206], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -2.8e215

   1. Initial program 22.2%

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

   3. Taylor expanded in y1 around inf 83.3%

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

   if -2.8e215 < y1 < -3.80000000000000008e43

   1. Initial program 16.0%

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

   3. Taylor expanded in y2 around inf 56.8%

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

   if -3.80000000000000008e43 < y1 < -1.94999999999999986e-260

   1. Initial program 27.9%

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

   3. Taylor expanded in t around inf 48.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 50.5%

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

   if -1.94999999999999986e-260 < y1 < 6.0000000000000004e-206

   1. Initial program 18.7%

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

   3. Taylor expanded in j around inf 39.6%

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

   4. Taylor expanded in y0 around inf 52.1%

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

   if 6.0000000000000004e-206 < y1

   1. Initial program 30.5%

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

   3. Taylor expanded in y4 around inf 50.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.8 \cdot 10^{+215}:\\ \;\;\;\;y1 \cdot \left(\left(a \cdot \left(z \cdot y3 - x \cdot y2\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y1 \leq -3.8 \cdot 10^{+43}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -1.95 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq 6 \cdot 10^{-206}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot y5 - y1 \cdot y4\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot t\_1 + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ t_4 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;y3 \leq -2.1 \cdot 10^{+234}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y3 \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(\left(t \cdot t\_4 + y3 \cdot t\_1\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -2.3 \cdot 10^{-278}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_2\right)\\ \mathbf{elif}\;y3 \leq 49000000000000:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t\_4\right) + y2 \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y0 y5) (* y1 y4)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3
         (*
          y3
          (+
           (* y (- (* c y4) (* a y5)))
           (+ (* j t_1) (* z (- (* a y1) (* c y0)))))))
        (t_4 (- (* b y4) (* i y5))))
   (if (<= y3 -2.1e+234)
     t_3
     (if (<= y3 -2.6e+104)
       (* j (+ (+ (* t t_4) (* y3 t_1)) (* x (- (* i y1) (* b y0)))))
       (if (<= y3 -2.3e-278)
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t t_2)))
         (if (<= y3 49000000000000.0)
           (* t (+ (+ (* z (- (* c i) (* a b))) (* j t_4)) (* y2 t_2)))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y5) - (y1 * y4);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (y3 <= -2.1e+234) {
		tmp = t_3;
	} else if (y3 <= -2.6e+104) {
		tmp = j * (((t * t_4) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	} else if (y3 <= -2.3e-278) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (y3 <= 49000000000000.0) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * t_2));
	} 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 = (y0 * y5) - (y1 * y4)
    t_2 = (a * y5) - (c * y4)
    t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
    t_4 = (b * y4) - (i * y5)
    if (y3 <= (-2.1d+234)) then
        tmp = t_3
    else if (y3 <= (-2.6d+104)) then
        tmp = j * (((t * t_4) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
    else if (y3 <= (-2.3d-278)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
    else if (y3 <= 49000000000000.0d0) then
        tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * t_2))
    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 = (y0 * y5) - (y1 * y4);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	double t_4 = (b * y4) - (i * y5);
	double tmp;
	if (y3 <= -2.1e+234) {
		tmp = t_3;
	} else if (y3 <= -2.6e+104) {
		tmp = j * (((t * t_4) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	} else if (y3 <= -2.3e-278) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	} else if (y3 <= 49000000000000.0) {
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * t_2));
	} 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 = (y0 * y5) - (y1 * y4)
	t_2 = (a * y5) - (c * y4)
	t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))))
	t_4 = (b * y4) - (i * y5)
	tmp = 0
	if y3 <= -2.1e+234:
		tmp = t_3
	elif y3 <= -2.6e+104:
		tmp = j * (((t * t_4) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))))
	elif y3 <= -2.3e-278:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2))
	elif y3 <= 49000000000000.0:
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * t_2))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * t_1) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0))))))
	t_4 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (y3 <= -2.1e+234)
		tmp = t_3;
	elseif (y3 <= -2.6e+104)
		tmp = Float64(j * Float64(Float64(Float64(t * t_4) + Float64(y3 * t_1)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y3 <= -2.3e-278)
		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_2)));
	elseif (y3 <= 49000000000000.0)
		tmp = Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_4)) + Float64(y2 * t_2)));
	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 = (y0 * y5) - (y1 * y4);
	t_2 = (a * y5) - (c * y4);
	t_3 = y3 * ((y * ((c * y4) - (a * y5))) + ((j * t_1) + (z * ((a * y1) - (c * y0)))));
	t_4 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (y3 <= -2.1e+234)
		tmp = t_3;
	elseif (y3 <= -2.6e+104)
		tmp = j * (((t * t_4) + (y3 * t_1)) + (x * ((i * y1) - (b * y0))));
	elseif (y3 <= -2.3e-278)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_2));
	elseif (y3 <= 49000000000000.0)
		tmp = t * (((z * ((c * i) - (a * b))) + (j * t_4)) + (y2 * t_2));
	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[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * t$95$1), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.1e+234], t$95$3, If[LessEqual[y3, -2.6e+104], N[(j * N[(N[(N[(t * t$95$4), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.3e-278], 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$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 49000000000000.0], N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -2.1e234 or 4.9e13 < y3

   1. Initial program 25.1%

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

   3. Taylor expanded in y3 around -inf 58.6%

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

   if -2.1e234 < y3 < -2.6e104

   1. Initial program 33.3%

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

   3. Taylor expanded in j around inf 69.8%

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

   if -2.6e104 < y3 < -2.30000000000000003e-278

   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 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 -2.30000000000000003e-278 < y3 < 4.9e13

   1. Initial program 24.2%

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

   3. Taylor expanded in t around inf 44.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 49.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - y2 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.1 \cdot 10^{+234}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \mathbf{elif}\;y3 \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -2.3 \cdot 10^{-278}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 49000000000000:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -245.0)
   (* b (* t (- (* j y4) (* z a))))
   (if (<= z -2.8e-52)
     (* a (- (* y5 (- (* t y2) (* y y3))) (* x (* y1 y2))))
     (if (<= z 1.55e-87)
       (*
        y4
        (+
         (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
         (* c (- (* y y3) (* t y2)))))
       (if (<= z 6.5e+95)
         (*
          y2
          (+
           (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (* t (* z (- (* c i) (* a 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 <= -245.0) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (z <= -2.8e-52) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (z <= 1.55e-87) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (z <= 6.5e+95) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t * (z * ((c * i) - (a * 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 <= (-245.0d0)) then
        tmp = b * (t * ((j * y4) - (z * a)))
    else if (z <= (-2.8d-52)) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
    else if (z <= 1.55d-87) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (z <= 6.5d+95) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else
        tmp = t * (z * ((c * i) - (a * 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 <= -245.0) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (z <= -2.8e-52) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (z <= 1.55e-87) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (z <= 6.5e+95) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else {
		tmp = t * (z * ((c * i) - (a * 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 <= -245.0:
		tmp = b * (t * ((j * y4) - (z * a)))
	elif z <= -2.8e-52:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
	elif z <= 1.55e-87:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif z <= 6.5e+95:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	else:
		tmp = t * (z * ((c * i) - (a * 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 <= -245.0)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (z <= -2.8e-52)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(x * Float64(y1 * y2))));
	elseif (z <= 1.55e-87)
		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 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (z <= 6.5e+95)
		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)))));
	else
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * 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 <= -245.0)
		tmp = b * (t * ((j * y4) - (z * a)));
	elseif (z <= -2.8e-52)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	elseif (z <= 1.55e-87)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (z <= 6.5e+95)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	else
		tmp = t * (z * ((c * i) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -245.0], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-52], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-87], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+95], 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], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -245

   1. Initial program 14.2%

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

   3. Taylor expanded in t around inf 37.9%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 50.6%

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

   if -245 < z < -2.79999999999999995e-52

   1. Initial program 27.9%

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

   3. Simplified 27.9%

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

   5. Taylor expanded in y2 around inf 55.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in a around -inf 81.8%

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

      1. associate-*r* 81.8%

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

      2. neg-mul-1 81.8%

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

   8. Simplified 81.8%

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

   if -2.79999999999999995e-52 < z < 1.54999999999999999e-87

   1. Initial program 32.3%

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

   3. Taylor expanded in y4 around inf 50.4%

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

   if 1.54999999999999999e-87 < z < 6.5e95

   1. Initial program 31.3%

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

   3. Taylor expanded in y2 around inf 50.5%

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

   if 6.5e95 < z

   1. Initial program 23.2%

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

   3. Taylor expanded in t around inf 37.3%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 50.2%

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

      1. mul-1-neg 50.2%

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

   6. Simplified 50.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot y3 - k \cdot y2\\ t_2 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(y5 \cdot t\_2 - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-197}:\\ \;\;\;\;y5 \cdot \left(a \cdot t\_2 + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot t\_1\right)\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot t\_1 + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j y3) (* k y2))) (t_2 (- (* t y2) (* y y3))))
   (if (<= a -9.5e-22)
     (* a (- (* y5 t_2) (* x (* y1 y2))))
     (if (<= a -1.15e-197)
       (* y5 (+ (* a t_2) (+ (* i (- (* y k) (* t j))) (* y0 t_1))))
       (if (<= a 3.4e-211)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))
         (if (<= a 9e-109)
           (* y0 (+ (* y5 t_1) (* c (* x y2))))
           (if (<= a 1.08e+58)
             (*
              t
              (+
               (* y5 (- (* b (/ (* j y4) y5)) (* i j)))
               (* y2 (- (* a y5) (* c y4)))))
             (* (* a b) (- (* x y) (* 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 t_1 = (j * y3) - (k * y2);
	double t_2 = (t * y2) - (y * y3);
	double tmp;
	if (a <= -9.5e-22) {
		tmp = a * ((y5 * t_2) - (x * (y1 * y2)));
	} else if (a <= -1.15e-197) {
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	} else if (a <= 3.4e-211) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 9e-109) {
		tmp = y0 * ((y5 * t_1) + (c * (x * y2)));
	} else if (a <= 1.08e+58) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * y3) - (k * y2)
    t_2 = (t * y2) - (y * y3)
    if (a <= (-9.5d-22)) then
        tmp = a * ((y5 * t_2) - (x * (y1 * y2)))
    else if (a <= (-1.15d-197)) then
        tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_1)))
    else if (a <= 3.4d-211) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (a <= 9d-109) then
        tmp = y0 * ((y5 * t_1) + (c * (x * y2)))
    else if (a <= 1.08d+58) then
        tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = (a * b) * ((x * y) - (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 t_1 = (j * y3) - (k * y2);
	double t_2 = (t * y2) - (y * y3);
	double tmp;
	if (a <= -9.5e-22) {
		tmp = a * ((y5 * t_2) - (x * (y1 * y2)));
	} else if (a <= -1.15e-197) {
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	} else if (a <= 3.4e-211) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 9e-109) {
		tmp = y0 * ((y5 * t_1) + (c * (x * y2)));
	} else if (a <= 1.08e+58) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	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 = (t * y2) - (y * y3)
	tmp = 0
	if a <= -9.5e-22:
		tmp = a * ((y5 * t_2) - (x * (y1 * y2)))
	elif a <= -1.15e-197:
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_1)))
	elif a <= 3.4e-211:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif a <= 9e-109:
		tmp = y0 * ((y5 * t_1) + (c * (x * y2)))
	elif a <= 1.08e+58:
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = (a * b) * ((x * y) - (z * t))
	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(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (a <= -9.5e-22)
		tmp = Float64(a * Float64(Float64(y5 * t_2) - Float64(x * Float64(y1 * y2))));
	elseif (a <= -1.15e-197)
		tmp = Float64(y5 * Float64(Float64(a * t_2) + Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(y0 * t_1))));
	elseif (a <= 3.4e-211)
		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 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (a <= 9e-109)
		tmp = Float64(y0 * Float64(Float64(y5 * t_1) + Float64(c * Float64(x * y2))));
	elseif (a <= 1.08e+58)
		tmp = Float64(t * Float64(Float64(y5 * Float64(Float64(b * Float64(Float64(j * y4) / y5)) - Float64(i * j))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - 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)
	t_1 = (j * y3) - (k * y2);
	t_2 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (a <= -9.5e-22)
		tmp = a * ((y5 * t_2) - (x * (y1 * y2)));
	elseif (a <= -1.15e-197)
		tmp = y5 * ((a * t_2) + ((i * ((y * k) - (t * j))) + (y0 * t_1)));
	elseif (a <= 3.4e-211)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (a <= 9e-109)
		tmp = y0 * ((y5 * t_1) + (c * (x * y2)));
	elseif (a <= 1.08e+58)
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = (a * b) * ((x * y) - (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_] := Block[{t$95$1 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e-22], N[(a * N[(N[(y5 * t$95$2), $MachinePrecision] - N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e-197], 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$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-211], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-109], N[(y0 * N[(N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e+58], N[(t * N[(N[(y5 * N[(N[(b * N[(N[(j * y4), $MachinePrecision] / y5), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -9.4999999999999994e-22

   1. Initial program 28.3%

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

   3. Simplified 28.3%

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

   5. Taylor expanded in y2 around inf 40.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in a around -inf 55.1%

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

      1. associate-*r* 55.1%

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

      2. neg-mul-1 55.1%

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

   8. Simplified 55.1%

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

   if -9.4999999999999994e-22 < a < -1.15e-197

   1. Initial program 25.5%

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

   3. Taylor expanded in y5 around -inf 48.1%

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

   if -1.15e-197 < a < 3.4000000000000001e-211

   1. Initial program 39.5%

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

   3. Taylor expanded in y4 around inf 51.5%

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

   if 3.4000000000000001e-211 < a < 9.0000000000000002e-109

   1. Initial program 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 56.3%

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

   if 9.0000000000000002e-109 < a < 1.0799999999999999e58

   1. Initial program 24.1%

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

   3. Taylor expanded in t around inf 41.7%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 55.5%

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

   5. Taylor expanded in z around 0 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in y5 around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. associate-/l* 55.8%

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

      5. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   if 1.0799999999999999e58 < a

   1. Initial program 20.1%

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

   3. Simplified 20.1%

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

   5. Taylor expanded in a around inf 56.5%

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

   6. Taylor expanded in b around inf 54.0%

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

      1. associate-*r* 54.0%

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

      2. +-commutative 54.0%

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

      3. mul-1-neg 54.0%

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

      4. unsub-neg 54.0%

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

   8. Simplified 54.0%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot \left(x \cdot y - t \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-197}:\\ \;\;\;\;y5 \cdot \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(i \cdot \left(y \cdot k - t \cdot j\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-211}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))))
   (if (<= a -1.05e-14)
     (* a (- (* y5 (- (* t y2) (* y y3))) (* x (* y1 y2))))
     (if (<= a -2.15e-120)
       t_1
       (if (<= a 6.5e-239)
         (* c (* y (- (* y3 y4) (* x i))))
         (if (<= a 1.3e-109)
           t_1
           (if (<= a 1.45e+57)
             (*
              t
              (+
               (* y5 (- (* b (/ (* j y4) y5)) (* i j)))
               (* y2 (- (* a y5) (* c y4)))))
             (* (* a b) (- (* x y) (* 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 t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	double tmp;
	if (a <= -1.05e-14) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= -2.15e-120) {
		tmp = t_1;
	} else if (a <= 6.5e-239) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 1.3e-109) {
		tmp = t_1;
	} else if (a <= 1.45e+57) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (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) :: t_1
    real(8) :: tmp
    t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    if (a <= (-1.05d-14)) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
    else if (a <= (-2.15d-120)) then
        tmp = t_1
    else if (a <= 6.5d-239) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (a <= 1.3d-109) then
        tmp = t_1
    else if (a <= 1.45d+57) then
        tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = (a * b) * ((x * y) - (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 t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	double tmp;
	if (a <= -1.05e-14) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= -2.15e-120) {
		tmp = t_1;
	} else if (a <= 6.5e-239) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 1.3e-109) {
		tmp = t_1;
	} else if (a <= 1.45e+57) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	tmp = 0
	if a <= -1.05e-14:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
	elif a <= -2.15e-120:
		tmp = t_1
	elif a <= 6.5e-239:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif a <= 1.3e-109:
		tmp = t_1
	elif a <= 1.45e+57:
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = (a * b) * ((x * y) - (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))))
	tmp = 0.0
	if (a <= -1.05e-14)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(x * Float64(y1 * y2))));
	elseif (a <= -2.15e-120)
		tmp = t_1;
	elseif (a <= 6.5e-239)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (a <= 1.3e-109)
		tmp = t_1;
	elseif (a <= 1.45e+57)
		tmp = Float64(t * Float64(Float64(y5 * Float64(Float64(b * Float64(Float64(j * y4) / y5)) - Float64(i * j))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - 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)
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	tmp = 0.0;
	if (a <= -1.05e-14)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	elseif (a <= -2.15e-120)
		tmp = t_1;
	elseif (a <= 6.5e-239)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (a <= 1.3e-109)
		tmp = t_1;
	elseif (a <= 1.45e+57)
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = (a * b) * ((x * y) - (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_] := Block[{t$95$1 = N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-14], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.15e-120], t$95$1, If[LessEqual[a, 6.5e-239], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-109], t$95$1, If[LessEqual[a, 1.45e+57], N[(t * N[(N[(y5 * N[(N[(b * N[(N[(j * y4), $MachinePrecision] / y5), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.0499999999999999e-14

   1. Initial program 29.9%

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

   3. Simplified 29.9%

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

   5. Taylor expanded in y2 around inf 41.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in a around -inf 54.5%

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

      1. associate-*r* 54.5%

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

      2. neg-mul-1 54.5%

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

   8. Simplified 54.5%

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

   if -1.0499999999999999e-14 < a < -2.14999999999999991e-120 or 6.5000000000000003e-239 < a < 1.2999999999999999e-109

   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 y2 around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 52.1%

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

   if -2.14999999999999991e-120 < a < 6.5000000000000003e-239

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   5. Taylor expanded in c around inf 47.2%

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

   6. Taylor expanded in y around -inf 37.2%

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

      1. associate-*r* 37.2%

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

      2. mul-1-neg 37.2%

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

   8. Simplified 37.2%

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

   if 1.2999999999999999e-109 < a < 1.4500000000000001e57

   1. Initial program 24.1%

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

   3. Taylor expanded in t around inf 41.7%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 55.5%

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

   5. Taylor expanded in z around 0 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in y5 around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. associate-/l* 55.8%

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

      5. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   if 1.4500000000000001e57 < a

   1. Initial program 20.1%

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

   3. Simplified 20.1%

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

   5. Taylor expanded in a around inf 56.5%

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

   6. Taylor expanded in b around inf 54.0%

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

      1. associate-*r* 54.0%

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

      2. +-commutative 54.0%

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

      3. mul-1-neg 54.0%

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

      4. unsub-neg 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-120}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-240}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))))
   (if (<= a -7.5e-15)
     (* a (- (* y5 (- (* t y2) (* y y3))) (* x (* y1 y2))))
     (if (<= a -1.9e-120)
       t_1
       (if (<= a 4e-240)
         (* c (* y (- (* y3 y4) (* x i))))
         (if (<= a 8.5e-110)
           t_1
           (if (<= a 1.22e+24)
             (* t (+ (* j (- (* b y4) (* i y5))) (* y2 (- (* a y5) (* c y4)))))
             (* (* a b) (- (* x y) (* 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 t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	double tmp;
	if (a <= -7.5e-15) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= -1.9e-120) {
		tmp = t_1;
	} else if (a <= 4e-240) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 8.5e-110) {
		tmp = t_1;
	} else if (a <= 1.22e+24) {
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (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) :: t_1
    real(8) :: tmp
    t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    if (a <= (-7.5d-15)) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
    else if (a <= (-1.9d-120)) then
        tmp = t_1
    else if (a <= 4d-240) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (a <= 8.5d-110) then
        tmp = t_1
    else if (a <= 1.22d+24) then
        tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = (a * b) * ((x * y) - (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 t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	double tmp;
	if (a <= -7.5e-15) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= -1.9e-120) {
		tmp = t_1;
	} else if (a <= 4e-240) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 8.5e-110) {
		tmp = t_1;
	} else if (a <= 1.22e+24) {
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	tmp = 0
	if a <= -7.5e-15:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
	elif a <= -1.9e-120:
		tmp = t_1
	elif a <= 4e-240:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif a <= 8.5e-110:
		tmp = t_1
	elif a <= 1.22e+24:
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = (a * b) * ((x * y) - (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))))
	tmp = 0.0
	if (a <= -7.5e-15)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(x * Float64(y1 * y2))));
	elseif (a <= -1.9e-120)
		tmp = t_1;
	elseif (a <= 4e-240)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (a <= 8.5e-110)
		tmp = t_1;
	elseif (a <= 1.22e+24)
		tmp = Float64(t * Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - 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)
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	tmp = 0.0;
	if (a <= -7.5e-15)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	elseif (a <= -1.9e-120)
		tmp = t_1;
	elseif (a <= 4e-240)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (a <= 8.5e-110)
		tmp = t_1;
	elseif (a <= 1.22e+24)
		tmp = t * ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = (a * b) * ((x * y) - (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_] := Block[{t$95$1 = N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e-15], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-120], t$95$1, If[LessEqual[a, 4e-240], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-110], t$95$1, If[LessEqual[a, 1.22e+24], N[(t * N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.4999999999999996e-15

   1. Initial program 29.9%

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

   3. Simplified 29.9%

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

   5. Taylor expanded in y2 around inf 41.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in a around -inf 54.5%

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

      1. associate-*r* 54.5%

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

      2. neg-mul-1 54.5%

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

   8. Simplified 54.5%

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

   if -7.4999999999999996e-15 < a < -1.8999999999999999e-120 or 3.9999999999999999e-240 < a < 8.50000000000000029e-110

   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 y2 around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 52.1%

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

   if -1.8999999999999999e-120 < a < 3.9999999999999999e-240

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   5. Taylor expanded in c around inf 47.2%

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

   6. Taylor expanded in y around -inf 37.2%

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

      1. associate-*r* 37.2%

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

      2. mul-1-neg 37.2%

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

   8. Simplified 37.2%

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

   if 8.50000000000000029e-110 < a < 1.21999999999999996e24

   1. Initial program 23.9%

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

   3. Taylor expanded in t around inf 40.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 56.4%

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

   5. Taylor expanded in z around 0 52.9%

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

      1. *-commutative 52.9%

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

      2. *-commutative 52.9%

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

   7. Simplified 52.9%

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

   if 1.21999999999999996e24 < a

   1. Initial program 20.4%

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

   3. Simplified 20.4%

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

   5. Taylor expanded in a around inf 56.1%

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

   6. Taylor expanded in b around inf 53.9%

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

      1. associate-*r* 53.9%

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

      2. +-commutative 53.9%

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

      3. mul-1-neg 53.9%

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

      4. unsub-neg 53.9%

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

   8. Simplified 53.9%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-120}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-240}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-110}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-129}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-87}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (+
           (+ (* t (- (* b y4) (* i y5))) (* y3 (- (* y0 y5) (* y1 y4))))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= j -6.5e+70)
     t_1
     (if (<= j -4.1e-129)
       (* a (- (* y5 (- (* t y2) (* y y3))) (* x (* y1 y2))))
       (if (<= j 2e-87)
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t 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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (j <= -6.5e+70) {
		tmp = t_1;
	} else if (j <= -4.1e-129) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (j <= 2e-87) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * 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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
    if (j <= (-6.5d+70)) then
        tmp = t_1
    else if (j <= (-4.1d-129)) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
    else if (j <= 2d-87) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * 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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (j <= -6.5e+70) {
		tmp = t_1;
	} else if (j <= -4.1e-129) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (j <= 2e-87) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * 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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if j <= -6.5e+70:
		tmp = t_1
	elif j <= -4.1e-129:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
	elif j <= 2e-87:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * 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(j * Float64(Float64(Float64(t * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (j <= -6.5e+70)
		tmp = t_1;
	elseif (j <= -4.1e-129)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(x * Float64(y1 * y2))));
	elseif (j <= 2e-87)
		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 * Float64(Float64(y * y3) - Float64(t * 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 = j * (((t * ((b * y4) - (i * y5))) + (y3 * ((y0 * y5) - (y1 * y4)))) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (j <= -6.5e+70)
		tmp = t_1;
	elseif (j <= -4.1e-129)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	elseif (j <= 2e-87)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * 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[(j * N[(N[(N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e+70], t$95$1, If[LessEqual[j, -4.1e-129], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e-87], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.49999999999999978e70 or 2.00000000000000004e-87 < j

   1. Initial program 21.5%

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

   3. Taylor expanded in j around inf 54.6%

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

   if -6.49999999999999978e70 < j < -4.1e-129

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in y2 around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in a around -inf 50.8%

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

      1. associate-*r* 50.8%

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

      2. neg-mul-1 50.8%

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

   8. Simplified 50.8%

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

   if -4.1e-129 < j < 2.00000000000000004e-87

   1. Initial program 32.6%

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

   3. Taylor expanded in y4 around inf 46.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-129}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-87}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot \left(b \cdot y4 - i \cdot y5\right) + y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-214}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + b \cdot \left(t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -6.2e-35)
   (* a (- (* y5 (- (* t y2) (* y y3))) (* x (* y1 y2))))
   (if (<= a 5.2e-214)
     (*
      y4
      (+
       (+ (* y1 (- (* k y2) (* j y3))) (* b (* t j)))
       (* c (- (* y y3) (* t y2)))))
     (if (<= a 5e-109)
       (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))
       (if (<= a 4.4e+57)
         (*
          t
          (+
           (* y5 (- (* b (/ (* j y4) y5)) (* i j)))
           (* y2 (- (* a y5) (* c y4)))))
         (* (* a b) (- (* x y) (* 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 (a <= -6.2e-35) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= 5.2e-214) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) + (b * (t * j))) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 5e-109) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 4.4e+57) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (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 (a <= (-6.2d-35)) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
    else if (a <= 5.2d-214) then
        tmp = y4 * (((y1 * ((k * y2) - (j * y3))) + (b * (t * j))) + (c * ((y * y3) - (t * y2))))
    else if (a <= 5d-109) then
        tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    else if (a <= 4.4d+57) then
        tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))))
    else
        tmp = (a * b) * ((x * y) - (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 (a <= -6.2e-35) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= 5.2e-214) {
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) + (b * (t * j))) + (c * ((y * y3) - (t * y2))));
	} else if (a <= 5e-109) {
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	} else if (a <= 4.4e+57) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	} else {
		tmp = (a * b) * ((x * y) - (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 a <= -6.2e-35:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
	elif a <= 5.2e-214:
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) + (b * (t * j))) + (c * ((y * y3) - (t * y2))))
	elif a <= 5e-109:
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	elif a <= 4.4e+57:
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))))
	else:
		tmp = (a * b) * ((x * y) - (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 (a <= -6.2e-35)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(x * Float64(y1 * y2))));
	elseif (a <= 5.2e-214)
		tmp = Float64(y4 * Float64(Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) + Float64(b * Float64(t * j))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (a <= 5e-109)
		tmp = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))));
	elseif (a <= 4.4e+57)
		tmp = Float64(t * Float64(Float64(y5 * Float64(Float64(b * Float64(Float64(j * y4) / y5)) - Float64(i * j))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4)))));
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - 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 (a <= -6.2e-35)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	elseif (a <= 5.2e-214)
		tmp = y4 * (((y1 * ((k * y2) - (j * y3))) + (b * (t * j))) + (c * ((y * y3) - (t * y2))));
	elseif (a <= 5e-109)
		tmp = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	elseif (a <= 4.4e+57)
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * ((a * y5) - (c * y4))));
	else
		tmp = (a * b) * ((x * y) - (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[a, -6.2e-35], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-214], N[(y4 * N[(N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-109], N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+57], N[(t * N[(N[(y5 * N[(N[(b * N[(N[(j * y4), $MachinePrecision] / y5), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.20000000000000024e-35

   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 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 y2 around inf 42.1%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in a around -inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

   8. Simplified 52.4%

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

   if -6.20000000000000024e-35 < a < 5.2e-214

   1. Initial program 32.4%

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

   3. Taylor expanded in t around inf 38.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y4 around inf 41.0%

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

   if 5.2e-214 < a < 5.0000000000000002e-109

   1. Initial program 16.9%

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

   3. Simplified 16.9%

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

   5. Taylor expanded in y2 around inf 36.7%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 56.3%

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

   if 5.0000000000000002e-109 < a < 4.4000000000000001e57

   1. Initial program 24.1%

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

   3. Taylor expanded in t around inf 41.7%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 55.5%

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

   5. Taylor expanded in z around 0 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in y5 around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. associate-/l* 55.8%

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

      5. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   if 4.4000000000000001e57 < a

   1. Initial program 20.1%

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

   3. Simplified 20.1%

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

   5. Taylor expanded in a around inf 56.5%

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

   6. Taylor expanded in b around inf 54.0%

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

      1. associate-*r* 54.0%

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

      2. +-commutative 54.0%

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

      3. mul-1-neg 54.0%

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

      4. unsub-neg 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-214}:\\ \;\;\;\;y4 \cdot \left(\left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) + b \cdot \left(t \cdot j\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y5 - c \cdot y4\\ \mathbf{if}\;y3 \leq -2.9 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -1.5 \cdot 10^{-267}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot t\_1\right)\\ \mathbf{elif}\;y3 \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot t\_1\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4))))
   (if (<= y3 -2.9e+104)
     (* j (* y4 (- (* t b) (* y1 y3))))
     (if (<= y3 -1.5e-267)
       (*
        y2
        (+
         (+ (* k (- (* y1 y4) (* y0 y5))) (* x (- (* c y0) (* a y1))))
         (* t t_1)))
       (if (<= y3 6.2e-77)
         (* t (+ (* y5 (- (* b (/ (* j y4) y5)) (* i j))) (* y2 t_1)))
         (if (<= y3 1.4e+119)
           (* b (* t (- (* j y4) (* z a))))
           (* c (* y3 (- (* y y4) (* z 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 = (a * y5) - (c * y4);
	double tmp;
	if (y3 <= -2.9e+104) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y3 <= -1.5e-267) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_1));
	} else if (y3 <= 6.2e-77) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * t_1));
	} else if (y3 <= 1.4e+119) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = c * (y3 * ((y * y4) - (z * 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 = (a * y5) - (c * y4)
    if (y3 <= (-2.9d+104)) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else if (y3 <= (-1.5d-267)) then
        tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_1))
    else if (y3 <= 6.2d-77) then
        tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * t_1))
    else if (y3 <= 1.4d+119) then
        tmp = b * (t * ((j * y4) - (z * a)))
    else
        tmp = c * (y3 * ((y * y4) - (z * 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 = (a * y5) - (c * y4);
	double tmp;
	if (y3 <= -2.9e+104) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else if (y3 <= -1.5e-267) {
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_1));
	} else if (y3 <= 6.2e-77) {
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * t_1));
	} else if (y3 <= 1.4e+119) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y5) - (c * y4)
	tmp = 0
	if y3 <= -2.9e+104:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	elif y3 <= -1.5e-267:
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_1))
	elif y3 <= 6.2e-77:
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * t_1))
	elif y3 <= 1.4e+119:
		tmp = b * (t * ((j * y4) - (z * a)))
	else:
		tmp = c * (y3 * ((y * y4) - (z * 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(a * y5) - Float64(c * y4))
	tmp = 0.0
	if (y3 <= -2.9e+104)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	elseif (y3 <= -1.5e-267)
		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_1)));
	elseif (y3 <= 6.2e-77)
		tmp = Float64(t * Float64(Float64(y5 * Float64(Float64(b * Float64(Float64(j * y4) / y5)) - Float64(i * j))) + Float64(y2 * t_1)));
	elseif (y3 <= 1.4e+119)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	else
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * 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 = (a * y5) - (c * y4);
	tmp = 0.0;
	if (y3 <= -2.9e+104)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	elseif (y3 <= -1.5e-267)
		tmp = y2 * (((k * ((y1 * y4) - (y0 * y5))) + (x * ((c * y0) - (a * y1)))) + (t * t_1));
	elseif (y3 <= 6.2e-77)
		tmp = t * ((y5 * ((b * ((j * y4) / y5)) - (i * j))) + (y2 * t_1));
	elseif (y3 <= 1.4e+119)
		tmp = b * (t * ((j * y4) - (z * a)));
	else
		tmp = c * (y3 * ((y * y4) - (z * 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[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -2.9e+104], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.5e-267], 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$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.2e-77], N[(t * N[(N[(y5 * N[(N[(b * N[(N[(j * y4), $MachinePrecision] / y5), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.4e+119], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -2.8999999999999998e104

   1. Initial program 28.1%

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

   3. Taylor expanded in j around inf 56.5%

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

   4. Taylor expanded in y4 around inf 52.9%

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

   if -2.8999999999999998e104 < y3 < -1.5e-267

   1. Initial program 24.3%

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

   3. Taylor expanded in y2 around inf 47.0%

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

   if -1.5e-267 < y3 < 6.20000000000000016e-77

   1. Initial program 25.0%

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

   3. Taylor expanded in t around inf 50.3%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 49.5%

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

   5. Taylor expanded in z around 0 46.3%

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

      1. *-commutative 46.3%

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

      2. *-commutative 46.3%

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

   7. Simplified 46.3%

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

   8. Taylor expanded in y5 around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. associate-/l* 47.9%

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

      5. *-commutative 47.9%

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

   10. Simplified 47.9%

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

   if 6.20000000000000016e-77 < y3 < 1.40000000000000007e119

   1. Initial program 25.8%

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

   3. Taylor expanded in t around inf 34.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 49.3%

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

   if 1.40000000000000007e119 < y3

   1. Initial program 26.5%

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

   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 c around inf 50.2%

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

   6. Taylor expanded in y3 around -inf 58.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 58.1%

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

      2. mul-1-neg 58.1%

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

   8. Simplified 58.1%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y3 \cdot \left(y0 \cdot z - y \cdot y4\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -2.9 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -1.5 \cdot 10^{-267}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;t \cdot \left(y5 \cdot \left(b \cdot \frac{j \cdot y4}{y5} - i \cdot j\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 3.95 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 780000:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (+ (* y5 (- (* j y3) (* k y2))) (* c (* x y2))))))
   (if (<= a -6e-15)
     (* a (- (* y5 (- (* t y2) (* y y3))) (* x (* y1 y2))))
     (if (<= a -1.35e-120)
       t_1
       (if (<= a 1.1e-239)
         (* c (* y (- (* y3 y4) (* x i))))
         (if (<= a 3.95e-109)
           t_1
           (if (<= a 780000.0)
             (* j (* y4 (- (* t b) (* y1 y3))))
             (* (* a b) (- (* x y) (* 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 t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	double tmp;
	if (a <= -6e-15) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= -1.35e-120) {
		tmp = t_1;
	} else if (a <= 1.1e-239) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 3.95e-109) {
		tmp = t_1;
	} else if (a <= 780000.0) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = (a * b) * ((x * y) - (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) :: t_1
    real(8) :: tmp
    t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
    if (a <= (-6d-15)) then
        tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
    else if (a <= (-1.35d-120)) then
        tmp = t_1
    else if (a <= 1.1d-239) then
        tmp = c * (y * ((y3 * y4) - (x * i)))
    else if (a <= 3.95d-109) then
        tmp = t_1
    else if (a <= 780000.0d0) then
        tmp = j * (y4 * ((t * b) - (y1 * y3)))
    else
        tmp = (a * b) * ((x * y) - (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 t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	double tmp;
	if (a <= -6e-15) {
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	} else if (a <= -1.35e-120) {
		tmp = t_1;
	} else if (a <= 1.1e-239) {
		tmp = c * (y * ((y3 * y4) - (x * i)));
	} else if (a <= 3.95e-109) {
		tmp = t_1;
	} else if (a <= 780000.0) {
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	} else {
		tmp = (a * b) * ((x * y) - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)))
	tmp = 0
	if a <= -6e-15:
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)))
	elif a <= -1.35e-120:
		tmp = t_1
	elif a <= 1.1e-239:
		tmp = c * (y * ((y3 * y4) - (x * i)))
	elif a <= 3.95e-109:
		tmp = t_1
	elif a <= 780000.0:
		tmp = j * (y4 * ((t * b) - (y1 * y3)))
	else:
		tmp = (a * b) * ((x * y) - (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * Float64(x * y2))))
	tmp = 0.0
	if (a <= -6e-15)
		tmp = Float64(a * Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(x * Float64(y1 * y2))));
	elseif (a <= -1.35e-120)
		tmp = t_1;
	elseif (a <= 1.1e-239)
		tmp = Float64(c * Float64(y * Float64(Float64(y3 * y4) - Float64(x * i))));
	elseif (a <= 3.95e-109)
		tmp = t_1;
	elseif (a <= 780000.0)
		tmp = Float64(j * Float64(y4 * Float64(Float64(t * b) - Float64(y1 * y3))));
	else
		tmp = Float64(Float64(a * b) * Float64(Float64(x * y) - 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)
	t_1 = y0 * ((y5 * ((j * y3) - (k * y2))) + (c * (x * y2)));
	tmp = 0.0;
	if (a <= -6e-15)
		tmp = a * ((y5 * ((t * y2) - (y * y3))) - (x * (y1 * y2)));
	elseif (a <= -1.35e-120)
		tmp = t_1;
	elseif (a <= 1.1e-239)
		tmp = c * (y * ((y3 * y4) - (x * i)));
	elseif (a <= 3.95e-109)
		tmp = t_1;
	elseif (a <= 780000.0)
		tmp = j * (y4 * ((t * b) - (y1 * y3)));
	else
		tmp = (a * b) * ((x * y) - (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_] := Block[{t$95$1 = N[(y0 * N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e-15], N[(a * N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.35e-120], t$95$1, If[LessEqual[a, 1.1e-239], N[(c * N[(y * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.95e-109], t$95$1, If[LessEqual[a, 780000.0], N[(j * N[(y4 * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6e-15

   1. Initial program 29.9%

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

   3. Simplified 29.9%

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

   5. Taylor expanded in y2 around inf 41.2%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in a around -inf 54.5%

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

      1. associate-*r* 54.5%

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

      2. neg-mul-1 54.5%

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

   8. Simplified 54.5%

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

   if -6e-15 < a < -1.3499999999999999e-120 or 1.09999999999999991e-239 < a < 3.9499999999999999e-109

   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 y2 around inf 44.8%

      \[\leadsto \color{blue}{x \cdot \left(y2 \cdot \left(-1 \cdot \left(a \cdot y1\right) + c \cdot y0\right)\right)} - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) \]

   6. Taylor expanded in y0 around inf 52.1%

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

   if -1.3499999999999999e-120 < a < 1.09999999999999991e-239

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   5. Taylor expanded in c around inf 47.2%

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

   6. Taylor expanded in y around -inf 37.2%

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

      1. associate-*r* 37.2%

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

      2. mul-1-neg 37.2%

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

   8. Simplified 37.2%

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

   if 3.9499999999999999e-109 < a < 7.8e5

   1. Initial program 27.2%

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

   3. Taylor expanded in j around inf 59.5%

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

   4. Taylor expanded in y4 around inf 51.1%

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

   if 7.8e5 < a

   1. Initial program 19.4%

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

   3. Simplified 19.4%

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

   5. Taylor expanded in a around inf 53.4%

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

   6. Taylor expanded in b around inf 52.9%

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

      1. associate-*r* 52.9%

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

      2. +-commutative 52.9%

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

      3. mul-1-neg 52.9%

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

      4. unsub-neg 52.9%

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

   8. Simplified 52.9%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-120}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4 - x \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 3.95 \cdot 10^{-109}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;a \leq 780000:\\ \;\;\;\;j \cdot \left(y4 \cdot \left(t \cdot b - y1 \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(x \cdot y - z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3.1 \cdot 10^{+178}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{+17}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot \left(y4 - \frac{x \cdot y0}{t}\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.2 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.1 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3.1e+178)
   (* j (* x (- (* i y1) (* b y0))))
   (if (<= y1 -2.25e+17)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= y1 -1.5e-101)
       (* b (* j (* t (- y4 (/ (* x y0) t)))))
       (if (<= y1 7.2e-299)
         (* t (* z (- (* c i) (* a b))))
         (if (<= y1 4.1e-169)
           (* j (* y0 (- (* y3 y5) (* x b))))
           (* y1 (* y4 (- (* k y2) (* j y3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.1e+178) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -2.25e+17) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= -1.5e-101) {
		tmp = b * (j * (t * (y4 - ((x * y0) / t))));
	} else if (y1 <= 7.2e-299) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y1 <= 4.1e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-3.1d+178)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y1 <= (-2.25d+17)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (y1 <= (-1.5d-101)) then
        tmp = b * (j * (t * (y4 - ((x * y0) / t))))
    else if (y1 <= 7.2d-299) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y1 <= 4.1d-169) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.1e+178) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -2.25e+17) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= -1.5e-101) {
		tmp = b * (j * (t * (y4 - ((x * y0) / t))));
	} else if (y1 <= 7.2e-299) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y1 <= 4.1e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -3.1e+178:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y1 <= -2.25e+17:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif y1 <= -1.5e-101:
		tmp = b * (j * (t * (y4 - ((x * y0) / t))))
	elif y1 <= 7.2e-299:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y1 <= 4.1e-169:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -3.1e+178)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y1 <= -2.25e+17)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y1 <= -1.5e-101)
		tmp = Float64(b * Float64(j * Float64(t * Float64(y4 - Float64(Float64(x * y0) / t)))));
	elseif (y1 <= 7.2e-299)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y1 <= 4.1e-169)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -3.1e+178)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y1 <= -2.25e+17)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (y1 <= -1.5e-101)
		tmp = b * (j * (t * (y4 - ((x * y0) / t))));
	elseif (y1 <= 7.2e-299)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y1 <= 4.1e-169)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -3.1e+178], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.25e+17], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.5e-101], N[(b * N[(j * N[(t * N[(y4 - N[(N[(x * y0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 7.2e-299], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.1e-169], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y1 < -3.09999999999999991e178

   1. Initial program 23.7%

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

   3. Taylor expanded in j around inf 44.1%

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

   4. Taylor expanded in x around inf 57.3%

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

   if -3.09999999999999991e178 < y1 < -2.25e17

   1. Initial program 14.8%

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

   3. Taylor expanded in y2 around inf 44.8%

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

   4. Taylor expanded in k around inf 45.2%

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

   if -2.25e17 < y1 < -1.5000000000000002e-101

   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 j around inf 50.4%

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

   4. Taylor expanded in b around inf 37.4%

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

   5. Taylor expanded in t around inf 45.4%

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

      1. mul-1-neg 45.4%

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

      2. unsub-neg 45.4%

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

      3. *-commutative 45.4%

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

   7. Simplified 45.4%

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

   if -1.5000000000000002e-101 < y1 < 7.2e-299

   1. Initial program 25.6%

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

   3. Taylor expanded in t around inf 48.3%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 47.1%

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

      1. mul-1-neg 47.1%

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

   6. Simplified 47.1%

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

   if 7.2e-299 < y1 < 4.0999999999999998e-169

   1. Initial program 14.9%

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

   3. Taylor expanded in j around inf 43.8%

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

   4. Taylor expanded in y0 around inf 57.8%

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

   if 4.0999999999999998e-169 < y1

   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 t around inf 35.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.1 \cdot 10^{+178}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2.25 \cdot 10^{+17}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -1.5 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot \left(y4 - \frac{x \cdot y0}{t}\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 7.2 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.1 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -6.5 \cdot 10^{+168}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{-256}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -6.5e+168)
   (* j (* x (- (* i y1) (* b y0))))
   (if (<= y1 -2.9e+62)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= y1 -2.2e-256)
       (* b (* t (- (* j y4) (* z a))))
       (if (<= y1 4.7e-169)
         (* j (* y0 (- (* y3 y5) (* x b))))
         (* y1 (* y4 (- (* k y2) (* j y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.5e+168) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -2.9e+62) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= -2.2e-256) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y1 <= 4.7e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-6.5d+168)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y1 <= (-2.9d+62)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (y1 <= (-2.2d-256)) then
        tmp = b * (t * ((j * y4) - (z * a)))
    else if (y1 <= 4.7d-169) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -6.5e+168) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -2.9e+62) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= -2.2e-256) {
		tmp = b * (t * ((j * y4) - (z * a)));
	} else if (y1 <= 4.7e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -6.5e+168:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y1 <= -2.9e+62:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif y1 <= -2.2e-256:
		tmp = b * (t * ((j * y4) - (z * a)))
	elif y1 <= 4.7e-169:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -6.5e+168)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y1 <= -2.9e+62)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y1 <= -2.2e-256)
		tmp = Float64(b * Float64(t * Float64(Float64(j * y4) - Float64(z * a))));
	elseif (y1 <= 4.7e-169)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -6.5e+168)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y1 <= -2.9e+62)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (y1 <= -2.2e-256)
		tmp = b * (t * ((j * y4) - (z * a)));
	elseif (y1 <= 4.7e-169)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -6.5e+168], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.9e+62], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.2e-256], N[(b * N[(t * N[(N[(j * y4), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.7e-169], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -6.49999999999999999e168

   1. Initial program 23.7%

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

   3. Taylor expanded in j around inf 44.1%

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

   4. Taylor expanded in x around inf 57.3%

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

   if -6.49999999999999999e168 < y1 < -2.89999999999999984e62

   1. Initial program 13.3%

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

   3. Taylor expanded in y2 around inf 53.7%

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

   4. Taylor expanded in k around inf 60.9%

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

   if -2.89999999999999984e62 < y1 < -2.2000000000000001e-256

   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 t around inf 45.7%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 39.8%

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

   if -2.2000000000000001e-256 < y1 < 4.6999999999999999e-169

   1. Initial program 19.9%

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

   3. Taylor expanded in j around inf 37.3%

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

   4. Taylor expanded in y0 around inf 49.8%

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

   if 4.6999999999999999e-169 < y1

   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 t around inf 35.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6.5 \cdot 10^{+168}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{-256}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4 - z \cdot a\right)\right)\\ \mathbf{elif}\;y1 \leq 4.7 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -3.2 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2 \cdot 10^{+55}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 2.45 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -3.2e+173)
   (* j (* x (- (* i y1) (* b y0))))
   (if (<= y1 -2e+55)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= y1 3.2e-299)
       (* t (* z (- (* c i) (* a b))))
       (if (<= y1 2.45e-169)
         (* j (* y0 (- (* y3 y5) (* x b))))
         (* y1 (* y4 (- (* k y2) (* j y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.2e+173) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -2e+55) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= 3.2e-299) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y1 <= 2.45e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-3.2d+173)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y1 <= (-2d+55)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (y1 <= 3.2d-299) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y1 <= 2.45d-169) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -3.2e+173) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -2e+55) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= 3.2e-299) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y1 <= 2.45e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -3.2e+173:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y1 <= -2e+55:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif y1 <= 3.2e-299:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y1 <= 2.45e-169:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -3.2e+173)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y1 <= -2e+55)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y1 <= 3.2e-299)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y1 <= 2.45e-169)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -3.2e+173)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y1 <= -2e+55)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (y1 <= 3.2e-299)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y1 <= 2.45e-169)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -3.2e+173], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2e+55], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.2e-299], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.45e-169], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -3.2000000000000003e173

   1. Initial program 23.7%

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

   3. Taylor expanded in j around inf 44.1%

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

   4. Taylor expanded in x around inf 57.3%

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

   if -3.2000000000000003e173 < y1 < -2.00000000000000002e55

   1. Initial program 11.1%

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

   3. Taylor expanded in y2 around inf 50.3%

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

   4. Taylor expanded in k around inf 56.3%

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

   if -2.00000000000000002e55 < y1 < 3.20000000000000008e-299

   1. Initial program 26.1%

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

   3. Taylor expanded in t around inf 44.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in z around inf 37.5%

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

      1. mul-1-neg 37.5%

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

   6. Simplified 37.5%

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

   if 3.20000000000000008e-299 < y1 < 2.45e-169

   1. Initial program 14.9%

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

   3. Taylor expanded in j around inf 43.8%

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

   4. Taylor expanded in y0 around inf 57.8%

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

   if 2.45e-169 < y1

   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 t around inf 35.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -3.2 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -2 \cdot 10^{+55}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 3.2 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 2.45 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+182}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 2.65 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -2.05e+182)
   (* j (* x (- (* i y1) (* b y0))))
   (if (<= y1 -8.2e+43)
     (* k (* y2 (- (* y1 y4) (* y0 y5))))
     (if (<= y1 5.2e-299)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y1 2.65e-169)
         (* j (* y0 (- (* y3 y5) (* x b))))
         (* y1 (* y4 (- (* k y2) (* j y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.05e+182) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -8.2e+43) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= 5.2e-299) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 2.65e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-2.05d+182)) then
        tmp = j * (x * ((i * y1) - (b * y0)))
    else if (y1 <= (-8.2d+43)) then
        tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
    else if (y1 <= 5.2d-299) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y1 <= 2.65d-169) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -2.05e+182) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (y1 <= -8.2e+43) {
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	} else if (y1 <= 5.2e-299) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y1 <= 2.65e-169) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -2.05e+182:
		tmp = j * (x * ((i * y1) - (b * y0)))
	elif y1 <= -8.2e+43:
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)))
	elif y1 <= 5.2e-299:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y1 <= 2.65e-169:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	else:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -2.05e+182)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (y1 <= -8.2e+43)
		tmp = Float64(k * Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))));
	elseif (y1 <= 5.2e-299)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y1 <= 2.65e-169)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	else
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -2.05e+182)
		tmp = j * (x * ((i * y1) - (b * y0)));
	elseif (y1 <= -8.2e+43)
		tmp = k * (y2 * ((y1 * y4) - (y0 * y5)));
	elseif (y1 <= 5.2e-299)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y1 <= 2.65e-169)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	else
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -2.05e+182], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -8.2e+43], N[(k * N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 5.2e-299], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 2.65e-169], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -2.05000000000000001e182

   1. Initial program 23.7%

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

   3. Taylor expanded in j around inf 44.1%

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

   4. Taylor expanded in x around inf 57.3%

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

   if -2.05000000000000001e182 < y1 < -8.2000000000000001e43

   1. Initial program 10.0%

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

   3. Taylor expanded in y2 around inf 55.3%

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

   4. Taylor expanded in k around inf 55.7%

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

   if -8.2000000000000001e43 < y1 < 5.1999999999999998e-299

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in a around inf 40.6%

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

   6. Taylor expanded in b around inf 37.0%

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

      1. +-commutative 37.0%

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

      2. mul-1-neg 37.0%

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

      3. unsub-neg 37.0%

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

   8. Simplified 37.0%

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

   if 5.1999999999999998e-299 < y1 < 2.65e-169

   1. Initial program 14.9%

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

   3. Taylor expanded in j around inf 43.8%

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

   4. Taylor expanded in y0 around inf 57.8%

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

   if 2.65e-169 < y1

   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 t around inf 35.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y1 around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -2.05 \cdot 10^{+182}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 5.2 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y1 \leq 2.65 \cdot 10^{-169}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+237}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -3.1e+237)
   (* c (* t (- (* z i) (* y2 y4))))
   (if (<= t -5.8e+72)
     (* a (* y5 (* t y2)))
     (if (<= t -4e-158)
       (* j (* y0 (- (* y3 y5) (* x b))))
       (if (<= t 1.4e+19)
         (* c (* y0 (- (* x y2) (* z y3))))
         (* 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 tmp;
	if (t <= -3.1e+237) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -5.8e+72) {
		tmp = a * (y5 * (t * y2));
	} else if (t <= -4e-158) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (t <= 1.4e+19) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} 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) :: tmp
    if (t <= (-3.1d+237)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= (-5.8d+72)) then
        tmp = a * (y5 * (t * y2))
    else if (t <= (-4d-158)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (t <= 1.4d+19) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    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 tmp;
	if (t <= -3.1e+237) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -5.8e+72) {
		tmp = a * (y5 * (t * y2));
	} else if (t <= -4e-158) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (t <= 1.4e+19) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} 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):
	tmp = 0
	if t <= -3.1e+237:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= -5.8e+72:
		tmp = a * (y5 * (t * y2))
	elif t <= -4e-158:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif t <= 1.4e+19:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	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)
	tmp = 0.0
	if (t <= -3.1e+237)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= -5.8e+72)
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	elseif (t <= -4e-158)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (t <= 1.4e+19)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	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)
	tmp = 0.0;
	if (t <= -3.1e+237)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= -5.8e+72)
		tmp = a * (y5 * (t * y2));
	elseif (t <= -4e-158)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (t <= 1.4e+19)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	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_] := If[LessEqual[t, -3.1e+237], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.8e+72], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-158], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+19], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $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 5 regimes

2. if t < -3.09999999999999991e237

   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 c around inf 33.2%

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

   6. Taylor expanded in t around inf 73.3%

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

   if -3.09999999999999991e237 < t < -5.80000000000000034e72

   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 t around inf 53.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 45.5%

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

   5. Taylor expanded in z around 0 45.3%

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

      1. *-commutative 45.3%

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

      2. *-commutative 45.3%

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

   7. Simplified 45.3%

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

   8. Taylor expanded in a around inf 36.1%

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

      1. associate-*r* 39.4%

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

   10. Simplified 39.4%

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

   if -5.80000000000000034e72 < t < -4.00000000000000026e-158

   1. Initial program 28.1%

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

   3. Taylor expanded in j around inf 42.4%

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

   4. Taylor expanded in y0 around inf 48.0%

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

   if -4.00000000000000026e-158 < t < 1.4e19

   1. Initial program 26.9%

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

   3. Simplified 26.9%

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

   5. Taylor expanded in c around inf 44.0%

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

   6. Taylor expanded in y0 around inf 33.7%

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

   if 1.4e19 < t

   1. Initial program 20.3%

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

   3. Taylor expanded in j around inf 41.2%

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

   4. Taylor expanded in b around inf 45.8%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+237}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-158}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (* x y0)))))
   (if (<= x -3.5e+173)
     t_1
     (if (<= x 9.2e-187)
       (* b (* t (* j y4)))
       (if (<= x 9e-138)
         (* (* t i) (* z c))
         (if (<= x 1.22e+69) (* a (* y5 (* t 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 * (y2 * (x * y0));
	double tmp;
	if (x <= -3.5e+173) {
		tmp = t_1;
	} else if (x <= 9.2e-187) {
		tmp = b * (t * (j * y4));
	} else if (x <= 9e-138) {
		tmp = (t * i) * (z * c);
	} else if (x <= 1.22e+69) {
		tmp = a * (y5 * (t * 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 * (y2 * (x * y0))
    if (x <= (-3.5d+173)) then
        tmp = t_1
    else if (x <= 9.2d-187) then
        tmp = b * (t * (j * y4))
    else if (x <= 9d-138) then
        tmp = (t * i) * (z * c)
    else if (x <= 1.22d+69) then
        tmp = a * (y5 * (t * 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 * (y2 * (x * y0));
	double tmp;
	if (x <= -3.5e+173) {
		tmp = t_1;
	} else if (x <= 9.2e-187) {
		tmp = b * (t * (j * y4));
	} else if (x <= 9e-138) {
		tmp = (t * i) * (z * c);
	} else if (x <= 1.22e+69) {
		tmp = a * (y5 * (t * 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 * (y2 * (x * y0))
	tmp = 0
	if x <= -3.5e+173:
		tmp = t_1
	elif x <= 9.2e-187:
		tmp = b * (t * (j * y4))
	elif x <= 9e-138:
		tmp = (t * i) * (z * c)
	elif x <= 1.22e+69:
		tmp = a * (y5 * (t * 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(y2 * Float64(x * y0)))
	tmp = 0.0
	if (x <= -3.5e+173)
		tmp = t_1;
	elseif (x <= 9.2e-187)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (x <= 9e-138)
		tmp = Float64(Float64(t * i) * Float64(z * c));
	elseif (x <= 1.22e+69)
		tmp = Float64(a * Float64(y5 * Float64(t * 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 * (y2 * (x * y0));
	tmp = 0.0;
	if (x <= -3.5e+173)
		tmp = t_1;
	elseif (x <= 9.2e-187)
		tmp = b * (t * (j * y4));
	elseif (x <= 9e-138)
		tmp = (t * i) * (z * c);
	elseif (x <= 1.22e+69)
		tmp = a * (y5 * (t * 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[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+173], t$95$1, If[LessEqual[x, 9.2e-187], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-138], N[(N[(t * i), $MachinePrecision] * N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e+69], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.4999999999999999e173 or 1.22e69 < x

   1. Initial program 20.9%

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

   3. Taylor expanded in y2 around inf 34.5%

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

   4. Taylor expanded in x around inf 31.5%

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

   5. Taylor expanded in c around inf 25.5%

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

      1. associate-*r* 31.3%

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

      2. *-commutative 31.3%

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

   7. Simplified 31.3%

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

   if -3.4999999999999999e173 < x < 9.19999999999999991e-187

   1. Initial program 29.9%

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

   3. Taylor expanded in t around inf 45.1%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 35.0%

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

   5. Taylor expanded in a around 0 24.1%

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

   if 9.19999999999999991e-187 < x < 9.00000000000000016e-138

   1. Initial program 36.4%

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

   3. Taylor expanded in t around inf 36.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 37.4%

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

   5. Taylor expanded in i around inf 38.4%

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

      1. associate-*r* 46.6%

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

      2. *-commutative 46.6%

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

      3. +-commutative 46.6%

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

      4. mul-1-neg 46.6%

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

      5. unsub-neg 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in c around inf 55.7%

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

      1. *-commutative 55.7%

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

   10. Simplified 55.7%

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

   if 9.00000000000000016e-138 < x < 1.22e69

   1. Initial program 21.5%

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

   3. Taylor expanded in t around inf 43.0%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 30.6%

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

   5. Taylor expanded in z around 0 35.1%

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

      1. *-commutative 35.1%

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

      2. *-commutative 35.1%

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

   7. Simplified 35.1%

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

   8. Taylor expanded in a around inf 31.3%

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

      1. associate-*r* 33.3%

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

   10. Simplified 33.3%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2\right) \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-138}:\\ \;\;\;\;\left(t \cdot i\right) \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -6.5e+74)
   (* t (* y2 (- (* a y5) (* c y4))))
   (if (<= t -9e-159)
     (* j (* y0 (- (* y3 y5) (* x b))))
     (if (<= t 9.8e+19)
       (* c (* y0 (- (* x y2) (* z y3))))
       (* 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 tmp;
	if (t <= -6.5e+74) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (t <= -9e-159) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (t <= 9.8e+19) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} 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) :: tmp
    if (t <= (-6.5d+74)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (t <= (-9d-159)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (t <= 9.8d+19) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    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 tmp;
	if (t <= -6.5e+74) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (t <= -9e-159) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (t <= 9.8e+19) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} 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):
	tmp = 0
	if t <= -6.5e+74:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif t <= -9e-159:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif t <= 9.8e+19:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	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)
	tmp = 0.0
	if (t <= -6.5e+74)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (t <= -9e-159)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (t <= 9.8e+19)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	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)
	tmp = 0.0;
	if (t <= -6.5e+74)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (t <= -9e-159)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (t <= 9.8e+19)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	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_] := If[LessEqual[t, -6.5e+74], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-159], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e+19], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $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 4 regimes

2. if t < -6.49999999999999962e74

   1. Initial program 27.5%

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

   3. Taylor expanded in y2 around inf 43.9%

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

   4. Taylor expanded in t around inf 44.4%

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

   if -6.49999999999999962e74 < t < -8.99999999999999977e-159

   1. Initial program 28.1%

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

   3. Taylor expanded in j around inf 42.4%

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

   4. Taylor expanded in y0 around inf 48.0%

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

   if -8.99999999999999977e-159 < t < 9.8e19

   1. Initial program 26.9%

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

   3. Simplified 26.9%

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

   5. Taylor expanded in c around inf 44.0%

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

   6. Taylor expanded in y0 around inf 33.7%

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

   if 9.8e19 < t

   1. Initial program 20.3%

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

   3. Taylor expanded in j around inf 41.2%

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

   4. Taylor expanded in b around inf 45.8%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -6.2e+69)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= a 5.9e-161)
     (* c (* y0 (- (* x y2) (* z y3))))
     (if (<= a 1.6e+19)
       (* j (* t (- (* b y4) (* i y5))))
       (* a (* b (- (* x y) (* 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 (a <= -6.2e+69) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (a <= 5.9e-161) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= 1.6e+19) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else {
		tmp = a * (b * ((x * y) - (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 (a <= (-6.2d+69)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (a <= 5.9d-161) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else if (a <= 1.6d+19) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else
        tmp = a * (b * ((x * y) - (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 (a <= -6.2e+69) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (a <= 5.9e-161) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else if (a <= 1.6e+19) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else {
		tmp = a * (b * ((x * y) - (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 a <= -6.2e+69:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif a <= 5.9e-161:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	elif a <= 1.6e+19:
		tmp = j * (t * ((b * y4) - (i * y5)))
	else:
		tmp = a * (b * ((x * y) - (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 (a <= -6.2e+69)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (a <= 5.9e-161)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (a <= 1.6e+19)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - 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 (a <= -6.2e+69)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (a <= 5.9e-161)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	elseif (a <= 1.6e+19)
		tmp = j * (t * ((b * y4) - (i * y5)));
	else
		tmp = a * (b * ((x * y) - (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[a, -6.2e+69], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.9e-161], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+19], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.1999999999999997e69

   1. Initial program 25.8%

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

   3. Simplified 25.8%

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

   5. Taylor expanded in a around inf 69.4%

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

   6. Taylor expanded in y3 around inf 46.8%

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

      1. *-commutative 46.8%

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

   8. Simplified 46.8%

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

   if -6.1999999999999997e69 < a < 5.9000000000000002e-161

   1. Initial program 29.6%

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

   3. Simplified 29.6%

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

   5. Taylor expanded in c around inf 38.7%

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

   6. Taylor expanded in y0 around inf 32.7%

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

   if 5.9000000000000002e-161 < a < 1.6e19

   1. Initial program 20.5%

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

   3. Taylor expanded in j around inf 50.6%

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

   4. Taylor expanded in t around inf 33.8%

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

   if 1.6e19 < a

   1. Initial program 20.4%

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

   3. Simplified 20.4%

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

   5. Taylor expanded in a around inf 56.1%

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

   6. Taylor expanded in b around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

   8. Simplified 53.9%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 20.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -9 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(a \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 2.9 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -9e+68)
   (* x (* y2 (* a (- y1))))
   (if (<= y2 -2.2e-20)
     (* b (* t (* j y4)))
     (if (<= y2 2.9e+168) (* b (* t (* z (- a)))) (* x (* (- a) (* y1 y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -9e+68) {
		tmp = x * (y2 * (a * -y1));
	} else if (y2 <= -2.2e-20) {
		tmp = b * (t * (j * y4));
	} else if (y2 <= 2.9e+168) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = x * (-a * (y1 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-9d+68)) then
        tmp = x * (y2 * (a * -y1))
    else if (y2 <= (-2.2d-20)) then
        tmp = b * (t * (j * y4))
    else if (y2 <= 2.9d+168) then
        tmp = b * (t * (z * -a))
    else
        tmp = x * (-a * (y1 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -9e+68) {
		tmp = x * (y2 * (a * -y1));
	} else if (y2 <= -2.2e-20) {
		tmp = b * (t * (j * y4));
	} else if (y2 <= 2.9e+168) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = x * (-a * (y1 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -9e+68:
		tmp = x * (y2 * (a * -y1))
	elif y2 <= -2.2e-20:
		tmp = b * (t * (j * y4))
	elif y2 <= 2.9e+168:
		tmp = b * (t * (z * -a))
	else:
		tmp = x * (-a * (y1 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -9e+68)
		tmp = Float64(x * Float64(y2 * Float64(a * Float64(-y1))));
	elseif (y2 <= -2.2e-20)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (y2 <= 2.9e+168)
		tmp = Float64(b * Float64(t * Float64(z * Float64(-a))));
	else
		tmp = Float64(x * Float64(Float64(-a) * Float64(y1 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -9e+68)
		tmp = x * (y2 * (a * -y1));
	elseif (y2 <= -2.2e-20)
		tmp = b * (t * (j * y4));
	elseif (y2 <= 2.9e+168)
		tmp = b * (t * (z * -a));
	else
		tmp = x * (-a * (y1 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -9e+68], N[(x * N[(y2 * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.2e-20], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.9e+168], N[(b * N[(t * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-a) * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -9.0000000000000007e68

   1. Initial program 19.3%

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

   3. Taylor expanded in y2 around inf 50.3%

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

   4. Taylor expanded in x around inf 49.0%

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

   5. Taylor expanded in c around 0 41.2%

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

      1. associate-*r* 41.2%

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

      2. *-commutative 41.2%

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

      3. neg-mul-1 41.2%

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

   7. Simplified 41.2%

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

   if -9.0000000000000007e68 < y2 < -2.19999999999999991e-20

   1. Initial program 32.4%

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

   3. Taylor expanded in t around inf 36.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 37.1%

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

   5. Taylor expanded in a around 0 37.3%

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

   if -2.19999999999999991e-20 < y2 < 2.9e168

   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 t around inf 41.5%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 31.6%

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

   5. Taylor expanded in a around inf 22.5%

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

      1. neg-mul-1 22.5%

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

      2. distribute-rgt-neg-in 22.5%

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

   7. Simplified 22.5%

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

   if 2.9e168 < y2

   1. Initial program 13.9%

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

   3. Taylor expanded in y2 around inf 68.2%

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

   4. Taylor expanded in x around inf 55.4%

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

   5. Taylor expanded in c around 0 55.0%

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

      1. associate-*r* 55.0%

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

      2. neg-mul-1 55.0%

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

   7. Simplified 55.0%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(a \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 2.9 \cdot 10^{+168}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.3 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(a \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.3e+68)
   (* x (* y2 (* a (- y1))))
   (if (<= y2 -1.85e-20)
     (* b (* t (* j y4)))
     (if (<= y2 4.6e+145) (* b (* t (* z (- a)))) (* a (* y5 (* t y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.3e+68) {
		tmp = x * (y2 * (a * -y1));
	} else if (y2 <= -1.85e-20) {
		tmp = b * (t * (j * y4));
	} else if (y2 <= 4.6e+145) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.3d+68)) then
        tmp = x * (y2 * (a * -y1))
    else if (y2 <= (-1.85d-20)) then
        tmp = b * (t * (j * y4))
    else if (y2 <= 4.6d+145) then
        tmp = b * (t * (z * -a))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.3e+68) {
		tmp = x * (y2 * (a * -y1));
	} else if (y2 <= -1.85e-20) {
		tmp = b * (t * (j * y4));
	} else if (y2 <= 4.6e+145) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.3e+68:
		tmp = x * (y2 * (a * -y1))
	elif y2 <= -1.85e-20:
		tmp = b * (t * (j * y4))
	elif y2 <= 4.6e+145:
		tmp = b * (t * (z * -a))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.3e+68)
		tmp = Float64(x * Float64(y2 * Float64(a * Float64(-y1))));
	elseif (y2 <= -1.85e-20)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (y2 <= 4.6e+145)
		tmp = Float64(b * Float64(t * Float64(z * Float64(-a))));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.3e+68)
		tmp = x * (y2 * (a * -y1));
	elseif (y2 <= -1.85e-20)
		tmp = b * (t * (j * y4));
	elseif (y2 <= 4.6e+145)
		tmp = b * (t * (z * -a));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.3e+68], N[(x * N[(y2 * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.85e-20], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.6e+145], N[(b * N[(t * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.2999999999999999e68

   1. Initial program 19.3%

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

   3. Taylor expanded in y2 around inf 50.3%

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

   4. Taylor expanded in x around inf 49.0%

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

   5. Taylor expanded in c around 0 41.2%

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

      1. associate-*r* 41.2%

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

      2. *-commutative 41.2%

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

      3. neg-mul-1 41.2%

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

   7. Simplified 41.2%

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

   if -1.2999999999999999e68 < y2 < -1.85e-20

   1. Initial program 32.4%

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

   3. Taylor expanded in t around inf 36.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 37.1%

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

   5. Taylor expanded in a around 0 37.3%

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

   if -1.85e-20 < y2 < 4.6e145

   1. Initial program 28.8%

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

   3. Taylor expanded in t around inf 41.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 30.7%

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

   5. Taylor expanded in a around inf 22.7%

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

      1. neg-mul-1 22.7%

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

      2. distribute-rgt-neg-in 22.7%

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

   7. Simplified 22.7%

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

   if 4.6e145 < y2

   1. Initial program 12.7%

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

   3. Taylor expanded in t around inf 25.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 29.6%

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

   5. Taylor expanded in z around 0 38.3%

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

      1. *-commutative 38.3%

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

      2. *-commutative 38.3%

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

   7. Simplified 38.3%

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

   8. Taylor expanded in a around inf 42.3%

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

      1. associate-*r* 46.4%

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

   10. Simplified 46.4%

       \[\leadsto \color{blue}{a \cdot \left(\left(t \cdot y2\right) \cdot y5\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.3 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(a \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y2 (* x y0)))))
   (if (<= x -2.8e+173)
     t_1
     (if (<= x 1.6e-143)
       (* b (* t (* j y4)))
       (if (<= x 1.22e+69) (* a (* y5 (* t 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 * (y2 * (x * y0));
	double tmp;
	if (x <= -2.8e+173) {
		tmp = t_1;
	} else if (x <= 1.6e-143) {
		tmp = b * (t * (j * y4));
	} else if (x <= 1.22e+69) {
		tmp = a * (y5 * (t * 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 * (y2 * (x * y0))
    if (x <= (-2.8d+173)) then
        tmp = t_1
    else if (x <= 1.6d-143) then
        tmp = b * (t * (j * y4))
    else if (x <= 1.22d+69) then
        tmp = a * (y5 * (t * 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 * (y2 * (x * y0));
	double tmp;
	if (x <= -2.8e+173) {
		tmp = t_1;
	} else if (x <= 1.6e-143) {
		tmp = b * (t * (j * y4));
	} else if (x <= 1.22e+69) {
		tmp = a * (y5 * (t * 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 * (y2 * (x * y0))
	tmp = 0
	if x <= -2.8e+173:
		tmp = t_1
	elif x <= 1.6e-143:
		tmp = b * (t * (j * y4))
	elif x <= 1.22e+69:
		tmp = a * (y5 * (t * 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(y2 * Float64(x * y0)))
	tmp = 0.0
	if (x <= -2.8e+173)
		tmp = t_1;
	elseif (x <= 1.6e-143)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	elseif (x <= 1.22e+69)
		tmp = Float64(a * Float64(y5 * Float64(t * 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 * (y2 * (x * y0));
	tmp = 0.0;
	if (x <= -2.8e+173)
		tmp = t_1;
	elseif (x <= 1.6e-143)
		tmp = b * (t * (j * y4));
	elseif (x <= 1.22e+69)
		tmp = a * (y5 * (t * 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[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+173], t$95$1, If[LessEqual[x, 1.6e-143], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e+69], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999982e173 or 1.22e69 < x

   1. Initial program 20.9%

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

   3. Taylor expanded in y2 around inf 34.5%

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

   4. Taylor expanded in x around inf 31.5%

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

   5. Taylor expanded in c around inf 25.5%

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

      1. associate-*r* 31.3%

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

      2. *-commutative 31.3%

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

   7. Simplified 31.3%

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

   if -2.79999999999999982e173 < x < 1.5999999999999999e-143

   1. Initial program 30.1%

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

   3. Taylor expanded in t around inf 44.3%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 35.0%

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

   5. Taylor expanded in a around 0 24.0%

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

   if 1.5999999999999999e-143 < x < 1.22e69

   1. Initial program 22.7%

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

   3. Taylor expanded in t around inf 43.3%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 29.5%

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

   5. Taylor expanded in z around 0 33.7%

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

      1. *-commutative 33.7%

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

      2. *-commutative 33.7%

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

   7. Simplified 33.7%

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

   8. Taylor expanded in a around inf 30.1%

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

      1. associate-*r* 32.0%

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

   10. Simplified 32.0%

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

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 31.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.05 \cdot 10^{+137} \lor \neg \left(y3 \leq 1.12 \cdot 10^{+60}\right):\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -1.05e+137) (not (<= y3 1.12e+60)))
   (* a (* y3 (- (* z y1) (* y y5))))
   (* a (* b (- (* x y) (* 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 ((y3 <= -1.05e+137) || !(y3 <= 1.12e+60)) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else {
		tmp = a * (b * ((x * y) - (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 ((y3 <= (-1.05d+137)) .or. (.not. (y3 <= 1.12d+60))) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else
        tmp = a * (b * ((x * y) - (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 ((y3 <= -1.05e+137) || !(y3 <= 1.12e+60)) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else {
		tmp = a * (b * ((x * y) - (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 (y3 <= -1.05e+137) or not (y3 <= 1.12e+60):
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	else:
		tmp = a * (b * ((x * y) - (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 ((y3 <= -1.05e+137) || !(y3 <= 1.12e+60))
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - 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 ((y3 <= -1.05e+137) || ~((y3 <= 1.12e+60)))
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	else
		tmp = a * (b * ((x * y) - (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[y3, -1.05e+137], N[Not[LessEqual[y3, 1.12e+60]], $MachinePrecision]], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < -1.05e137 or 1.1199999999999999e60 < y3

   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 a around inf 34.3%

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

   6. Taylor expanded in y3 around inf 44.8%

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

      1. *-commutative 44.8%

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

   8. Simplified 44.8%

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

   if -1.05e137 < y3 < 1.1199999999999999e60

   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 a around inf 41.6%

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

   6. Taylor expanded in b around inf 32.0%

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

      1. +-commutative 32.0%

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

      2. mul-1-neg 32.0%

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

      3. unsub-neg 32.0%

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

   8. Simplified 32.0%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y - t \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.05 \cdot 10^{+137} \lor \neg \left(y3 \leq 1.12 \cdot 10^{+60}\right):\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 30.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-160}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -1.05e+72)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= a 2.55e-160)
     (* c (* y0 (- (* x y2) (* z y3))))
     (* a (* b (- (* x y) (* 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 (a <= -1.05e+72) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (a <= 2.55e-160) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = a * (b * ((x * y) - (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 (a <= (-1.05d+72)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (a <= 2.55d-160) then
        tmp = c * (y0 * ((x * y2) - (z * y3)))
    else
        tmp = a * (b * ((x * y) - (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 (a <= -1.05e+72) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (a <= 2.55e-160) {
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	} else {
		tmp = a * (b * ((x * y) - (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 a <= -1.05e+72:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif a <= 2.55e-160:
		tmp = c * (y0 * ((x * y2) - (z * y3)))
	else:
		tmp = a * (b * ((x * y) - (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 (a <= -1.05e+72)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (a <= 2.55e-160)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - 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 (a <= -1.05e+72)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (a <= 2.55e-160)
		tmp = c * (y0 * ((x * y2) - (z * y3)));
	else
		tmp = a * (b * ((x * y) - (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[a, -1.05e+72], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e-160], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.0500000000000001e72

   1. Initial program 25.8%

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

   3. Simplified 25.8%

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

   5. Taylor expanded in a around inf 69.4%

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

   6. Taylor expanded in y3 around inf 46.8%

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

      1. *-commutative 46.8%

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

   8. Simplified 46.8%

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

   if -1.0500000000000001e72 < a < 2.55e-160

   1. Initial program 29.4%

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

   3. Simplified 29.4%

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

   5. Taylor expanded in c around inf 39.2%

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

   6. Taylor expanded in y0 around inf 33.3%

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

   if 2.55e-160 < a

   1. Initial program 20.7%

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

   3. Simplified 20.7%

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

   5. Taylor expanded in a around inf 47.1%

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

   6. Taylor expanded in b around inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

   8. Simplified 41.5%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-160}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 29.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= a -5.8e-88)
   (* a (* y3 (- (* z y1) (* y y5))))
   (if (<= a 1.14e-7)
     (* b (* j (- (* t y4) (* x y0))))
     (* a (* b (- (* x y) (* 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 (a <= -5.8e-88) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (a <= 1.14e-7) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (b * ((x * y) - (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 (a <= (-5.8d-88)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (a <= 1.14d-7) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = a * (b * ((x * y) - (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 (a <= -5.8e-88) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (a <= 1.14e-7) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = a * (b * ((x * y) - (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 a <= -5.8e-88:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif a <= 1.14e-7:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = a * (b * ((x * y) - (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 (a <= -5.8e-88)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (a <= 1.14e-7)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - 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 (a <= -5.8e-88)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (a <= 1.14e-7)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = a * (b * ((x * y) - (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[a, -5.8e-88], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.14e-7], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8000000000000003e-88

   1. Initial program 28.9%

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

   3. Simplified 28.9%

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

   5. Taylor expanded in a around inf 52.6%

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

   6. Taylor expanded in y3 around inf 32.9%

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

      1. *-commutative 32.9%

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

   8. Simplified 32.9%

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

   if -5.8000000000000003e-88 < a < 1.14000000000000002e-7

   1. Initial program 27.3%

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

   3. Taylor expanded in j around inf 44.0%

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

   4. Taylor expanded in b around inf 32.1%

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

   if 1.14000000000000002e-7 < a

   1. Initial program 19.1%

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

   3. Simplified 19.1%

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

   5. Taylor expanded in a around inf 52.5%

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

   6. Taylor expanded in b around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

   8. Simplified 52.1%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq 1.14 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 28.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -9 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(a \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -9e+101)
   (* x (* y2 (* a (- y1))))
   (if (<= y2 4.2e+164)
     (* a (* b (- (* x y) (* z t))))
     (* x (* (- a) (* y1 y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -9e+101) {
		tmp = x * (y2 * (a * -y1));
	} else if (y2 <= 4.2e+164) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = x * (-a * (y1 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-9d+101)) then
        tmp = x * (y2 * (a * -y1))
    else if (y2 <= 4.2d+164) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = x * (-a * (y1 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -9e+101) {
		tmp = x * (y2 * (a * -y1));
	} else if (y2 <= 4.2e+164) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = x * (-a * (y1 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -9e+101:
		tmp = x * (y2 * (a * -y1))
	elif y2 <= 4.2e+164:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = x * (-a * (y1 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -9e+101)
		tmp = Float64(x * Float64(y2 * Float64(a * Float64(-y1))));
	elseif (y2 <= 4.2e+164)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(x * Float64(Float64(-a) * Float64(y1 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -9e+101)
		tmp = x * (y2 * (a * -y1));
	elseif (y2 <= 4.2e+164)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = x * (-a * (y1 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -9e+101], N[(x * N[(y2 * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e+164], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-a) * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -9.0000000000000004e101

   1. Initial program 17.9%

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

   3. Taylor expanded in y2 around inf 55.7%

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

   4. Taylor expanded in x around inf 52.0%

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

   5. Taylor expanded in c around 0 43.0%

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

      1. associate-*r* 43.0%

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

      2. *-commutative 43.0%

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

      3. neg-mul-1 43.0%

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

   7. Simplified 43.0%

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

   if -9.0000000000000004e101 < y2 < 4.1999999999999998e164

   1. Initial program 28.9%

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

   3. Simplified 28.9%

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

   5. Taylor expanded in a around inf 37.6%

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

   6. Taylor expanded in b around inf 30.4%

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

      1. +-commutative 30.4%

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

      2. mul-1-neg 30.4%

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

      3. unsub-neg 30.4%

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

   8. Simplified 30.4%

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

   if 4.1999999999999998e164 < y2

   1. Initial program 13.9%

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

   3. Taylor expanded in y2 around inf 68.2%

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

   4. Taylor expanded in x around inf 55.4%

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

   5. Taylor expanded in c around 0 55.0%

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

      1. associate-*r* 55.0%

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

      2. neg-mul-1 55.0%

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

   7. Simplified 55.0%

      \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -9 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(a \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(-a\right) \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 21.8% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -1.5e+105)
   (* t (* b (* j y4)))
   (if (<= j 2.2e+70) (* b (* t (* z (- a)))) (* t (* i (* j (- 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 (j <= -1.5e+105) {
		tmp = t * (b * (j * y4));
	} else if (j <= 2.2e+70) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = t * (i * (j * -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 (j <= (-1.5d+105)) then
        tmp = t * (b * (j * y4))
    else if (j <= 2.2d+70) then
        tmp = b * (t * (z * -a))
    else
        tmp = t * (i * (j * -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 (j <= -1.5e+105) {
		tmp = t * (b * (j * y4));
	} else if (j <= 2.2e+70) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = t * (i * (j * -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 j <= -1.5e+105:
		tmp = t * (b * (j * y4))
	elif j <= 2.2e+70:
		tmp = b * (t * (z * -a))
	else:
		tmp = t * (i * (j * -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 (j <= -1.5e+105)
		tmp = Float64(t * Float64(b * Float64(j * y4)));
	elseif (j <= 2.2e+70)
		tmp = Float64(b * Float64(t * Float64(z * Float64(-a))));
	else
		tmp = Float64(t * Float64(i * Float64(j * Float64(-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 (j <= -1.5e+105)
		tmp = t * (b * (j * y4));
	elseif (j <= 2.2e+70)
		tmp = b * (t * (z * -a));
	else
		tmp = t * (i * (j * -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[j, -1.5e+105], N[(t * N[(b * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.2e+70], N[(b * N[(t * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(i * N[(j * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.5e105

   1. Initial program 22.8%

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

   3. Taylor expanded in t around inf 38.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 47.2%

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

   5. Taylor expanded in z around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in b around inf 48.0%

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

   if -1.5e105 < j < 2.20000000000000001e70

   1. Initial program 29.2%

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

   3. Taylor expanded in t around inf 44.3%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 25.5%

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

   5. Taylor expanded in a around inf 22.6%

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

      1. neg-mul-1 22.6%

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

      2. distribute-rgt-neg-in 22.6%

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

   7. Simplified 22.6%

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

   if 2.20000000000000001e70 < j

   1. Initial program 16.0%

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

   3. Taylor expanded in t around inf 20.2%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 24.4%

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

   5. Taylor expanded in z around 0 24.6%

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

      1. *-commutative 24.6%

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

      2. *-commutative 24.6%

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

   7. Simplified 24.6%

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

   8. Taylor expanded in i around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. *-commutative 33.0%

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

   10. Simplified 33.0%

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

4. Final simplification 28.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(i \cdot \left(j \cdot \left(-y5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 21.8% accurate, 5.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.55 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= j -2.55e+104)
   (* t (* b (* j y4)))
   (if (<= j 1.5e+36) (* b (* t (* z (- a)))) (* b (* t (* j y4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -2.55e+104) {
		tmp = t * (b * (j * y4));
	} else if (j <= 1.5e+36) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = b * (t * (j * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (j <= (-2.55d+104)) then
        tmp = t * (b * (j * y4))
    else if (j <= 1.5d+36) then
        tmp = b * (t * (z * -a))
    else
        tmp = b * (t * (j * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (j <= -2.55e+104) {
		tmp = t * (b * (j * y4));
	} else if (j <= 1.5e+36) {
		tmp = b * (t * (z * -a));
	} else {
		tmp = b * (t * (j * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if j <= -2.55e+104:
		tmp = t * (b * (j * y4))
	elif j <= 1.5e+36:
		tmp = b * (t * (z * -a))
	else:
		tmp = b * (t * (j * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (j <= -2.55e+104)
		tmp = Float64(t * Float64(b * Float64(j * y4)));
	elseif (j <= 1.5e+36)
		tmp = Float64(b * Float64(t * Float64(z * Float64(-a))));
	else
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (j <= -2.55e+104)
		tmp = t * (b * (j * y4));
	elseif (j <= 1.5e+36)
		tmp = b * (t * (z * -a));
	else
		tmp = b * (t * (j * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[j, -2.55e+104], N[(t * N[(b * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+36], N[(b * N[(t * N[(z * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.5500000000000001e104

   1. Initial program 22.8%

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

   3. Taylor expanded in t around inf 38.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 47.2%

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

   5. Taylor expanded in z around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in b around inf 48.0%

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

   if -2.5500000000000001e104 < j < 1.5e36

   1. Initial program 30.4%

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

   3. Taylor expanded in t around inf 45.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 25.7%

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

   5. Taylor expanded in a around inf 23.3%

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

      1. neg-mul-1 23.3%

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

      2. distribute-rgt-neg-in 23.3%

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

   7. Simplified 23.3%

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

   if 1.5e36 < j

   1. Initial program 15.1%

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

   3. Taylor expanded in t around inf 20.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 32.5%

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

   5. Taylor expanded in a around 0 27.8%

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

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.55 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(b \cdot \left(j \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(t \cdot \left(z \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 21.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2.1 \cdot 10^{+128} \lor \neg \left(y2 \leq 1.52 \cdot 10^{-90}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -2.1e+128) (not (<= y2 1.52e-90)))
   (* a (* y5 (* t y2)))
   (* b (* t (* j y4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -2.1e+128) || !(y2 <= 1.52e-90)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = b * (t * (j * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-2.1d+128)) .or. (.not. (y2 <= 1.52d-90))) then
        tmp = a * (y5 * (t * y2))
    else
        tmp = b * (t * (j * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -2.1e+128) || !(y2 <= 1.52e-90)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = b * (t * (j * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -2.1e+128) or not (y2 <= 1.52e-90):
		tmp = a * (y5 * (t * y2))
	else:
		tmp = b * (t * (j * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -2.1e+128) || !(y2 <= 1.52e-90))
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	else
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -2.1e+128) || ~((y2 <= 1.52e-90)))
		tmp = a * (y5 * (t * y2));
	else
		tmp = b * (t * (j * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -2.1e+128], N[Not[LessEqual[y2, 1.52e-90]], $MachinePrecision]], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -2.1e128 or 1.51999999999999991e-90 < y2

   1. Initial program 24.6%

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

   3. Taylor expanded in t around inf 40.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 38.1%

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

   5. Taylor expanded in z around 0 34.9%

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

      1. *-commutative 34.9%

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

      2. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   8. Taylor expanded in a around inf 29.1%

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

      1. associate-*r* 29.9%

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

   10. Simplified 29.9%

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

   if -2.1e128 < y2 < 1.51999999999999991e-90

   1. Initial program 26.6%

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

   3. Taylor expanded in t around inf 37.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 31.6%

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

   5. Taylor expanded in a around 0 21.9%

      \[\leadsto b \cdot \left(t \cdot \color{blue}{\left(j \cdot y4\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.1 \cdot 10^{+128} \lor \neg \left(y2 \leq 1.52 \cdot 10^{-90}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 21.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -2.4 \cdot 10^{+128} \lor \neg \left(y2 \leq 2.45 \cdot 10^{-89}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y2 -2.4e+128) (not (<= y2 2.45e-89)))
   (* a (* y5 (* t y2)))
   (* b (* j (* t y4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -2.4e+128) || !(y2 <= 2.45e-89)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y2 <= (-2.4d+128)) .or. (.not. (y2 <= 2.45d-89))) then
        tmp = a * (y5 * (t * y2))
    else
        tmp = b * (j * (t * y4))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y2 <= -2.4e+128) || !(y2 <= 2.45e-89)) {
		tmp = a * (y5 * (t * y2));
	} else {
		tmp = b * (j * (t * y4));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y2 <= -2.4e+128) or not (y2 <= 2.45e-89):
		tmp = a * (y5 * (t * y2))
	else:
		tmp = b * (j * (t * y4))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y2 <= -2.4e+128) || !(y2 <= 2.45e-89))
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	else
		tmp = Float64(b * Float64(j * Float64(t * y4)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y2 <= -2.4e+128) || ~((y2 <= 2.45e-89)))
		tmp = a * (y5 * (t * y2));
	else
		tmp = b * (j * (t * y4));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y2, -2.4e+128], N[Not[LessEqual[y2, 2.45e-89]], $MachinePrecision]], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y2 < -2.4000000000000002e128 or 2.45e-89 < y2

   1. Initial program 24.6%

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

   3. Taylor expanded in t around inf 40.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 38.1%

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

   5. Taylor expanded in z around 0 34.9%

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

      1. *-commutative 34.9%

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

      2. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   8. Taylor expanded in a around inf 29.1%

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

      1. associate-*r* 29.9%

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

   10. Simplified 29.9%

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

   if -2.4000000000000002e128 < y2 < 2.45e-89

   1. Initial program 26.6%

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

   3. Taylor expanded in j around inf 40.9%

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

   4. Taylor expanded in b around inf 25.5%

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

   5. Taylor expanded in t around inf 19.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(t \cdot y4\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.4 \cdot 10^{+128} \lor \neg \left(y2 \leq 2.45 \cdot 10^{-89}\right):\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 21.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -8.6 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -8.6e+128)
   (* c (* x (* y0 y2)))
   (if (<= y2 2.7e-90) (* b (* t (* j y4))) (* a (* y5 (* t y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.6e+128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.7e-90) {
		tmp = b * (t * (j * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-8.6d+128)) then
        tmp = c * (x * (y0 * y2))
    else if (y2 <= 2.7d-90) then
        tmp = b * (t * (j * y4))
    else
        tmp = a * (y5 * (t * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.6e+128) {
		tmp = c * (x * (y0 * y2));
	} else if (y2 <= 2.7e-90) {
		tmp = b * (t * (j * y4));
	} else {
		tmp = a * (y5 * (t * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -8.6e+128:
		tmp = c * (x * (y0 * y2))
	elif y2 <= 2.7e-90:
		tmp = b * (t * (j * y4))
	else:
		tmp = a * (y5 * (t * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -8.6e+128)
		tmp = Float64(c * Float64(x * Float64(y0 * y2)));
	elseif (y2 <= 2.7e-90)
		tmp = Float64(b * Float64(t * Float64(j * y4)));
	else
		tmp = Float64(a * Float64(y5 * Float64(t * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -8.6e+128)
		tmp = c * (x * (y0 * y2));
	elseif (y2 <= 2.7e-90)
		tmp = b * (t * (j * y4));
	else
		tmp = a * (y5 * (t * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -8.6e+128], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.7e-90], N[(b * N[(t * N[(j * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -8.59999999999999949e128

   1. Initial program 18.6%

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

   3. Taylor expanded in y2 around inf 56.0%

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

   4. Taylor expanded in x around inf 49.8%

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

   5. Taylor expanded in c around inf 33.5%

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

   if -8.59999999999999949e128 < y2 < 2.69999999999999996e-90

   1. Initial program 26.6%

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

   3. Taylor expanded in t around inf 37.6%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in b around inf 31.6%

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

   5. Taylor expanded in a around 0 21.9%

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

   if 2.69999999999999996e-90 < y2

   1. Initial program 28.2%

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

   3. Taylor expanded in t around inf 40.8%

      \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in t around inf 38.2%

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

   5. Taylor expanded in z around 0 33.2%

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

      1. *-commutative 33.2%

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

      2. *-commutative 33.2%

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

   7. Simplified 33.2%

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

   8. Taylor expanded in a around inf 28.0%

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

      1. associate-*r* 28.0%

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

   10. Simplified 28.0%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.6 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-90}:\\ \;\;\;\;b \cdot \left(t \cdot \left(j \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 17.3% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y5 * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 25.7%

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

3. Taylor expanded in t around inf 38.8%

   \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

4. Taylor expanded in t around inf 35.2%

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

5. Taylor expanded in z around 0 30.7%

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

   1. *-commutative 30.7%

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

   2. *-commutative 30.7%

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

7. Simplified 30.7%

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

8. Taylor expanded in a around inf 15.6%

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

   1. associate-*r* 16.3%

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

10. Simplified 16.3%

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

11. Final simplification 16.3%

    \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2\right)\right) \]
12. Add Preprocessing

Alternative 39: 17.2% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 25.7%

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

3. Taylor expanded in t around inf 38.8%

   \[\leadsto \left(\color{blue}{t \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

4. Taylor expanded in t around inf 35.2%

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

5. Taylor expanded in z around 0 30.7%

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

   1. *-commutative 30.7%

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

   2. *-commutative 30.7%

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

7. Simplified 30.7%

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

8. Taylor expanded in a around inf 15.6%

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

Developer Target 1: 27.8% 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 2024135 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y4 -7206256231996481000000000000000000000000000000000000000000000) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3364603505246317/1000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -3000016263921529/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 1343792624811499/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 29872667587737/6250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 4570448308253367/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))))))))

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