Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.6% → 38.9%

Time: 2.0min

Alternatives: 34

Speedup: 2.1×

• 89.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 29.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 38.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := t\_1 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_3 := b \cdot y4 - i \cdot y5\\ t_4 := c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -5.8 \cdot 10^{+257}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+150}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(\left(z \cdot \left(c \cdot i - a \cdot b\right) + j \cdot t\_3\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) + t\_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-173}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y4 \cdot \left(\frac{j \cdot \left(y0 \cdot y5\right)}{y4} - j \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq 115000:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot t\_3\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+122}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j - \left(a \cdot y2 - \frac{y4 \cdot t\_1}{x}\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(t \cdot j - y \cdot k\right) \cdot y4\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right) + t\_2\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+187}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+272}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (* t_1 (- (* y1 y4) (* y0 y5))))
        (t_3 (- (* b y4) (* i y5)))
        (t_4
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
           (* y4 (- (* y y3) (* t y2)))))))
   (if (<= c -5.8e+257)
     (* c (* y3 (- (* y y4) (* z y0))))
     (if (<= c -2.2e+246)
       (* x (* y (- (* a b) (* c i))))
       (if (<= c -3.2e+150)
         t_4
         (if (<= c -1.25e-260)
           (+
            (*
             t
             (+
              (+ (* z (- (* c i) (* a b))) (* j t_3))
              (* y2 (- (* a y5) (* c y4)))))
            t_2)
           (if (<= c 2.2e-173)
             (*
              y3
              (+
               (* y (- (* c y4) (* a y5)))
               (+
                (* z (- (* a y1) (* c y0)))
                (* y4 (- (/ (* j (* y0 y5)) y4) (* j y1))))))
             (if (<= c 115000.0)
               (*
                j
                (+
                 (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t t_3))
                 (* x (- (* i y1) (* b y0)))))
               (if (<= c 1.35e+122)
                 (* y1 (* x (- (* i j) (- (* a y2) (/ (* y4 t_1) x)))))
                 (if (<= c 1.02e+154)
                   (+
                    (*
                     b
                     (+
                      (+ (* a (- (* x y) (* z t))) (* (- (* t j) (* y k)) y4))
                      (* y0 (- (* z k) (* x j)))))
                    t_2)
                   (if (<= c 3e+187)
                     (* c (* x (- (* y0 y2) (* y i))))
                     (if (<= c 3.4e+272) t_2 t_4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = t_1 * ((y1 * y4) - (y0 * y5));
	double t_3 = (b * y4) - (i * y5);
	double t_4 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (c <= -5.8e+257) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (c <= -2.2e+246) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (c <= -3.2e+150) {
		tmp = t_4;
	} else if (c <= -1.25e-260) {
		tmp = (t * (((z * ((c * i) - (a * b))) + (j * t_3)) + (y2 * ((a * y5) - (c * y4))))) + t_2;
	} else if (c <= 2.2e-173) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))));
	} else if (c <= 115000.0) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_3)) + (x * ((i * y1) - (b * y0))));
	} else if (c <= 1.35e+122) {
		tmp = y1 * (x * ((i * j) - ((a * y2) - ((y4 * t_1) / x))));
	} else if (c <= 1.02e+154) {
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * ((z * k) - (x * j))))) + t_2;
	} else if (c <= 3e+187) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (c <= 3.4e+272) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = t_1 * ((y1 * y4) - (y0 * y5))
    t_3 = (b * y4) - (i * y5)
    t_4 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    if (c <= (-5.8d+257)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (c <= (-2.2d+246)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (c <= (-3.2d+150)) then
        tmp = t_4
    else if (c <= (-1.25d-260)) then
        tmp = (t * (((z * ((c * i) - (a * b))) + (j * t_3)) + (y2 * ((a * y5) - (c * y4))))) + t_2
    else if (c <= 2.2d-173) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))))
    else if (c <= 115000.0d0) then
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_3)) + (x * ((i * y1) - (b * y0))))
    else if (c <= 1.35d+122) then
        tmp = y1 * (x * ((i * j) - ((a * y2) - ((y4 * t_1) / x))))
    else if (c <= 1.02d+154) then
        tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * ((z * k) - (x * j))))) + t_2
    else if (c <= 3d+187) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (c <= 3.4d+272) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = t_1 * ((y1 * y4) - (y0 * y5));
	double t_3 = (b * y4) - (i * y5);
	double t_4 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	double tmp;
	if (c <= -5.8e+257) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (c <= -2.2e+246) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (c <= -3.2e+150) {
		tmp = t_4;
	} else if (c <= -1.25e-260) {
		tmp = (t * (((z * ((c * i) - (a * b))) + (j * t_3)) + (y2 * ((a * y5) - (c * y4))))) + t_2;
	} else if (c <= 2.2e-173) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))));
	} else if (c <= 115000.0) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_3)) + (x * ((i * y1) - (b * y0))));
	} else if (c <= 1.35e+122) {
		tmp = y1 * (x * ((i * j) - ((a * y2) - ((y4 * t_1) / x))));
	} else if (c <= 1.02e+154) {
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * ((z * k) - (x * j))))) + t_2;
	} else if (c <= 3e+187) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (c <= 3.4e+272) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = t_1 * ((y1 * y4) - (y0 * y5))
	t_3 = (b * y4) - (i * y5)
	t_4 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	tmp = 0
	if c <= -5.8e+257:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif c <= -2.2e+246:
		tmp = x * (y * ((a * b) - (c * i)))
	elif c <= -3.2e+150:
		tmp = t_4
	elif c <= -1.25e-260:
		tmp = (t * (((z * ((c * i) - (a * b))) + (j * t_3)) + (y2 * ((a * y5) - (c * y4))))) + t_2
	elif c <= 2.2e-173:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))))
	elif c <= 115000.0:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_3)) + (x * ((i * y1) - (b * y0))))
	elif c <= 1.35e+122:
		tmp = y1 * (x * ((i * j) - ((a * y2) - ((y4 * t_1) / x))))
	elif c <= 1.02e+154:
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * ((z * k) - (x * j))))) + t_2
	elif c <= 3e+187:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif c <= 3.4e+272:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(t_1 * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_3 = Float64(Float64(b * y4) - Float64(i * y5))
	t_4 = 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)))))
	tmp = 0.0
	if (c <= -5.8e+257)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (c <= -2.2e+246)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (c <= -3.2e+150)
		tmp = t_4;
	elseif (c <= -1.25e-260)
		tmp = Float64(Float64(t * Float64(Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(j * t_3)) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))) + t_2);
	elseif (c <= 2.2e-173)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(y4 * Float64(Float64(Float64(j * Float64(y0 * y5)) / y4) - Float64(j * y1))))));
	elseif (c <= 115000.0)
		tmp = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * t_3)) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= 1.35e+122)
		tmp = Float64(y1 * Float64(x * Float64(Float64(i * j) - Float64(Float64(a * y2) - Float64(Float64(y4 * t_1) / x)))));
	elseif (c <= 1.02e+154)
		tmp = Float64(Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * y4)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))) + t_2);
	elseif (c <= 3e+187)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (c <= 3.4e+272)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = t_1 * ((y1 * y4) - (y0 * y5));
	t_3 = (b * y4) - (i * y5);
	t_4 = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (c <= -5.8e+257)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (c <= -2.2e+246)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (c <= -3.2e+150)
		tmp = t_4;
	elseif (c <= -1.25e-260)
		tmp = (t * (((z * ((c * i) - (a * b))) + (j * t_3)) + (y2 * ((a * y5) - (c * y4))))) + t_2;
	elseif (c <= 2.2e-173)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((z * ((a * y1) - (c * y0))) + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))));
	elseif (c <= 115000.0)
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * t_3)) + (x * ((i * y1) - (b * y0))));
	elseif (c <= 1.35e+122)
		tmp = y1 * (x * ((i * j) - ((a * y2) - ((y4 * t_1) / x))));
	elseif (c <= 1.02e+154)
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * ((z * k) - (x * j))))) + t_2;
	elseif (c <= 3e+187)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (c <= 3.4e+272)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = 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[c, -5.8e+257], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.2e+246], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.2e+150], t$95$4, If[LessEqual[c, -1.25e-260], N[(N[(t * N[(N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, 2.2e-173], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(N[(j * N[(y0 * y5), $MachinePrecision]), $MachinePrecision] / y4), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 115000.0], N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e+122], N[(y1 * N[(x * N[(N[(i * j), $MachinePrecision] - N[(N[(a * y2), $MachinePrecision] - N[(N[(y4 * t$95$1), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.02e+154], N[(N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[c, 3e+187], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+272], t$95$2, t$95$4]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -5.7999999999999998e257

   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 y3 around -inf 45.0%

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

   4. Taylor expanded in c around inf 80.0%

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

   if -5.7999999999999998e257 < c < -2.19999999999999988e246

   1. Initial program 16.7%

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

   3. Taylor expanded in x around inf 33.3%

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

   4. Taylor expanded in y around inf 100.0%

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

   if -2.19999999999999988e246 < c < -3.20000000000000016e150 or 3.4000000000000001e272 < c

   1. Initial program 8.0%

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

   3. Simplified 8.0%

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

   5. Taylor expanded in c around inf 77.0%

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

   if -3.20000000000000016e150 < c < -1.2500000000000001e-260

   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 t around inf 58.5%

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

   if -1.2500000000000001e-260 < c < 2.1999999999999999e-173

   1. Initial program 27.8%

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

   3. Taylor expanded in y3 around -inf 48.3%

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

   4. Taylor expanded in y4 around inf 52.8%

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

   if 2.1999999999999999e-173 < c < 115000

   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 j around inf 60.9%

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

   if 115000 < c < 1.3499999999999999e122

   1. Initial program 9.8%

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

   3. Taylor expanded in x around inf 38.1%

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

   4. Taylor expanded in y1 around inf 66.9%

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

   5. Taylor expanded in x around inf 66.9%

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

   if 1.3499999999999999e122 < c < 1.02000000000000007e154

   1. Initial program 37.3%

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

   3. Taylor expanded in b around inf 87.1%

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

   if 1.02000000000000007e154 < c < 2.9999999999999999e187

   1. Initial program 16.7%

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

   3. Taylor expanded in x around inf 0.0%

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

   4. Taylor expanded in c around inf 67.3%

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

   if 2.9999999999999999e187 < c < 3.4000000000000001e272

   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 x around inf 27.8%

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

   4. Taylor expanded in x around 0 62.1%

      \[\leadsto \color{blue}{\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+257}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+150}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -1.25 \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) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-173}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y4 \cdot \left(\frac{j \cdot \left(y0 \cdot y5\right)}{y4} - j \cdot y1\right)\right)\right)\\ \mathbf{elif}\;c \leq 115000:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+122}:\\ \;\;\;\;y1 \cdot \left(x \cdot \left(i \cdot j - \left(a \cdot y2 - \frac{y4 \cdot \left(k \cdot y2 - j \cdot y3\right)}{x}\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(t \cdot j - y \cdot k\right) \cdot y4\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+187}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+272}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;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)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.3% accurate, 0.5× speedup

Math

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

FPCore

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (((((t_1 * ((c * i) - (a * b))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((t * y2) - (y * y3)) * ((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 = c * (((i * t_1) + (y0 * t_2)) + (y4 * ((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 = (z * t) - (x * y)
	t_2 = (x * y2) - (z * y3)
	t_3 = (((((t_1 * ((c * i) - (a * b))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = c * (((i * t_1) + (y0 * t_2)) + (y4 * ((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(z * t) - Float64(x * y))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(t_1 * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(c * Float64(Float64(Float64(i * t_1) + Float64(y0 * t_2)) + Float64(y4 * 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 = (z * t) - (x * y);
	t_2 = (x * y2) - (z * y3);
	t_3 = (((((t_1 * ((c * i) - (a * b))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((t * j) - (y * k)) * ((b * y4) - (i * y5)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = c * (((i * t_1) + (y0 * t_2)) + (y4 * ((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[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(t$95$1 * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(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[(c * N[(N[(N[(i * t$95$1), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.1%

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

   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 1.0%

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

   5. Taylor expanded in c around inf 40.2%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.0%

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

Alternative 3: 25.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ t_2 := y3 \cdot y5 - x \cdot b\\ t_3 := j \cdot \left(y0 \cdot t\_2\right)\\ \mathbf{if}\;y2 \leq -1.55 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -8.2 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-134}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{-220}:\\ \;\;\;\;y0 \cdot \left(j \cdot t\_2\right)\\ \mathbf{elif}\;y2 \leq 7.6 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 1.58 \cdot 10^{-133}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 9 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 7.4 \cdot 10^{+180}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5)))))
        (t_2 (- (* y3 y5) (* x b)))
        (t_3 (* j (* y0 t_2))))
   (if (<= y2 -1.55e+245)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= y2 -8.2e+154)
       (* k (* y1 (* y2 y4)))
       (if (<= y2 -2.5e-134)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y2 -1.7e-206)
           t_1
           (if (<= y2 2.7e-265)
             (* c (* y0 (* z (- y3))))
             (if (<= y2 6.5e-220)
               (* y0 (* j t_2))
               (if (<= y2 7.6e-147)
                 t_1
                 (if (<= y2 1.58e-133)
                   t_3
                   (if (<= y2 4.6e-84)
                     (* a (* y (- (* x b) (* y3 y5))))
                     (if (<= y2 9e+21)
                       (* j (* y1 (* y3 (- y4))))
                       (if (<= y2 8.5e+46)
                         (* c (* y2 (- (* x y0) (* t y4))))
                         (if (<= y2 7.4e+180) t_3 t_1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = (y3 * y5) - (x * b);
	double t_3 = j * (y0 * t_2);
	double tmp;
	if (y2 <= -1.55e+245) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -8.2e+154) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -2.5e-134) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -1.7e-206) {
		tmp = t_1;
	} else if (y2 <= 2.7e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 6.5e-220) {
		tmp = y0 * (j * t_2);
	} else if (y2 <= 7.6e-147) {
		tmp = t_1;
	} else if (y2 <= 1.58e-133) {
		tmp = t_3;
	} else if (y2 <= 4.6e-84) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 9e+21) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 8.5e+46) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= 7.4e+180) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    t_2 = (y3 * y5) - (x * b)
    t_3 = j * (y0 * t_2)
    if (y2 <= (-1.55d+245)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y2 <= (-8.2d+154)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-2.5d-134)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= (-1.7d-206)) then
        tmp = t_1
    else if (y2 <= 2.7d-265) then
        tmp = c * (y0 * (z * -y3))
    else if (y2 <= 6.5d-220) then
        tmp = y0 * (j * t_2)
    else if (y2 <= 7.6d-147) then
        tmp = t_1
    else if (y2 <= 1.58d-133) then
        tmp = t_3
    else if (y2 <= 4.6d-84) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y2 <= 9d+21) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y2 <= 8.5d+46) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (y2 <= 7.4d+180) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = (y3 * y5) - (x * b);
	double t_3 = j * (y0 * t_2);
	double tmp;
	if (y2 <= -1.55e+245) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -8.2e+154) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -2.5e-134) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -1.7e-206) {
		tmp = t_1;
	} else if (y2 <= 2.7e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 6.5e-220) {
		tmp = y0 * (j * t_2);
	} else if (y2 <= 7.6e-147) {
		tmp = t_1;
	} else if (y2 <= 1.58e-133) {
		tmp = t_3;
	} else if (y2 <= 4.6e-84) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 9e+21) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 8.5e+46) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (y2 <= 7.4e+180) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	t_2 = (y3 * y5) - (x * b)
	t_3 = j * (y0 * t_2)
	tmp = 0
	if y2 <= -1.55e+245:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y2 <= -8.2e+154:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -2.5e-134:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= -1.7e-206:
		tmp = t_1
	elif y2 <= 2.7e-265:
		tmp = c * (y0 * (z * -y3))
	elif y2 <= 6.5e-220:
		tmp = y0 * (j * t_2)
	elif y2 <= 7.6e-147:
		tmp = t_1
	elif y2 <= 1.58e-133:
		tmp = t_3
	elif y2 <= 4.6e-84:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y2 <= 9e+21:
		tmp = j * (y1 * (y3 * -y4))
	elif y2 <= 8.5e+46:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif y2 <= 7.4e+180:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	t_2 = Float64(Float64(y3 * y5) - Float64(x * b))
	t_3 = Float64(j * Float64(y0 * t_2))
	tmp = 0.0
	if (y2 <= -1.55e+245)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y2 <= -8.2e+154)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -2.5e-134)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= -1.7e-206)
		tmp = t_1;
	elseif (y2 <= 2.7e-265)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y2 <= 6.5e-220)
		tmp = Float64(y0 * Float64(j * t_2));
	elseif (y2 <= 7.6e-147)
		tmp = t_1;
	elseif (y2 <= 1.58e-133)
		tmp = t_3;
	elseif (y2 <= 4.6e-84)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= 9e+21)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 8.5e+46)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (y2 <= 7.4e+180)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	t_2 = (y3 * y5) - (x * b);
	t_3 = j * (y0 * t_2);
	tmp = 0.0;
	if (y2 <= -1.55e+245)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y2 <= -8.2e+154)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -2.5e-134)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= -1.7e-206)
		tmp = t_1;
	elseif (y2 <= 2.7e-265)
		tmp = c * (y0 * (z * -y3));
	elseif (y2 <= 6.5e-220)
		tmp = y0 * (j * t_2);
	elseif (y2 <= 7.6e-147)
		tmp = t_1;
	elseif (y2 <= 1.58e-133)
		tmp = t_3;
	elseif (y2 <= 4.6e-84)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y2 <= 9e+21)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y2 <= 8.5e+46)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (y2 <= 7.4e+180)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.55e+245], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8.2e+154], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.5e-134], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.7e-206], t$95$1, If[LessEqual[y2, 2.7e-265], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.5e-220], N[(y0 * N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.6e-147], t$95$1, If[LessEqual[y2, 1.58e-133], t$95$3, If[LessEqual[y2, 4.6e-84], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9e+21], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8.5e+46], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.4e+180], t$95$3, t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y2 < -1.5499999999999999e245

   1. Initial program 38.9%

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

   3. Taylor expanded in y2 around inf 83.3%

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

   4. Taylor expanded in x around inf 72.6%

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

   if -1.5499999999999999e245 < y2 < -8.2e154

   1. Initial program 13.0%

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

   3. Taylor expanded in x around inf 30.4%

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

   4. Taylor expanded in y1 around inf 35.8%

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

   5. Taylor expanded in k around inf 52.6%

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

   if -8.2e154 < y2 < -2.5000000000000002e-134

   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 x around inf 42.2%

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

   4. Taylor expanded in b around inf 39.6%

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

   if -2.5000000000000002e-134 < y2 < -1.69999999999999992e-206 or 6.50000000000000005e-220 < y2 < 7.60000000000000055e-147 or 7.4000000000000003e180 < y2

   1. Initial program 25.3%

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

   3. Simplified 25.3%

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

   5. Taylor expanded in a around inf 42.6%

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

   6. Taylor expanded in y3 around inf 54.6%

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

   if -1.69999999999999992e-206 < y2 < 2.7000000000000002e-265

   1. Initial program 29.3%

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

   3. Taylor expanded in y0 around inf 48.0%

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

   4. Taylor expanded in c around inf 59.9%

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

   5. Taylor expanded in x around 0 65.5%

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

      1. associate-*r* 65.5%

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

      2. mul-1-neg 65.5%

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

   7. Simplified 65.5%

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

   if 2.7000000000000002e-265 < y2 < 6.50000000000000005e-220

   1. Initial program 10.9%

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

   3. Taylor expanded in y0 around inf 60.1%

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

   4. Taylor expanded in j around inf 60.3%

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

   if 7.60000000000000055e-147 < y2 < 1.58e-133 or 8.4999999999999996e46 < y2 < 7.4000000000000003e180

   1. Initial program 17.1%

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

   3. Taylor expanded in y0 around inf 32.1%

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

   4. Taylor expanded in j around inf 59.3%

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

   if 1.58e-133 < y2 < 4.59999999999999961e-84

   1. Initial program 19.9%

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

   3. Simplified 19.9%

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

   5. Taylor expanded in a around inf 60.7%

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

   6. Taylor expanded in y around inf 61.7%

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

   if 4.59999999999999961e-84 < y2 < 9e21

   1. Initial program 6.4%

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

   3. Taylor expanded in x around inf 36.3%

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

   4. Taylor expanded in y1 around inf 47.5%

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

   5. Taylor expanded in y3 around inf 42.1%

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

      1. associate-*r* 42.1%

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

      2. neg-mul-1 42.1%

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

   7. Simplified 42.1%

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

   if 9e21 < y2 < 8.4999999999999996e46

   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 y2 around inf 66.7%

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

   4. Taylor expanded in c around inf 67.1%

      \[\leadsto \color{blue}{c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.55 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -8.2 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-134}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -1.7 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.7 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{-220}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 7.6 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.58 \cdot 10^{-133}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 4.6 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 9 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 7.4 \cdot 10^{+180}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 26.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ t_2 := y3 \cdot y5 - x \cdot b\\ t_3 := j \cdot \left(y0 \cdot t\_2\right)\\ \mathbf{if}\;y2 \leq -1.5 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -9.6 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-147}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y2 \leq -3.1 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-220}:\\ \;\;\;\;y0 \cdot \left(j \cdot t\_2\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 4.25 \cdot 10^{-137}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y2 \leq 2.35 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.9 \cdot 10^{+181}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5)))))
        (t_2 (- (* y3 y5) (* x b)))
        (t_3 (* j (* y0 t_2))))
   (if (<= y2 -1.5e+245)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= y2 -9.6e+154)
       (* k (* y1 (* y2 y4)))
       (if (<= y2 -1.35e+116)
         (* y0 (* x (- (* c y2) (* b j))))
         (if (<= y2 -1.8e-64)
           (* x (* y (- (* a b) (* c i))))
           (if (<= y2 -4.6e-147)
             t_3
             (if (<= y2 -3.1e-206)
               t_1
               (if (<= y2 2.8e-265)
                 (* c (* y0 (* z (- y3))))
                 (if (<= y2 4.5e-220)
                   (* y0 (* j t_2))
                   (if (<= y2 1.25e-146)
                     t_1
                     (if (<= y2 4.25e-137)
                       t_3
                       (if (<= y2 2.35e-73)
                         (* a (* y (- (* x b) (* y3 y5))))
                         (if (<= y2 3.9e+181) t_3 t_1))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = (y3 * y5) - (x * b);
	double t_3 = j * (y0 * t_2);
	double tmp;
	if (y2 <= -1.5e+245) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -9.6e+154) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -1.35e+116) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y2 <= -1.8e-64) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= -4.6e-147) {
		tmp = t_3;
	} else if (y2 <= -3.1e-206) {
		tmp = t_1;
	} else if (y2 <= 2.8e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 4.5e-220) {
		tmp = y0 * (j * t_2);
	} else if (y2 <= 1.25e-146) {
		tmp = t_1;
	} else if (y2 <= 4.25e-137) {
		tmp = t_3;
	} else if (y2 <= 2.35e-73) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 3.9e+181) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    t_2 = (y3 * y5) - (x * b)
    t_3 = j * (y0 * t_2)
    if (y2 <= (-1.5d+245)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y2 <= (-9.6d+154)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-1.35d+116)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y2 <= (-1.8d-64)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y2 <= (-4.6d-147)) then
        tmp = t_3
    else if (y2 <= (-3.1d-206)) then
        tmp = t_1
    else if (y2 <= 2.8d-265) then
        tmp = c * (y0 * (z * -y3))
    else if (y2 <= 4.5d-220) then
        tmp = y0 * (j * t_2)
    else if (y2 <= 1.25d-146) then
        tmp = t_1
    else if (y2 <= 4.25d-137) then
        tmp = t_3
    else if (y2 <= 2.35d-73) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y2 <= 3.9d+181) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = (y3 * y5) - (x * b);
	double t_3 = j * (y0 * t_2);
	double tmp;
	if (y2 <= -1.5e+245) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -9.6e+154) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -1.35e+116) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y2 <= -1.8e-64) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y2 <= -4.6e-147) {
		tmp = t_3;
	} else if (y2 <= -3.1e-206) {
		tmp = t_1;
	} else if (y2 <= 2.8e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 4.5e-220) {
		tmp = y0 * (j * t_2);
	} else if (y2 <= 1.25e-146) {
		tmp = t_1;
	} else if (y2 <= 4.25e-137) {
		tmp = t_3;
	} else if (y2 <= 2.35e-73) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 3.9e+181) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	t_2 = (y3 * y5) - (x * b)
	t_3 = j * (y0 * t_2)
	tmp = 0
	if y2 <= -1.5e+245:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y2 <= -9.6e+154:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -1.35e+116:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y2 <= -1.8e-64:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y2 <= -4.6e-147:
		tmp = t_3
	elif y2 <= -3.1e-206:
		tmp = t_1
	elif y2 <= 2.8e-265:
		tmp = c * (y0 * (z * -y3))
	elif y2 <= 4.5e-220:
		tmp = y0 * (j * t_2)
	elif y2 <= 1.25e-146:
		tmp = t_1
	elif y2 <= 4.25e-137:
		tmp = t_3
	elif y2 <= 2.35e-73:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y2 <= 3.9e+181:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	t_2 = Float64(Float64(y3 * y5) - Float64(x * b))
	t_3 = Float64(j * Float64(y0 * t_2))
	tmp = 0.0
	if (y2 <= -1.5e+245)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y2 <= -9.6e+154)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -1.35e+116)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y2 <= -1.8e-64)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y2 <= -4.6e-147)
		tmp = t_3;
	elseif (y2 <= -3.1e-206)
		tmp = t_1;
	elseif (y2 <= 2.8e-265)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y2 <= 4.5e-220)
		tmp = Float64(y0 * Float64(j * t_2));
	elseif (y2 <= 1.25e-146)
		tmp = t_1;
	elseif (y2 <= 4.25e-137)
		tmp = t_3;
	elseif (y2 <= 2.35e-73)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= 3.9e+181)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	t_2 = (y3 * y5) - (x * b);
	t_3 = j * (y0 * t_2);
	tmp = 0.0;
	if (y2 <= -1.5e+245)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y2 <= -9.6e+154)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -1.35e+116)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y2 <= -1.8e-64)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y2 <= -4.6e-147)
		tmp = t_3;
	elseif (y2 <= -3.1e-206)
		tmp = t_1;
	elseif (y2 <= 2.8e-265)
		tmp = c * (y0 * (z * -y3));
	elseif (y2 <= 4.5e-220)
		tmp = y0 * (j * t_2);
	elseif (y2 <= 1.25e-146)
		tmp = t_1;
	elseif (y2 <= 4.25e-137)
		tmp = t_3;
	elseif (y2 <= 2.35e-73)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y2 <= 3.9e+181)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.5e+245], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -9.6e+154], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.35e+116], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.8e-64], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -4.6e-147], t$95$3, If[LessEqual[y2, -3.1e-206], t$95$1, If[LessEqual[y2, 2.8e-265], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.5e-220], N[(y0 * N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.25e-146], t$95$1, If[LessEqual[y2, 4.25e-137], t$95$3, If[LessEqual[y2, 2.35e-73], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.9e+181], t$95$3, t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -1.5e245

   1. Initial program 38.9%

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

   3. Taylor expanded in y2 around inf 83.3%

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

   4. Taylor expanded in x around inf 72.6%

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

   if -1.5e245 < y2 < -9.60000000000000059e154

   1. Initial program 13.0%

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

   3. Taylor expanded in x around inf 30.4%

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

   4. Taylor expanded in y1 around inf 35.8%

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

   5. Taylor expanded in k around inf 52.6%

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

   if -9.60000000000000059e154 < y2 < -1.35e116

   1. Initial program 37.5%

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

   3. Taylor expanded in y0 around inf 37.7%

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

   4. Taylor expanded in x around inf 63.9%

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

   if -1.35e116 < y2 < -1.7999999999999999e-64

   1. Initial program 19.1%

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

   3. Taylor expanded in x around inf 40.8%

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

   4. Taylor expanded in y around inf 44.9%

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

   if -1.7999999999999999e-64 < y2 < -4.59999999999999981e-147 or 1.24999999999999989e-146 < y2 < 4.2500000000000001e-137 or 2.34999999999999997e-73 < y2 < 3.9e181

   1. Initial program 17.5%

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

   3. Taylor expanded in y0 around inf 34.2%

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

   4. Taylor expanded in j around inf 46.7%

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

   if -4.59999999999999981e-147 < y2 < -3.1000000000000003e-206 or 4.49999999999999967e-220 < y2 < 1.24999999999999989e-146 or 3.9e181 < y2

   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 41.5%

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

   6. Taylor expanded in y3 around inf 55.6%

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

   if -3.1000000000000003e-206 < y2 < 2.80000000000000023e-265

   1. Initial program 29.3%

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

   3. Taylor expanded in y0 around inf 48.0%

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

   4. Taylor expanded in c around inf 59.9%

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

   5. Taylor expanded in x around 0 65.5%

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

      1. associate-*r* 65.5%

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

      2. mul-1-neg 65.5%

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

   7. Simplified 65.5%

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

   if 2.80000000000000023e-265 < y2 < 4.49999999999999967e-220

   1. Initial program 10.9%

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

   3. Taylor expanded in y0 around inf 60.1%

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

   4. Taylor expanded in j around inf 60.3%

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

   if 4.2500000000000001e-137 < y2 < 2.34999999999999997e-73

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   5. Taylor expanded in a around inf 63.1%

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

   6. Taylor expanded in y around inf 64.1%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.5 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -9.6 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1.35 \cdot 10^{+116}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y2 \leq -1.8 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y2 \leq -4.6 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -3.1 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.8 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{-220}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.25 \cdot 10^{-146}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 4.25 \cdot 10^{-137}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.35 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 3.9 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ t_2 := y0 \cdot y5 - y1 \cdot y4\\ t_3 := y \cdot \left(c \cdot y4 - a \cdot y5\right)\\ t_4 := x \cdot y2 - z \cdot y3\\ t_5 := c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t\_4\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_6 := z \cdot \left(a \cdot y1 - c \cdot y0\right)\\ t_7 := z \cdot k - x \cdot j\\ \mathbf{if}\;i \leq -1.06 \cdot 10^{+216}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{+88}:\\ \;\;\;\;y3 \cdot \left(\left(t\_6 + j \cdot t\_2\right) + t\_3\right)\\ \mathbf{elif}\;i \leq -2.05 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(t \cdot j - y \cdot k\right) \cdot y4\right) + y0 \cdot t\_7\right) + t\_1\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-76}:\\ \;\;\;\;y3 \cdot \left(t\_3 + \left(t\_6 + y4 \cdot \left(\frac{j \cdot \left(y0 \cdot y5\right)}{y4} - j \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot t\_2 + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 25500000:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot t\_4\right) + b \cdot t\_7\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+125}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))
        (t_2 (- (* y0 y5) (* y1 y4)))
        (t_3 (* y (- (* c y4) (* a y5))))
        (t_4 (- (* x y2) (* z y3)))
        (t_5
         (*
          c
          (+
           (+ (* i (- (* z t) (* x y))) (* y0 t_4))
           (* y4 (- (* y y3) (* t y2))))))
        (t_6 (* z (- (* a y1) (* c y0))))
        (t_7 (- (* z k) (* x j))))
   (if (<= i -1.06e+216)
     t_5
     (if (<= i -2.15e+88)
       (* y3 (+ (+ t_6 (* j t_2)) t_3))
       (if (<= i -2.05e-31)
         (+
          (*
           b
           (+
            (+ (* a (- (* x y) (* z t))) (* (- (* t j) (* y k)) y4))
            (* y0 t_7)))
          t_1)
         (if (<= i -2.45e-76)
           (* y3 (+ t_3 (+ t_6 (* y4 (- (/ (* j (* y0 y5)) y4) (* j y1))))))
           (if (<= i 9e-263)
             t_1
             (if (<= i 3.8e-120)
               (*
                j
                (+
                 (+ (* y3 t_2) (* t (- (* b y4) (* i y5))))
                 (* x (- (* i y1) (* b y0)))))
               (if (<= i 25500000.0)
                 (*
                  y0
                  (+ (+ (* y5 (- (* j y3) (* k y2))) (* c t_4)) (* b t_7)))
                 (if (<= i 1.25e+125)
                   t_5
                   (* i (* t (- (* z c) (* 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 t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = y * ((c * y4) - (a * y5));
	double t_4 = (x * y2) - (z * y3);
	double t_5 = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * ((y * y3) - (t * y2))));
	double t_6 = z * ((a * y1) - (c * y0));
	double t_7 = (z * k) - (x * j);
	double tmp;
	if (i <= -1.06e+216) {
		tmp = t_5;
	} else if (i <= -2.15e+88) {
		tmp = y3 * ((t_6 + (j * t_2)) + t_3);
	} else if (i <= -2.05e-31) {
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * t_7))) + t_1;
	} else if (i <= -2.45e-76) {
		tmp = y3 * (t_3 + (t_6 + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))));
	} else if (i <= 9e-263) {
		tmp = t_1;
	} else if (i <= 3.8e-120) {
		tmp = j * (((y3 * t_2) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (i <= 25500000.0) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * t_7));
	} else if (i <= 1.25e+125) {
		tmp = t_5;
	} else {
		tmp = i * (t * ((z * c) - (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
    t_2 = (y0 * y5) - (y1 * y4)
    t_3 = y * ((c * y4) - (a * y5))
    t_4 = (x * y2) - (z * y3)
    t_5 = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * ((y * y3) - (t * y2))))
    t_6 = z * ((a * y1) - (c * y0))
    t_7 = (z * k) - (x * j)
    if (i <= (-1.06d+216)) then
        tmp = t_5
    else if (i <= (-2.15d+88)) then
        tmp = y3 * ((t_6 + (j * t_2)) + t_3)
    else if (i <= (-2.05d-31)) then
        tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * t_7))) + t_1
    else if (i <= (-2.45d-76)) then
        tmp = y3 * (t_3 + (t_6 + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))))
    else if (i <= 9d-263) then
        tmp = t_1
    else if (i <= 3.8d-120) then
        tmp = j * (((y3 * t_2) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    else if (i <= 25500000.0d0) then
        tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * t_7))
    else if (i <= 1.25d+125) then
        tmp = t_5
    else
        tmp = i * (t * ((z * c) - (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 t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double t_2 = (y0 * y5) - (y1 * y4);
	double t_3 = y * ((c * y4) - (a * y5));
	double t_4 = (x * y2) - (z * y3);
	double t_5 = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * ((y * y3) - (t * y2))));
	double t_6 = z * ((a * y1) - (c * y0));
	double t_7 = (z * k) - (x * j);
	double tmp;
	if (i <= -1.06e+216) {
		tmp = t_5;
	} else if (i <= -2.15e+88) {
		tmp = y3 * ((t_6 + (j * t_2)) + t_3);
	} else if (i <= -2.05e-31) {
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * t_7))) + t_1;
	} else if (i <= -2.45e-76) {
		tmp = y3 * (t_3 + (t_6 + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))));
	} else if (i <= 9e-263) {
		tmp = t_1;
	} else if (i <= 3.8e-120) {
		tmp = j * (((y3 * t_2) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else if (i <= 25500000.0) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * t_7));
	} else if (i <= 1.25e+125) {
		tmp = t_5;
	} else {
		tmp = i * (t * ((z * c) - (j * y5)));
	}
	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)) * ((y1 * y4) - (y0 * y5))
	t_2 = (y0 * y5) - (y1 * y4)
	t_3 = y * ((c * y4) - (a * y5))
	t_4 = (x * y2) - (z * y3)
	t_5 = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * ((y * y3) - (t * y2))))
	t_6 = z * ((a * y1) - (c * y0))
	t_7 = (z * k) - (x * j)
	tmp = 0
	if i <= -1.06e+216:
		tmp = t_5
	elif i <= -2.15e+88:
		tmp = y3 * ((t_6 + (j * t_2)) + t_3)
	elif i <= -2.05e-31:
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * t_7))) + t_1
	elif i <= -2.45e-76:
		tmp = y3 * (t_3 + (t_6 + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))))
	elif i <= 9e-263:
		tmp = t_1
	elif i <= 3.8e-120:
		tmp = j * (((y3 * t_2) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	elif i <= 25500000.0:
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * t_7))
	elif i <= 1.25e+125:
		tmp = t_5
	else:
		tmp = i * (t * ((z * c) - (j * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	t_2 = Float64(Float64(y0 * y5) - Float64(y1 * y4))
	t_3 = Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))
	t_4 = Float64(Float64(x * y2) - Float64(z * y3))
	t_5 = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_4)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_6 = Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))
	t_7 = Float64(Float64(z * k) - Float64(x * j))
	tmp = 0.0
	if (i <= -1.06e+216)
		tmp = t_5;
	elseif (i <= -2.15e+88)
		tmp = Float64(y3 * Float64(Float64(t_6 + Float64(j * t_2)) + t_3));
	elseif (i <= -2.05e-31)
		tmp = Float64(Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * y4)) + Float64(y0 * t_7))) + t_1);
	elseif (i <= -2.45e-76)
		tmp = Float64(y3 * Float64(t_3 + Float64(t_6 + Float64(y4 * Float64(Float64(Float64(j * Float64(y0 * y5)) / y4) - Float64(j * y1))))));
	elseif (i <= 9e-263)
		tmp = t_1;
	elseif (i <= 3.8e-120)
		tmp = Float64(j * Float64(Float64(Float64(y3 * t_2) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (i <= 25500000.0)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * t_4)) + Float64(b * t_7)));
	elseif (i <= 1.25e+125)
		tmp = t_5;
	else
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * 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)
	t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	t_2 = (y0 * y5) - (y1 * y4);
	t_3 = y * ((c * y4) - (a * y5));
	t_4 = (x * y2) - (z * y3);
	t_5 = c * (((i * ((z * t) - (x * y))) + (y0 * t_4)) + (y4 * ((y * y3) - (t * y2))));
	t_6 = z * ((a * y1) - (c * y0));
	t_7 = (z * k) - (x * j);
	tmp = 0.0;
	if (i <= -1.06e+216)
		tmp = t_5;
	elseif (i <= -2.15e+88)
		tmp = y3 * ((t_6 + (j * t_2)) + t_3);
	elseif (i <= -2.05e-31)
		tmp = (b * (((a * ((x * y) - (z * t))) + (((t * j) - (y * k)) * y4)) + (y0 * t_7))) + t_1;
	elseif (i <= -2.45e-76)
		tmp = y3 * (t_3 + (t_6 + (y4 * (((j * (y0 * y5)) / y4) - (j * y1)))));
	elseif (i <= 9e-263)
		tmp = t_1;
	elseif (i <= 3.8e-120)
		tmp = j * (((y3 * t_2) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	elseif (i <= 25500000.0)
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_4)) + (b * t_7));
	elseif (i <= 1.25e+125)
		tmp = t_5;
	else
		tmp = i * (t * ((z * c) - (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_] := Block[{t$95$1 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.06e+216], t$95$5, If[LessEqual[i, -2.15e+88], N[(y3 * N[(N[(t$95$6 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.05e-31], N[(N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * y4), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[i, -2.45e-76], N[(y3 * N[(t$95$3 + N[(t$95$6 + N[(y4 * N[(N[(N[(j * N[(y0 * y5), $MachinePrecision]), $MachinePrecision] / y4), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e-263], t$95$1, If[LessEqual[i, 3.8e-120], N[(j * N[(N[(N[(y3 * t$95$2), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 25500000.0], N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(b * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e+125], t$95$5, N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -1.06e216 or 2.55e7 < i < 1.24999999999999991e125

   1. Initial program 5.1%

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

   3. Simplified 10.3%

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

   5. Taylor expanded in c around inf 59.2%

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

   if -1.06e216 < i < -2.14999999999999987e88

   1. Initial program 9.8%

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

   3. Taylor expanded in y3 around -inf 53.7%

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

   if -2.14999999999999987e88 < i < -2.0499999999999998e-31

   1. Initial program 15.0%

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

   3. Taylor expanded in b around inf 66.9%

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

   if -2.0499999999999998e-31 < i < -2.44999999999999986e-76

   1. Initial program 10.5%

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

   3. Taylor expanded in y3 around -inf 50.6%

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

   4. Taylor expanded in y4 around inf 60.6%

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

   if -2.44999999999999986e-76 < i < 8.9999999999999994e-263

   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 x around inf 52.8%

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

   4. Taylor expanded in x around 0 58.1%

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

   if 8.9999999999999994e-263 < i < 3.7999999999999997e-120

   1. Initial program 36.8%

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

   3. Taylor expanded in j around inf 54.2%

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

   if 3.7999999999999997e-120 < i < 2.55e7

   1. Initial program 23.3%

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

   3. Taylor expanded in y0 around inf 63.8%

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

   if 1.24999999999999991e125 < i

   1. Initial program 18.2%

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

   3. Taylor expanded in t around inf 39.4%

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

   4. Taylor expanded in i around -inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. *-commutative 55.4%

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

      3. distribute-rgt-neg-in 55.4%

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

      4. +-commutative 55.4%

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

      5. mul-1-neg 55.4%

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

      6. unsub-neg 55.4%

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

      7. *-commutative 55.4%

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

   6. Simplified 55.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.06 \cdot 10^{+216}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{+88}:\\ \;\;\;\;y3 \cdot \left(\left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq -2.05 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(t \cdot j - y \cdot k\right) \cdot y4\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-76}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + y4 \cdot \left(\frac{j \cdot \left(y0 \cdot y5\right)}{y4} - j \cdot y1\right)\right)\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-263}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 25500000:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+125}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y1 \cdot y4 - y0 \cdot y5\\ t_3 := t\_1 \cdot t\_2\\ \mathbf{if}\;k \leq -6 \cdot 10^{+98}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;k \leq -1.7 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.1 \cdot 10^{-256}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot t\_2 + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1 \cdot 10^{-280}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 2.45 \cdot 10^{-290}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right) + y1 \cdot t\_1\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+186}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* y1 y4) (* y0 y5)))
        (t_3 (* t_1 t_2)))
   (if (<= k -6e+98)
     t_3
     (if (<= k -1.7e-108)
       (*
        c
        (+
         (+ (* i (- (* z t) (* x y))) (* y0 (- (* x y2) (* z y3))))
         (* y4 (- (* y y3) (* t y2)))))
       (if (<= k -3.1e-256)
         (*
          y2
          (+
           (+ (* k t_2) (* x (- (* c y0) (* a y1))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= k -1e-280)
           (* i (* t (- (* z c) (* j y5))))
           (if (<= k 2.45e-290)
             (* y4 (+ (* t (- (* b j) (* c y2))) (* y1 t_1)))
             (if (<= k 1.3e-157)
               (* b (* x (- (* y a) (* j y0))))
               (if (<= k 7.2e+186)
                 (*
                  j
                  (+
                   (+
                    (* y3 (- (* y0 y5) (* y1 y4)))
                    (* t (- (* b y4) (* i y5))))
                   (* x (- (* i y1) (* b y0)))))
                 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = t_1 * t_2;
	double tmp;
	if (k <= -6e+98) {
		tmp = t_3;
	} else if (k <= -1.7e-108) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (k <= -3.1e-256) {
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (k <= -1e-280) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 2.45e-290) {
		tmp = y4 * ((t * ((b * j) - (c * y2))) + (y1 * t_1));
	} else if (k <= 1.3e-157) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 7.2e+186) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (y1 * y4) - (y0 * y5)
    t_3 = t_1 * t_2
    if (k <= (-6d+98)) then
        tmp = t_3
    else if (k <= (-1.7d-108)) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
    else if (k <= (-3.1d-256)) then
        tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
    else if (k <= (-1d-280)) then
        tmp = i * (t * ((z * c) - (j * y5)))
    else if (k <= 2.45d-290) then
        tmp = y4 * ((t * ((b * j) - (c * y2))) + (y1 * t_1))
    else if (k <= 1.3d-157) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (k <= 7.2d+186) then
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    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 = (k * y2) - (j * y3);
	double t_2 = (y1 * y4) - (y0 * y5);
	double t_3 = t_1 * t_2;
	double tmp;
	if (k <= -6e+98) {
		tmp = t_3;
	} else if (k <= -1.7e-108) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	} else if (k <= -3.1e-256) {
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	} else if (k <= -1e-280) {
		tmp = i * (t * ((z * c) - (j * y5)));
	} else if (k <= 2.45e-290) {
		tmp = y4 * ((t * ((b * j) - (c * y2))) + (y1 * t_1));
	} else if (k <= 1.3e-157) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (k <= 7.2e+186) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	} 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 = (k * y2) - (j * y3)
	t_2 = (y1 * y4) - (y0 * y5)
	t_3 = t_1 * t_2
	tmp = 0
	if k <= -6e+98:
		tmp = t_3
	elif k <= -1.7e-108:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))))
	elif k <= -3.1e-256:
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))))
	elif k <= -1e-280:
		tmp = i * (t * ((z * c) - (j * y5)))
	elif k <= 2.45e-290:
		tmp = y4 * ((t * ((b * j) - (c * y2))) + (y1 * t_1))
	elif k <= 1.3e-157:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif k <= 7.2e+186:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(y1 * y4) - Float64(y0 * y5))
	t_3 = Float64(t_1 * t_2)
	tmp = 0.0
	if (k <= -6e+98)
		tmp = t_3;
	elseif (k <= -1.7e-108)
		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 (k <= -3.1e-256)
		tmp = Float64(y2 * Float64(Float64(Float64(k * t_2) + Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (k <= -1e-280)
		tmp = Float64(i * Float64(t * Float64(Float64(z * c) - Float64(j * y5))));
	elseif (k <= 2.45e-290)
		tmp = Float64(y4 * Float64(Float64(t * Float64(Float64(b * j) - Float64(c * y2))) + Float64(y1 * t_1)));
	elseif (k <= 1.3e-157)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (k <= 7.2e+186)
		tmp = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))));
	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 = (k * y2) - (j * y3);
	t_2 = (y1 * y4) - (y0 * y5);
	t_3 = t_1 * t_2;
	tmp = 0.0;
	if (k <= -6e+98)
		tmp = t_3;
	elseif (k <= -1.7e-108)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * ((x * y2) - (z * y3)))) + (y4 * ((y * y3) - (t * y2))));
	elseif (k <= -3.1e-256)
		tmp = y2 * (((k * t_2) + (x * ((c * y0) - (a * y1)))) + (t * ((a * y5) - (c * y4))));
	elseif (k <= -1e-280)
		tmp = i * (t * ((z * c) - (j * y5)));
	elseif (k <= 2.45e-290)
		tmp = y4 * ((t * ((b * j) - (c * y2))) + (y1 * t_1));
	elseif (k <= 1.3e-157)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (k <= 7.2e+186)
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * t$95$2), $MachinePrecision]}, If[LessEqual[k, -6e+98], t$95$3, If[LessEqual[k, -1.7e-108], 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[k, -3.1e-256], N[(y2 * N[(N[(N[(k * t$95$2), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -1e-280], N[(i * N[(t * N[(N[(z * c), $MachinePrecision] - N[(j * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.45e-290], N[(y4 * N[(N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.3e-157], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.2e+186], N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -6.0000000000000003e98 or 7.2000000000000003e186 < k

   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 x around inf 44.4%

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

   4. Taylor expanded in x around 0 62.5%

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

   if -6.0000000000000003e98 < k < -1.70000000000000001e-108

   1. Initial program 21.2%

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

   3. Simplified 23.3%

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

   5. Taylor expanded in c around inf 59.7%

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

   if -1.70000000000000001e-108 < k < -3.09999999999999986e-256

   1. Initial program 28.7%

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

   3. Taylor expanded in y2 around inf 62.1%

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

   if -3.09999999999999986e-256 < k < -9.9999999999999996e-281

   1. Initial program 50.5%

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

   3. Taylor expanded in t around inf 60.0%

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

   4. Taylor expanded in i around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. *-commutative 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. +-commutative 80.3%

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

      5. mul-1-neg 80.3%

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

      6. unsub-neg 80.3%

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

      7. *-commutative 80.3%

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

   6. Simplified 80.3%

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

   if -9.9999999999999996e-281 < k < 2.45e-290

   1. Initial program 28.6%

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

   3. Taylor expanded in t around inf 57.2%

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

   4. Taylor expanded in y4 around inf 58.4%

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

   if 2.45e-290 < k < 1.29999999999999994e-157

   1. Initial program 25.2%

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

   3. Taylor expanded in x around inf 53.6%

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

   4. Taylor expanded in b around inf 61.5%

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

   if 1.29999999999999994e-157 < k < 7.2000000000000003e186

   1. Initial program 16.5%

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

   3. Taylor expanded in j around inf 48.9%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6 \cdot 10^{+98}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;k \leq -1.7 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq -3.1 \cdot 10^{-256}:\\ \;\;\;\;y2 \cdot \left(\left(k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -1 \cdot 10^{-280}:\\ \;\;\;\;i \cdot \left(t \cdot \left(z \cdot c - j \cdot y5\right)\right)\\ \mathbf{elif}\;k \leq 2.45 \cdot 10^{-290}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+186}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 26.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ t_2 := y3 \cdot y5 - x \cdot b\\ \mathbf{if}\;y2 \leq -1.65 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -1.35 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-219}:\\ \;\;\;\;y0 \cdot \left(j \cdot t\_2\right)\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y2 \leq 1.75 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(y0 \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5))))) (t_2 (- (* y3 y5) (* x b))))
   (if (<= y2 -1.65e+245)
     (* x (* y2 (- (* c y0) (* a y1))))
     (if (<= y2 -8e+154)
       (* k (* y1 (* y2 y4)))
       (if (<= y2 -3.8e-140)
         (* b (* x (- (* y a) (* j y0))))
         (if (<= y2 -1.35e-206)
           t_1
           (if (<= y2 2.6e-265)
             (* c (* y0 (* z (- y3))))
             (if (<= y2 1.7e-219)
               (* y0 (* j t_2))
               (if (<= y2 2.3e-139)
                 t_1
                 (if (<= y2 1.75e-85)
                   (* a (* y (- (* x b) (* y3 y5))))
                   (if (<= y2 2.4e+41)
                     (* y1 (* j (- (* x i) (* y3 y4))))
                     (if (<= y2 4.5e+181) (* j (* y0 t_2)) t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = (y3 * y5) - (x * b);
	double tmp;
	if (y2 <= -1.65e+245) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -8e+154) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -3.8e-140) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -1.35e-206) {
		tmp = t_1;
	} else if (y2 <= 2.6e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 1.7e-219) {
		tmp = y0 * (j * t_2);
	} else if (y2 <= 2.3e-139) {
		tmp = t_1;
	} else if (y2 <= 1.75e-85) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 2.4e+41) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y2 <= 4.5e+181) {
		tmp = j * (y0 * t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    t_2 = (y3 * y5) - (x * b)
    if (y2 <= (-1.65d+245)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (y2 <= (-8d+154)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-3.8d-140)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (y2 <= (-1.35d-206)) then
        tmp = t_1
    else if (y2 <= 2.6d-265) then
        tmp = c * (y0 * (z * -y3))
    else if (y2 <= 1.7d-219) then
        tmp = y0 * (j * t_2)
    else if (y2 <= 2.3d-139) then
        tmp = t_1
    else if (y2 <= 1.75d-85) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y2 <= 2.4d+41) then
        tmp = y1 * (j * ((x * i) - (y3 * y4)))
    else if (y2 <= 4.5d+181) then
        tmp = j * (y0 * t_2)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = (y3 * y5) - (x * b);
	double tmp;
	if (y2 <= -1.65e+245) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (y2 <= -8e+154) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -3.8e-140) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (y2 <= -1.35e-206) {
		tmp = t_1;
	} else if (y2 <= 2.6e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 1.7e-219) {
		tmp = y0 * (j * t_2);
	} else if (y2 <= 2.3e-139) {
		tmp = t_1;
	} else if (y2 <= 1.75e-85) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y2 <= 2.4e+41) {
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	} else if (y2 <= 4.5e+181) {
		tmp = j * (y0 * t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	t_2 = (y3 * y5) - (x * b)
	tmp = 0
	if y2 <= -1.65e+245:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif y2 <= -8e+154:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -3.8e-140:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif y2 <= -1.35e-206:
		tmp = t_1
	elif y2 <= 2.6e-265:
		tmp = c * (y0 * (z * -y3))
	elif y2 <= 1.7e-219:
		tmp = y0 * (j * t_2)
	elif y2 <= 2.3e-139:
		tmp = t_1
	elif y2 <= 1.75e-85:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y2 <= 2.4e+41:
		tmp = y1 * (j * ((x * i) - (y3 * y4)))
	elif y2 <= 4.5e+181:
		tmp = j * (y0 * t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	t_2 = Float64(Float64(y3 * y5) - Float64(x * b))
	tmp = 0.0
	if (y2 <= -1.65e+245)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (y2 <= -8e+154)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -3.8e-140)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (y2 <= -1.35e-206)
		tmp = t_1;
	elseif (y2 <= 2.6e-265)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y2 <= 1.7e-219)
		tmp = Float64(y0 * Float64(j * t_2));
	elseif (y2 <= 2.3e-139)
		tmp = t_1;
	elseif (y2 <= 1.75e-85)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y2 <= 2.4e+41)
		tmp = Float64(y1 * Float64(j * Float64(Float64(x * i) - Float64(y3 * y4))));
	elseif (y2 <= 4.5e+181)
		tmp = Float64(j * Float64(y0 * t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	t_2 = (y3 * y5) - (x * b);
	tmp = 0.0;
	if (y2 <= -1.65e+245)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (y2 <= -8e+154)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -3.8e-140)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (y2 <= -1.35e-206)
		tmp = t_1;
	elseif (y2 <= 2.6e-265)
		tmp = c * (y0 * (z * -y3));
	elseif (y2 <= 1.7e-219)
		tmp = y0 * (j * t_2);
	elseif (y2 <= 2.3e-139)
		tmp = t_1;
	elseif (y2 <= 1.75e-85)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y2 <= 2.4e+41)
		tmp = y1 * (j * ((x * i) - (y3 * y4)));
	elseif (y2 <= 4.5e+181)
		tmp = j * (y0 * t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.65e+245], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -8e+154], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.8e-140], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.35e-206], t$95$1, If[LessEqual[y2, 2.6e-265], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.7e-219], N[(y0 * N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.3e-139], t$95$1, If[LessEqual[y2, 1.75e-85], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.4e+41], N[(y1 * N[(j * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.5e+181], N[(j * N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y2 < -1.65000000000000005e245

   1. Initial program 38.9%

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

   3. Taylor expanded in y2 around inf 83.3%

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

   4. Taylor expanded in x around inf 72.6%

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

   if -1.65000000000000005e245 < y2 < -8.0000000000000003e154

   1. Initial program 13.0%

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

   3. Taylor expanded in x around inf 30.4%

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

   4. Taylor expanded in y1 around inf 35.8%

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

   5. Taylor expanded in k around inf 52.6%

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

   if -8.0000000000000003e154 < y2 < -3.79999999999999998e-140

   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 x around inf 42.2%

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

   4. Taylor expanded in b around inf 39.6%

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

   if -3.79999999999999998e-140 < y2 < -1.35e-206 or 1.6999999999999999e-219 < y2 < 2.30000000000000012e-139 or 4.5e181 < y2

   1. Initial program 23.5%

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

   3. Simplified 23.5%

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

   5. Taylor expanded in a around inf 41.5%

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

   6. Taylor expanded in y3 around inf 52.5%

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

   if -1.35e-206 < y2 < 2.6000000000000001e-265

   1. Initial program 29.3%

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

   3. Taylor expanded in y0 around inf 48.0%

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

   4. Taylor expanded in c around inf 59.9%

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

   5. Taylor expanded in x around 0 65.5%

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

      1. associate-*r* 65.5%

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

      2. mul-1-neg 65.5%

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

   7. Simplified 65.5%

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

   if 2.6000000000000001e-265 < y2 < 1.6999999999999999e-219

   1. Initial program 10.9%

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

   3. Taylor expanded in y0 around inf 60.1%

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

   4. Taylor expanded in j around inf 60.3%

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

   if 2.30000000000000012e-139 < y2 < 1.74999999999999989e-85

   1. Initial program 19.9%

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

   3. Simplified 19.9%

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

   5. Taylor expanded in a around inf 60.7%

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

   6. Taylor expanded in y around inf 55.0%

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

   if 1.74999999999999989e-85 < y2 < 2.4000000000000002e41

   1. Initial program 13.5%

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

   3. Taylor expanded in x around inf 44.2%

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

   4. Taylor expanded in y1 around inf 43.9%

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

   5. Taylor expanded in j around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   if 2.4000000000000002e41 < y2 < 4.5e181

   1. Initial program 18.9%

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

   3. Taylor expanded in y0 around inf 32.7%

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

   4. Taylor expanded in j around inf 57.6%

      \[\leadsto \color{blue}{j \cdot \left(y0 \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.65 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq -8 \cdot 10^{+154}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq -1.35 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.6 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.7 \cdot 10^{-219}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{-139}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 1.75 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y2 \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;y1 \cdot \left(j \cdot \left(x \cdot i - y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.5 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 31.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-220}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+42}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y3 (* y4 (- (* y c) (* j y1))))))
   (if (<= t -1.2e+69)
     (* y2 (* t (- (* a y5) (* c y4))))
     (if (<= t -4.5e+18)
       (* x (* y (- (* a b) (* c i))))
       (if (<= t -3.5e-72)
         t_1
         (if (<= t -9.6e-173)
           (* c (* t (- (* z i) (* y2 y4))))
           (if (<= t -1.12e-220)
             (* a (* y (- (* x b) (* y3 y5))))
             (if (<= t 7.2e-275)
               (* j (* y3 (- (* y0 y5) (* y1 y4))))
               (if (<= t 9e-257)
                 (* c (* i (* x (- y))))
                 (if (<= t 9.5e-238)
                   t_1
                   (if (<= t 1.36e+42)
                     (* y0 (* x (- (* c y2) (* b j))))
                     (* a (* t (- (* y2 y5) (* z 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 t_1 = y3 * (y4 * ((y * c) - (j * y1)));
	double tmp;
	if (t <= -1.2e+69) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -4.5e+18) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -3.5e-72) {
		tmp = t_1;
	} else if (t <= -9.6e-173) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -1.12e-220) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 7.2e-275) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (t <= 9e-257) {
		tmp = c * (i * (x * -y));
	} else if (t <= 9.5e-238) {
		tmp = t_1;
	} else if (t <= 1.36e+42) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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) :: t_1
    real(8) :: tmp
    t_1 = y3 * (y4 * ((y * c) - (j * y1)))
    if (t <= (-1.2d+69)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (t <= (-4.5d+18)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (t <= (-3.5d-72)) then
        tmp = t_1
    else if (t <= (-9.6d-173)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= (-1.12d-220)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 7.2d-275) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (t <= 9d-257) then
        tmp = c * (i * (x * -y))
    else if (t <= 9.5d-238) then
        tmp = t_1
    else if (t <= 1.36d+42) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else
        tmp = a * (t * ((y2 * y5) - (z * 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 t_1 = y3 * (y4 * ((y * c) - (j * y1)));
	double tmp;
	if (t <= -1.2e+69) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -4.5e+18) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -3.5e-72) {
		tmp = t_1;
	} else if (t <= -9.6e-173) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -1.12e-220) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 7.2e-275) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (t <= 9e-257) {
		tmp = c * (i * (x * -y));
	} else if (t <= 9.5e-238) {
		tmp = t_1;
	} else if (t <= 1.36e+42) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y3 * (y4 * ((y * c) - (j * y1)))
	tmp = 0
	if t <= -1.2e+69:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif t <= -4.5e+18:
		tmp = x * (y * ((a * b) - (c * i)))
	elif t <= -3.5e-72:
		tmp = t_1
	elif t <= -9.6e-173:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= -1.12e-220:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 7.2e-275:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif t <= 9e-257:
		tmp = c * (i * (x * -y))
	elif t <= 9.5e-238:
		tmp = t_1
	elif t <= 1.36e+42:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	else:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))))
	tmp = 0.0
	if (t <= -1.2e+69)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (t <= -4.5e+18)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (t <= -3.5e-72)
		tmp = t_1;
	elseif (t <= -9.6e-173)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= -1.12e-220)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 7.2e-275)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (t <= 9e-257)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (t <= 9.5e-238)
		tmp = t_1;
	elseif (t <= 1.36e+42)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * 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)
	t_1 = y3 * (y4 * ((y * c) - (j * y1)));
	tmp = 0.0;
	if (t <= -1.2e+69)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (t <= -4.5e+18)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (t <= -3.5e-72)
		tmp = t_1;
	elseif (t <= -9.6e-173)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= -1.12e-220)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 7.2e-275)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (t <= 9e-257)
		tmp = c * (i * (x * -y));
	elseif (t <= 9.5e-238)
		tmp = t_1;
	elseif (t <= 1.36e+42)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	else
		tmp = a * (t * ((y2 * y5) - (z * b)));
	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[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+69], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e+18], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-72], t$95$1, If[LessEqual[t, -9.6e-173], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e-220], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-275], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-257], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-238], t$95$1, If[LessEqual[t, 1.36e+42], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if t < -1.2000000000000001e69

   1. Initial program 14.0%

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

   3. Taylor expanded in y2 around inf 36.5%

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

   4. Taylor expanded in t around inf 52.2%

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

   if -1.2000000000000001e69 < t < -4.5e18

   1. Initial program 13.8%

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

   3. Taylor expanded in x around inf 46.7%

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

   4. Taylor expanded in y around inf 47.7%

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

   if -4.5e18 < t < -3.5e-72 or 9.0000000000000005e-257 < t < 9.50000000000000059e-238

   1. Initial program 27.0%

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

   3. Taylor expanded in y3 around -inf 44.6%

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

   4. Taylor expanded in y4 around inf 53.5%

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

   if -3.5e-72 < t < -9.60000000000000068e-173

   1. Initial program 23.4%

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

   3. Taylor expanded in t around inf 53.0%

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

   4. Taylor expanded in c around inf 53.8%

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

      1. *-commutative 53.8%

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

   6. Simplified 53.8%

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

   if -9.60000000000000068e-173 < t < -1.12000000000000008e-220

   1. Initial program 44.4%

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

   3. Simplified 44.4%

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

   5. Taylor expanded in a around inf 44.8%

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

   6. Taylor expanded in y around inf 57.0%

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

   if -1.12000000000000008e-220 < t < 7.1999999999999994e-275

   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 x around inf 25.0%

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

   4. Taylor expanded in y3 around inf 60.6%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.6%

         \[\leadsto \color{blue}{-j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   6. Simplified 60.6%

      \[\leadsto \color{blue}{-j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if 7.1999999999999994e-275 < t < 9.0000000000000005e-257

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 62.4%

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

   4. Taylor expanded in i around -inf 44.1%

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

      1. mul-1-neg 44.1%

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

   6. Simplified 44.1%

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

   7. Taylor expanded in c around inf 80.1%

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

   if 9.50000000000000059e-238 < t < 1.35999999999999999e42

   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 y0 around inf 48.9%

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

   4. Taylor expanded in x around inf 49.3%

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

   if 1.35999999999999999e42 < t

   1. Initial program 22.8%

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

   3. Simplified 22.8%

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

   5. Taylor expanded in a around inf 52.8%

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

   6. Taylor expanded in t around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-72}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-173}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-220}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-238}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+42}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+68}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -19000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-122}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot \left(y2 - y3 \cdot \frac{z}{x}\right)\right)\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-177}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-221}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 10^{-237}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -5.5e+68)
   (* y2 (* t (- (* a y5) (* c y4))))
   (if (<= t -19000000000.0)
     (* x (* y (- (* a b) (* c i))))
     (if (<= t -9e-122)
       (* y0 (* c (* x (- y2 (* y3 (/ z x))))))
       (if (<= t -7.4e-177)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= t -7.2e-221)
           (* a (* y (- (* x b) (* y3 y5))))
           (if (<= t 9e-275)
             (* j (* y3 (- (* y0 y5) (* y1 y4))))
             (if (<= t 2.7e-257)
               (* c (* i (* x (- y))))
               (if (<= t 1e-237)
                 (* y3 (* y4 (- (* y c) (* j y1))))
                 (if (<= t 1.1e+42)
                   (* y0 (* x (- (* c y2) (* b j))))
                   (* a (* t (- (* y2 y5) (* z 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 (t <= -5.5e+68) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -19000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -9e-122) {
		tmp = y0 * (c * (x * (y2 - (y3 * (z / x)))));
	} else if (t <= -7.4e-177) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -7.2e-221) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 9e-275) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (t <= 2.7e-257) {
		tmp = c * (i * (x * -y));
	} else if (t <= 1e-237) {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	} else if (t <= 1.1e+42) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= (-5.5d+68)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (t <= (-19000000000.0d0)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (t <= (-9d-122)) then
        tmp = y0 * (c * (x * (y2 - (y3 * (z / x)))))
    else if (t <= (-7.4d-177)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= (-7.2d-221)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 9d-275) then
        tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
    else if (t <= 2.7d-257) then
        tmp = c * (i * (x * -y))
    else if (t <= 1d-237) then
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    else if (t <= 1.1d+42) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else
        tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -5.5e+68) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -19000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -9e-122) {
		tmp = y0 * (c * (x * (y2 - (y3 * (z / x)))));
	} else if (t <= -7.4e-177) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -7.2e-221) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 9e-275) {
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	} else if (t <= 2.7e-257) {
		tmp = c * (i * (x * -y));
	} else if (t <= 1e-237) {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	} else if (t <= 1.1e+42) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 t <= -5.5e+68:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif t <= -19000000000.0:
		tmp = x * (y * ((a * b) - (c * i)))
	elif t <= -9e-122:
		tmp = y0 * (c * (x * (y2 - (y3 * (z / x)))))
	elif t <= -7.4e-177:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= -7.2e-221:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 9e-275:
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)))
	elif t <= 2.7e-257:
		tmp = c * (i * (x * -y))
	elif t <= 1e-237:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	elif t <= 1.1e+42:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	else:
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -5.5e+68)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (t <= -19000000000.0)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (t <= -9e-122)
		tmp = Float64(y0 * Float64(c * Float64(x * Float64(y2 - Float64(y3 * Float64(z / x))))));
	elseif (t <= -7.4e-177)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= -7.2e-221)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 9e-275)
		tmp = Float64(j * Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))));
	elseif (t <= 2.7e-257)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (t <= 1e-237)
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	elseif (t <= 1.1e+42)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * 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 (t <= -5.5e+68)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (t <= -19000000000.0)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (t <= -9e-122)
		tmp = y0 * (c * (x * (y2 - (y3 * (z / x)))));
	elseif (t <= -7.4e-177)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= -7.2e-221)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 9e-275)
		tmp = j * (y3 * ((y0 * y5) - (y1 * y4)));
	elseif (t <= 2.7e-257)
		tmp = c * (i * (x * -y));
	elseif (t <= 1e-237)
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	elseif (t <= 1.1e+42)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	else
		tmp = a * (t * ((y2 * y5) - (z * 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[t, -5.5e+68], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -19000000000.0], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-122], N[(y0 * N[(c * N[(x * N[(y2 - N[(y3 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.4e-177], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-221], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-275], N[(j * N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-257], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-237], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+42], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if t < -5.5000000000000004e68

   1. Initial program 14.0%

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

   3. Taylor expanded in y2 around inf 36.5%

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

   4. Taylor expanded in t around inf 52.2%

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

   if -5.5000000000000004e68 < t < -1.9e10

   1. Initial program 12.9%

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

   3. Taylor expanded in x around inf 43.8%

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

   4. Taylor expanded in y around inf 51.0%

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

   if -1.9e10 < t < -8.99999999999999959e-122

   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 y0 around inf 44.7%

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

   4. Taylor expanded in c around inf 45.0%

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

   5. Taylor expanded in x around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

      3. associate-/l* 57.1%

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

   7. Simplified 57.1%

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

   if -8.99999999999999959e-122 < t < -7.39999999999999986e-177

   1. Initial program 21.3%

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

   3. Taylor expanded in t around inf 57.2%

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

   4. Taylor expanded in c around inf 51.0%

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

      1. *-commutative 51.0%

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

   6. Simplified 51.0%

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

   if -7.39999999999999986e-177 < t < -7.20000000000000022e-221

   1. Initial program 44.4%

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

   3. Simplified 44.4%

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

   5. Taylor expanded in a around inf 44.8%

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

   6. Taylor expanded in y around inf 57.0%

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

   if -7.20000000000000022e-221 < t < 8.99999999999999957e-275

   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 x around inf 25.0%

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

   4. Taylor expanded in y3 around inf 60.6%

      \[\leadsto \color{blue}{-1 \cdot \left(j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.6%

         \[\leadsto \color{blue}{-j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   6. Simplified 60.6%

      \[\leadsto \color{blue}{-j \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   if 8.99999999999999957e-275 < t < 2.6999999999999999e-257

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 62.4%

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

   4. Taylor expanded in i around -inf 44.1%

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

      1. mul-1-neg 44.1%

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

   6. Simplified 44.1%

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

   7. Taylor expanded in c around inf 80.1%

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

   if 2.6999999999999999e-257 < t < 9.9999999999999999e-238

   1. Initial program 24.0%

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

   3. Taylor expanded in y3 around -inf 13.3%

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

   4. Taylor expanded in y4 around inf 56.4%

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

   if 9.9999999999999999e-238 < t < 1.1000000000000001e42

   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 y0 around inf 48.9%

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

   4. Taylor expanded in x around inf 49.3%

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

   if 1.1000000000000001e42 < t

   1. Initial program 22.8%

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

   3. Simplified 22.8%

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

   5. Taylor expanded in a around inf 52.8%

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

   6. Taylor expanded in t around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   8. Simplified 57.0%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+68}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -19000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-122}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot \left(y2 - y3 \cdot \frac{z}{x}\right)\right)\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-177}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-221}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 10^{-237}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 33.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{if}\;y5 \leq -6.2 \cdot 10^{+231}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -5.2 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq -2.05 \cdot 10^{-271}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq -1.65 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 6.8 \cdot 10^{-200}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 6.8:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5)))))
   (if (<= y5 -6.2e+231)
     (* a (* y3 (- (* z y1) (* y y5))))
     (if (<= y5 -5.2e-130)
       t_1
       (if (<= y5 -4.4e-210)
         (* a (* b (- (* x y) (* z t))))
         (if (<= y5 -2.05e-271)
           (* y3 (* y4 (- (* y c) (* j y1))))
           (if (<= y5 -1.65e-278)
             (* c (* x (- (* y0 y2) (* y i))))
             (if (<= y5 6.8e-200)
               (* y0 (* x (- (* c y2) (* b j))))
               (if (<= y5 6.8)
                 (* t (* z (- (* c i) (* a b))))
                 (if (<= y5 7.5e+52)
                   (* y0 (* b (- (* z k) (* x j))))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double tmp;
	if (y5 <= -6.2e+231) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y5 <= -5.2e-130) {
		tmp = t_1;
	} else if (y5 <= -4.4e-210) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= -2.05e-271) {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	} else if (y5 <= -1.65e-278) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= 6.8e-200) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y5 <= 6.8) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y5 <= 7.5e+52) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} 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 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
    if (y5 <= (-6.2d+231)) then
        tmp = a * (y3 * ((z * y1) - (y * y5)))
    else if (y5 <= (-5.2d-130)) then
        tmp = t_1
    else if (y5 <= (-4.4d-210)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y5 <= (-2.05d-271)) then
        tmp = y3 * (y4 * ((y * c) - (j * y1)))
    else if (y5 <= (-1.65d-278)) then
        tmp = c * (x * ((y0 * y2) - (y * i)))
    else if (y5 <= 6.8d-200) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y5 <= 6.8d0) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y5 <= 7.5d+52) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	double tmp;
	if (y5 <= -6.2e+231) {
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	} else if (y5 <= -5.2e-130) {
		tmp = t_1;
	} else if (y5 <= -4.4e-210) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y5 <= -2.05e-271) {
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	} else if (y5 <= -1.65e-278) {
		tmp = c * (x * ((y0 * y2) - (y * i)));
	} else if (y5 <= 6.8e-200) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y5 <= 6.8) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y5 <= 7.5e+52) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
	tmp = 0
	if y5 <= -6.2e+231:
		tmp = a * (y3 * ((z * y1) - (y * y5)))
	elif y5 <= -5.2e-130:
		tmp = t_1
	elif y5 <= -4.4e-210:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y5 <= -2.05e-271:
		tmp = y3 * (y4 * ((y * c) - (j * y1)))
	elif y5 <= -1.65e-278:
		tmp = c * (x * ((y0 * y2) - (y * i)))
	elif y5 <= 6.8e-200:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y5 <= 6.8:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y5 <= 7.5e+52:
		tmp = y0 * (b * ((z * k) - (x * j)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5)))
	tmp = 0.0
	if (y5 <= -6.2e+231)
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))));
	elseif (y5 <= -5.2e-130)
		tmp = t_1;
	elseif (y5 <= -4.4e-210)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y5 <= -2.05e-271)
		tmp = Float64(y3 * Float64(y4 * Float64(Float64(y * c) - Float64(j * y1))));
	elseif (y5 <= -1.65e-278)
		tmp = Float64(c * Float64(x * Float64(Float64(y0 * y2) - Float64(y * i))));
	elseif (y5 <= 6.8e-200)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y5 <= 6.8)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y5 <= 7.5e+52)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	tmp = 0.0;
	if (y5 <= -6.2e+231)
		tmp = a * (y3 * ((z * y1) - (y * y5)));
	elseif (y5 <= -5.2e-130)
		tmp = t_1;
	elseif (y5 <= -4.4e-210)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y5 <= -2.05e-271)
		tmp = y3 * (y4 * ((y * c) - (j * y1)));
	elseif (y5 <= -1.65e-278)
		tmp = c * (x * ((y0 * y2) - (y * i)));
	elseif (y5 <= 6.8e-200)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y5 <= 6.8)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y5 <= 7.5e+52)
		tmp = y0 * (b * ((z * k) - (x * j)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -6.2e+231], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -5.2e-130], t$95$1, If[LessEqual[y5, -4.4e-210], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -2.05e-271], N[(y3 * N[(y4 * N[(N[(y * c), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.65e-278], N[(c * N[(x * N[(N[(y0 * y2), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.8e-200], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6.8], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 7.5e+52], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -6.1999999999999998e231

   1. Initial program 8.3%

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

   3. Simplified 8.3%

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

   5. Taylor expanded in a around inf 17.6%

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

   6. Taylor expanded in y3 around inf 58.5%

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

   if -6.1999999999999998e231 < y5 < -5.2000000000000001e-130 or 7.49999999999999995e52 < y5

   1. Initial program 22.4%

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

   3. Taylor expanded in x around inf 39.3%

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

   4. Taylor expanded in x around 0 55.0%

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

   if -5.2000000000000001e-130 < y5 < -4.39999999999999979e-210

   1. Initial program 21.2%

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

   3. Simplified 21.2%

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

   5. Taylor expanded in a around inf 54.8%

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

   6. Taylor expanded in b around inf 55.5%

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

   if -4.39999999999999979e-210 < y5 < -2.0500000000000001e-271

   1. Initial program 14.3%

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

   3. Taylor expanded in y3 around -inf 43.0%

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

   4. Taylor expanded in y4 around inf 64.5%

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

   if -2.0500000000000001e-271 < y5 < -1.6499999999999999e-278

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in c around inf 100.0%

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

   if -1.6499999999999999e-278 < y5 < 6.8000000000000006e-200

   1. Initial program 21.9%

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

   3. Taylor expanded in y0 around inf 38.3%

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

   4. Taylor expanded in x around inf 52.2%

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

   if 6.8000000000000006e-200 < y5 < 6.79999999999999982

   1. Initial program 21.9%

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

   3. Taylor expanded in t around inf 54.4%

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

   4. Taylor expanded in z around inf 58.1%

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

   if 6.79999999999999982 < y5 < 7.49999999999999995e52

   1. Initial program 41.7%

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

   3. Taylor expanded in y0 around inf 58.4%

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

   4. Taylor expanded in b around inf 67.6%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -6.2 \cdot 10^{+231}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -5.2 \cdot 10^{-130}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \mathbf{elif}\;y5 \leq -4.4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y5 \leq -2.05 \cdot 10^{-271}:\\ \;\;\;\;y3 \cdot \left(y4 \cdot \left(y \cdot c - j \cdot y1\right)\right)\\ \mathbf{elif}\;y5 \leq -1.65 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2 - y \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq 6.8 \cdot 10^{-200}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 6.8:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;y5 \leq -1.35 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -6.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -3.4 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq 3.1 \cdot 10^{-200}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 0.195:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 4.1 \cdot 10^{+51}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          j
          (+
           (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
           (* x (- (* i y1) (* b y0)))))))
   (if (<= y5 -1.35e+112)
     (* a (* t (- (* y2 y5) (* z b))))
     (if (<= y5 -1.45e-155)
       t_1
       (if (<= y5 -6.2e-208)
         (* x (* y (- (* a b) (* c i))))
         (if (<= y5 -3.4e-234)
           t_1
           (if (<= y5 3.1e-200)
             (* y0 (* x (- (* c y2) (* b j))))
             (if (<= y5 0.195)
               (* t (* z (- (* c i) (* a b))))
               (if (<= y5 4.1e+51)
                 (* y0 (* b (- (* z k) (* x j))))
                 (* (- (* k y2) (* j y3)) (- (* y1 y4) (* y0 y5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -1.35e+112) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y5 <= -1.45e-155) {
		tmp = t_1;
	} else if (y5 <= -6.2e-208) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y5 <= -3.4e-234) {
		tmp = t_1;
	} else if (y5 <= 3.1e-200) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y5 <= 0.195) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y5 <= 4.1e+51) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else {
		tmp = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
    if (y5 <= (-1.35d+112)) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (y5 <= (-1.45d-155)) then
        tmp = t_1
    else if (y5 <= (-6.2d-208)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (y5 <= (-3.4d-234)) then
        tmp = t_1
    else if (y5 <= 3.1d-200) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y5 <= 0.195d0) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y5 <= 4.1d+51) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else
        tmp = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	double tmp;
	if (y5 <= -1.35e+112) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (y5 <= -1.45e-155) {
		tmp = t_1;
	} else if (y5 <= -6.2e-208) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (y5 <= -3.4e-234) {
		tmp = t_1;
	} else if (y5 <= 3.1e-200) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y5 <= 0.195) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y5 <= 4.1e+51) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else {
		tmp = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))))
	tmp = 0
	if y5 <= -1.35e+112:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif y5 <= -1.45e-155:
		tmp = t_1
	elif y5 <= -6.2e-208:
		tmp = x * (y * ((a * b) - (c * i)))
	elif y5 <= -3.4e-234:
		tmp = t_1
	elif y5 <= 3.1e-200:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y5 <= 0.195:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y5 <= 4.1e+51:
		tmp = y0 * (b * ((z * k) - (x * j)))
	else:
		tmp = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (y5 <= -1.35e+112)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (y5 <= -1.45e-155)
		tmp = t_1;
	elseif (y5 <= -6.2e-208)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (y5 <= -3.4e-234)
		tmp = t_1;
	elseif (y5 <= 3.1e-200)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y5 <= 0.195)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y5 <= 4.1e+51)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	else
		tmp = Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y1 * y4) - Float64(y0 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (y5 <= -1.35e+112)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (y5 <= -1.45e-155)
		tmp = t_1;
	elseif (y5 <= -6.2e-208)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (y5 <= -3.4e-234)
		tmp = t_1;
	elseif (y5 <= 3.1e-200)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y5 <= 0.195)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y5 <= 4.1e+51)
		tmp = y0 * (b * ((z * k) - (x * j)));
	else
		tmp = ((k * y2) - (j * y3)) * ((y1 * y4) - (y0 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -1.35e+112], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.45e-155], t$95$1, If[LessEqual[y5, -6.2e-208], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -3.4e-234], t$95$1, If[LessEqual[y5, 3.1e-200], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 0.195], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 4.1e+51], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $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]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y5 < -1.3500000000000001e112

   1. Initial program 14.7%

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

   3. Simplified 14.7%

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

   5. Taylor expanded in a around inf 35.6%

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

   6. Taylor expanded in t around -inf 56.2%

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

      1. mul-1-neg 56.2%

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

   8. Simplified 56.2%

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

   if -1.3500000000000001e112 < y5 < -1.45000000000000005e-155 or -6.1999999999999996e-208 < y5 < -3.39999999999999986e-234

   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 63.2%

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

   if -1.45000000000000005e-155 < y5 < -6.1999999999999996e-208

   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 x around inf 53.7%

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

   4. Taylor expanded in y around inf 62.0%

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

   if -3.39999999999999986e-234 < y5 < 3.0999999999999999e-200

   1. Initial program 19.4%

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

   3. Taylor expanded in y0 around inf 38.8%

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

   4. Taylor expanded in x around inf 49.7%

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

   if 3.0999999999999999e-200 < y5 < 0.19500000000000001

   1. Initial program 21.9%

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

   3. Taylor expanded in t around inf 54.4%

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

   4. Taylor expanded in z around inf 58.1%

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

   if 0.19500000000000001 < y5 < 4.10000000000000011e51

   1. Initial program 41.7%

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

   3. Taylor expanded in y0 around inf 58.4%

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

   4. Taylor expanded in b around inf 67.6%

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

   if 4.10000000000000011e51 < y5

   1. Initial program 16.3%

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

   3. Taylor expanded in x around inf 42.2%

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

   4. Taylor expanded in x around 0 59.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -1.35 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq -1.45 \cdot 10^{-155}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -6.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;y5 \leq -3.4 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 3.1 \cdot 10^{-200}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq 0.195:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y5 \leq 4.1 \cdot 10^{+51}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ t_2 := j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+178}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5)))))
        (t_2 (* j (* y0 (- (* y3 y5) (* x b))))))
   (if (<= a -6.8e+211)
     (* x (* y (- (* a b) (* c i))))
     (if (<= a -1.35e+187)
       t_1
       (if (<= a -7.2e+52)
         (* a (* y (- (* x b) (* y3 y5))))
         (if (<= a -6e-56)
           t_2
           (if (<= a -3.4e-161)
             t_1
             (if (<= a -1.25e-278)
               t_2
               (if (<= a 7.6e+178)
                 (* c (* t (- (* z i) (* y2 y4))))
                 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = j * (y0 * ((y3 * y5) - (x * b)));
	double tmp;
	if (a <= -6.8e+211) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (a <= -1.35e+187) {
		tmp = t_1;
	} else if (a <= -7.2e+52) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -6e-56) {
		tmp = t_2;
	} else if (a <= -3.4e-161) {
		tmp = t_1;
	} else if (a <= -1.25e-278) {
		tmp = t_2;
	} else if (a <= 7.6e+178) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    t_2 = j * (y0 * ((y3 * y5) - (x * b)))
    if (a <= (-6.8d+211)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (a <= (-1.35d+187)) then
        tmp = t_1
    else if (a <= (-7.2d+52)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= (-6d-56)) then
        tmp = t_2
    else if (a <= (-3.4d-161)) then
        tmp = t_1
    else if (a <= (-1.25d-278)) then
        tmp = t_2
    else if (a <= 7.6d+178) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double t_2 = j * (y0 * ((y3 * y5) - (x * b)));
	double tmp;
	if (a <= -6.8e+211) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (a <= -1.35e+187) {
		tmp = t_1;
	} else if (a <= -7.2e+52) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -6e-56) {
		tmp = t_2;
	} else if (a <= -3.4e-161) {
		tmp = t_1;
	} else if (a <= -1.25e-278) {
		tmp = t_2;
	} else if (a <= 7.6e+178) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	t_2 = j * (y0 * ((y3 * y5) - (x * b)))
	tmp = 0
	if a <= -6.8e+211:
		tmp = x * (y * ((a * b) - (c * i)))
	elif a <= -1.35e+187:
		tmp = t_1
	elif a <= -7.2e+52:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= -6e-56:
		tmp = t_2
	elif a <= -3.4e-161:
		tmp = t_1
	elif a <= -1.25e-278:
		tmp = t_2
	elif a <= 7.6e+178:
		tmp = c * (t * ((z * i) - (y2 * 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(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	t_2 = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))))
	tmp = 0.0
	if (a <= -6.8e+211)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (a <= -1.35e+187)
		tmp = t_1;
	elseif (a <= -7.2e+52)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= -6e-56)
		tmp = t_2;
	elseif (a <= -3.4e-161)
		tmp = t_1;
	elseif (a <= -1.25e-278)
		tmp = t_2;
	elseif (a <= 7.6e+178)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	t_2 = j * (y0 * ((y3 * y5) - (x * b)));
	tmp = 0.0;
	if (a <= -6.8e+211)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (a <= -1.35e+187)
		tmp = t_1;
	elseif (a <= -7.2e+52)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= -6e-56)
		tmp = t_2;
	elseif (a <= -3.4e-161)
		tmp = t_1;
	elseif (a <= -1.25e-278)
		tmp = t_2;
	elseif (a <= 7.6e+178)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e+211], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.35e+187], t$95$1, If[LessEqual[a, -7.2e+52], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-56], t$95$2, If[LessEqual[a, -3.4e-161], t$95$1, If[LessEqual[a, -1.25e-278], t$95$2, If[LessEqual[a, 7.6e+178], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.7999999999999998e211

   1. Initial program 25.9%

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

   3. Taylor expanded in x around inf 44.7%

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

   4. Taylor expanded in y around inf 48.6%

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

   if -6.7999999999999998e211 < a < -1.35000000000000004e187 or -5.99999999999999979e-56 < a < -3.39999999999999982e-161 or 7.59999999999999997e178 < a

   1. Initial program 18.5%

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

   3. Simplified 20.3%

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

   5. Taylor expanded in a around inf 50.4%

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

   6. Taylor expanded in y3 around inf 60.2%

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

   if -1.35000000000000004e187 < a < -7.2e52

   1. Initial program 19.6%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in a around inf 54.4%

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

   6. Taylor expanded in y around inf 47.1%

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

   if -7.2e52 < a < -5.99999999999999979e-56 or -3.39999999999999982e-161 < a < -1.24999999999999996e-278

   1. Initial program 25.3%

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

   3. Taylor expanded in y0 around inf 37.4%

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

   4. Taylor expanded in j around inf 47.6%

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

   if -1.24999999999999996e-278 < a < 7.59999999999999997e178

   1. Initial program 20.9%

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

   3. Taylor expanded in t around inf 40.6%

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

   4. Taylor expanded in c around inf 38.2%

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

      1. *-commutative 38.2%

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

   6. Simplified 38.2%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-278}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+178}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+72}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -44000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+60}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -1.65e+72)
   (* y2 (* t (- (* a y5) (* c y4))))
   (if (<= t -44000000000.0)
     (* x (* y (- (* a b) (* c i))))
     (if (<= t -6.6e-18)
       (* y0 (* c (- (* x y2) (* z y3))))
       (if (<= t -1.4e-171)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= t 6e-305)
           (* a (* y (- (* x b) (* y3 y5))))
           (if (<= t 1.7e-238)
             (* c (* i (* x (- y))))
             (if (<= t 1.22e+60)
               (* y0 (* x (- (* c y2) (* b j))))
               (* a (* y3 (- (* z y1) (* y 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 (t <= -1.65e+72) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -44000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -6.6e-18) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= -1.4e-171) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= 6e-305) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 1.7e-238) {
		tmp = c * (i * (x * -y));
	} else if (t <= 1.22e+60) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * 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 (t <= (-1.65d+72)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (t <= (-44000000000.0d0)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (t <= (-6.6d-18)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (t <= (-1.4d-171)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= 6d-305) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 1.7d-238) then
        tmp = c * (i * (x * -y))
    else if (t <= 1.22d+60) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else
        tmp = a * (y3 * ((z * y1) - (y * 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 (t <= -1.65e+72) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -44000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -6.6e-18) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= -1.4e-171) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= 6e-305) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 1.7e-238) {
		tmp = c * (i * (x * -y));
	} else if (t <= 1.22e+60) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (y3 * ((z * y1) - (y * 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 t <= -1.65e+72:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif t <= -44000000000.0:
		tmp = x * (y * ((a * b) - (c * i)))
	elif t <= -6.6e-18:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif t <= -1.4e-171:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= 6e-305:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 1.7e-238:
		tmp = c * (i * (x * -y))
	elif t <= 1.22e+60:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	else:
		tmp = a * (y3 * ((z * y1) - (y * 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 (t <= -1.65e+72)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (t <= -44000000000.0)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (t <= -6.6e-18)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (t <= -1.4e-171)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= 6e-305)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 1.7e-238)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (t <= 1.22e+60)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	else
		tmp = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * 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 (t <= -1.65e+72)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (t <= -44000000000.0)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (t <= -6.6e-18)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (t <= -1.4e-171)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= 6e-305)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 1.7e-238)
		tmp = c * (i * (x * -y));
	elseif (t <= 1.22e+60)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	else
		tmp = a * (y3 * ((z * y1) - (y * 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[t, -1.65e+72], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -44000000000.0], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.6e-18], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-171], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-305], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-238], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+60], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.65e72

   1. Initial program 14.0%

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

   3. Taylor expanded in y2 around inf 36.5%

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

   4. Taylor expanded in t around inf 52.2%

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

   if -1.65e72 < t < -4.4e10

   1. Initial program 12.9%

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

   3. Taylor expanded in x around inf 43.8%

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

   4. Taylor expanded in y around inf 51.0%

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

   if -4.4e10 < t < -6.6000000000000003e-18

   1. Initial program 41.0%

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

   3. Taylor expanded in y0 around inf 62.1%

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

   4. Taylor expanded in c around inf 62.1%

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

   if -6.6000000000000003e-18 < t < -1.40000000000000011e-171

   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 52.0%

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

   4. Taylor expanded in c around inf 48.9%

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

      1. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if -1.40000000000000011e-171 < t < 6.0000000000000002e-305

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in a around inf 43.5%

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

   6. Taylor expanded in y around inf 48.3%

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

   if 6.0000000000000002e-305 < t < 1.69999999999999992e-238

   1. Initial program 15.8%

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

   3. Taylor expanded in x around inf 41.1%

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

   4. Taylor expanded in i around -inf 46.9%

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

      1. mul-1-neg 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in c around inf 45.6%

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

   if 1.69999999999999992e-238 < t < 1.21999999999999995e60

   1. Initial program 27.1%

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

   3. Taylor expanded in y0 around inf 46.9%

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

   4. Taylor expanded in x around inf 47.1%

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

   if 1.21999999999999995e60 < t

   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 a around inf 50.0%

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

   6. Taylor expanded in y3 around inf 44.9%

      \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z - y \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+72}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -44000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+60}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+72}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -2200000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-17}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-238}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+42}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -9.5e+72)
   (* y2 (* t (- (* a y5) (* c y4))))
   (if (<= t -2200000000.0)
     (* x (* y (- (* a b) (* c i))))
     (if (<= t -5.1e-17)
       (* y0 (* c (- (* x y2) (* z y3))))
       (if (<= t -1.66e-171)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= t 3.2e-305)
           (* a (* y (- (* x b) (* y3 y5))))
           (if (<= t 2.1e-238)
             (* c (* i (* x (- y))))
             (if (<= t 2.15e+42)
               (* y0 (* x (- (* c y2) (* b j))))
               (* a (* t (- (* y2 y5) (* z 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 (t <= -9.5e+72) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -2200000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -5.1e-17) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= -1.66e-171) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= 3.2e-305) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 2.1e-238) {
		tmp = c * (i * (x * -y));
	} else if (t <= 2.15e+42) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= (-9.5d+72)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (t <= (-2200000000.0d0)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (t <= (-5.1d-17)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (t <= (-1.66d-171)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= 3.2d-305) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 2.1d-238) then
        tmp = c * (i * (x * -y))
    else if (t <= 2.15d+42) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else
        tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -9.5e+72) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -2200000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -5.1e-17) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= -1.66e-171) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= 3.2e-305) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 2.1e-238) {
		tmp = c * (i * (x * -y));
	} else if (t <= 2.15e+42) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 t <= -9.5e+72:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif t <= -2200000000.0:
		tmp = x * (y * ((a * b) - (c * i)))
	elif t <= -5.1e-17:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif t <= -1.66e-171:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= 3.2e-305:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 2.1e-238:
		tmp = c * (i * (x * -y))
	elif t <= 2.15e+42:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	else:
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -9.5e+72)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (t <= -2200000000.0)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (t <= -5.1e-17)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (t <= -1.66e-171)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= 3.2e-305)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 2.1e-238)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (t <= 2.15e+42)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * 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 (t <= -9.5e+72)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (t <= -2200000000.0)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (t <= -5.1e-17)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (t <= -1.66e-171)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= 3.2e-305)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 2.1e-238)
		tmp = c * (i * (x * -y));
	elseif (t <= 2.15e+42)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	else
		tmp = a * (t * ((y2 * y5) - (z * 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[t, -9.5e+72], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2200000000.0], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.1e-17], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.66e-171], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-305], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-238], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+42], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -9.50000000000000054e72

   1. Initial program 14.0%

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

   3. Taylor expanded in y2 around inf 36.5%

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

   4. Taylor expanded in t around inf 52.2%

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

   if -9.50000000000000054e72 < t < -2.2e9

   1. Initial program 12.9%

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

   3. Taylor expanded in x around inf 43.8%

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

   4. Taylor expanded in y around inf 51.0%

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

   if -2.2e9 < t < -5.1000000000000003e-17

   1. Initial program 41.0%

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

   3. Taylor expanded in y0 around inf 62.1%

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

   4. Taylor expanded in c around inf 62.1%

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

   if -5.1000000000000003e-17 < t < -1.65999999999999998e-171

   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 52.0%

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

   4. Taylor expanded in c around inf 48.9%

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

      1. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if -1.65999999999999998e-171 < t < 3.20000000000000009e-305

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in a around inf 43.5%

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

   6. Taylor expanded in y around inf 48.3%

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

   if 3.20000000000000009e-305 < t < 2.1000000000000001e-238

   1. Initial program 15.8%

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

   3. Taylor expanded in x around inf 41.1%

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

   4. Taylor expanded in i around -inf 46.9%

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

      1. mul-1-neg 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in c around inf 45.6%

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

   if 2.1000000000000001e-238 < t < 2.1499999999999999e42

   1. Initial program 26.0%

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

   3. Taylor expanded in y0 around inf 49.0%

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

   4. Taylor expanded in x around inf 49.3%

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

   if 2.1499999999999999e42 < t

   1. Initial program 22.8%

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

   3. Simplified 22.8%

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

   5. Taylor expanded in a around inf 52.8%

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

   6. Taylor expanded in t around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   8. Simplified 57.0%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+72}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -2200000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-17}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-238}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+42}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+79}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -72000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -9.5e+79)
   (* y2 (* t (- (* a y5) (* c y4))))
   (if (<= t -72000000000.0)
     (* x (* y (- (* a b) (* c i))))
     (if (<= t -8.5e-18)
       (* y0 (* c (- (* x y2) (* z y3))))
       (if (<= t -1.4e-171)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= t -2.6e-252)
           (* a (* y (- (* x b) (* y3 y5))))
           (if (<= t 2.55e-238)
             (* i (* x (- (* j y1) (* y c))))
             (if (<= t 2e+43)
               (* y0 (* x (- (* c y2) (* b j))))
               (* a (* t (- (* y2 y5) (* z 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 (t <= -9.5e+79) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -72000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -8.5e-18) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= -1.4e-171) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -2.6e-252) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 2.55e-238) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (t <= 2e+43) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= (-9.5d+79)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (t <= (-72000000000.0d0)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (t <= (-8.5d-18)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (t <= (-1.4d-171)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= (-2.6d-252)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 2.55d-238) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else if (t <= 2d+43) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else
        tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -9.5e+79) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -72000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -8.5e-18) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (t <= -1.4e-171) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -2.6e-252) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 2.55e-238) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (t <= 2e+43) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 t <= -9.5e+79:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif t <= -72000000000.0:
		tmp = x * (y * ((a * b) - (c * i)))
	elif t <= -8.5e-18:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif t <= -1.4e-171:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= -2.6e-252:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 2.55e-238:
		tmp = i * (x * ((j * y1) - (y * c)))
	elif t <= 2e+43:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	else:
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -9.5e+79)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (t <= -72000000000.0)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (t <= -8.5e-18)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (t <= -1.4e-171)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= -2.6e-252)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 2.55e-238)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (t <= 2e+43)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * 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 (t <= -9.5e+79)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (t <= -72000000000.0)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (t <= -8.5e-18)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (t <= -1.4e-171)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= -2.6e-252)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 2.55e-238)
		tmp = i * (x * ((j * y1) - (y * c)));
	elseif (t <= 2e+43)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	else
		tmp = a * (t * ((y2 * y5) - (z * 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[t, -9.5e+79], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -72000000000.0], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-18], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-171], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-252], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-238], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+43], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -9.49999999999999994e79

   1. Initial program 14.0%

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

   3. Taylor expanded in y2 around inf 36.5%

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

   4. Taylor expanded in t around inf 52.2%

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

   if -9.49999999999999994e79 < t < -7.2e10

   1. Initial program 12.9%

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

   3. Taylor expanded in x around inf 43.8%

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

   4. Taylor expanded in y around inf 51.0%

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

   if -7.2e10 < t < -8.4999999999999995e-18

   1. Initial program 41.0%

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

   3. Taylor expanded in y0 around inf 62.1%

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

   4. Taylor expanded in c around inf 62.1%

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

   if -8.4999999999999995e-18 < t < -1.40000000000000011e-171

   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 52.0%

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

   4. Taylor expanded in c around inf 48.9%

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

      1. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if -1.40000000000000011e-171 < t < -2.5999999999999999e-252

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in a around inf 40.3%

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

   6. Taylor expanded in y around inf 51.3%

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

   if -2.5999999999999999e-252 < t < 2.55e-238

   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 x around inf 33.0%

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

   4. Taylor expanded in i around -inf 46.7%

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

      1. mul-1-neg 46.7%

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

   6. Simplified 46.7%

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

   if 2.55e-238 < t < 2.00000000000000003e43

   1. Initial program 26.0%

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

   3. Taylor expanded in y0 around inf 49.0%

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

   4. Taylor expanded in x around inf 49.3%

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

   if 2.00000000000000003e43 < t

   1. Initial program 22.8%

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

   3. Simplified 22.8%

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

   5. Taylor expanded in a around inf 52.8%

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

   6. Taylor expanded in t around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   8. Simplified 57.0%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+79}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -72000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -3000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-172}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-248}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= t -5.4e+70)
   (* y2 (* t (- (* a y5) (* c y4))))
   (if (<= t -3000000000.0)
     (* x (* y (- (* a b) (* c i))))
     (if (<= t -2.3e-132)
       (* c (* y3 (- (* y y4) (* z y0))))
       (if (<= t -2.55e-172)
         (* c (* t (- (* z i) (* y2 y4))))
         (if (<= t -7e-248)
           (* a (* y (- (* x b) (* y3 y5))))
           (if (<= t 1.7e-238)
             (* i (* x (- (* j y1) (* y c))))
             (if (<= t 4.5e+43)
               (* y0 (* x (- (* c y2) (* b j))))
               (* a (* t (- (* y2 y5) (* z 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 (t <= -5.4e+70) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -3000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -2.3e-132) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (t <= -2.55e-172) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -7e-248) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 1.7e-238) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (t <= 4.5e+43) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= (-5.4d+70)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (t <= (-3000000000.0d0)) then
        tmp = x * (y * ((a * b) - (c * i)))
    else if (t <= (-2.3d-132)) then
        tmp = c * (y3 * ((y * y4) - (z * y0)))
    else if (t <= (-2.55d-172)) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else if (t <= (-7d-248)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (t <= 1.7d-238) then
        tmp = i * (x * ((j * y1) - (y * c)))
    else if (t <= 4.5d+43) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else
        tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -5.4e+70) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (t <= -3000000000.0) {
		tmp = x * (y * ((a * b) - (c * i)));
	} else if (t <= -2.3e-132) {
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	} else if (t <= -2.55e-172) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else if (t <= -7e-248) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (t <= 1.7e-238) {
		tmp = i * (x * ((j * y1) - (y * c)));
	} else if (t <= 4.5e+43) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * 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 t <= -5.4e+70:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif t <= -3000000000.0:
		tmp = x * (y * ((a * b) - (c * i)))
	elif t <= -2.3e-132:
		tmp = c * (y3 * ((y * y4) - (z * y0)))
	elif t <= -2.55e-172:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	elif t <= -7e-248:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif t <= 1.7e-238:
		tmp = i * (x * ((j * y1) - (y * c)))
	elif t <= 4.5e+43:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	else:
		tmp = a * (t * ((y2 * y5) - (z * 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 (t <= -5.4e+70)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (t <= -3000000000.0)
		tmp = Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i))));
	elseif (t <= -2.3e-132)
		tmp = Float64(c * Float64(y3 * Float64(Float64(y * y4) - Float64(z * y0))));
	elseif (t <= -2.55e-172)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	elseif (t <= -7e-248)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (t <= 1.7e-238)
		tmp = Float64(i * Float64(x * Float64(Float64(j * y1) - Float64(y * c))));
	elseif (t <= 4.5e+43)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * 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 (t <= -5.4e+70)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (t <= -3000000000.0)
		tmp = x * (y * ((a * b) - (c * i)));
	elseif (t <= -2.3e-132)
		tmp = c * (y3 * ((y * y4) - (z * y0)));
	elseif (t <= -2.55e-172)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	elseif (t <= -7e-248)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (t <= 1.7e-238)
		tmp = i * (x * ((j * y1) - (y * c)));
	elseif (t <= 4.5e+43)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	else
		tmp = a * (t * ((y2 * y5) - (z * 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[t, -5.4e+70], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3000000000.0], N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e-132], N[(c * N[(y3 * N[(N[(y * y4), $MachinePrecision] - N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.55e-172], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e-248], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-238], N[(i * N[(x * N[(N[(j * y1), $MachinePrecision] - N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+43], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -5.3999999999999999e70

   1. Initial program 14.0%

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

   3. Taylor expanded in y2 around inf 36.5%

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

   4. Taylor expanded in t around inf 52.2%

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

   if -5.3999999999999999e70 < t < -3e9

   1. Initial program 12.9%

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

   3. Taylor expanded in x around inf 43.8%

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

   4. Taylor expanded in y around inf 51.0%

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

   if -3e9 < t < -2.30000000000000003e-132

   1. Initial program 29.7%

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

   3. Taylor expanded in y3 around -inf 70.9%

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

   4. Taylor expanded in c around inf 48.3%

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

   if -2.30000000000000003e-132 < t < -2.5499999999999999e-172

   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 53.9%

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

   4. Taylor expanded in c around inf 54.9%

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

      1. *-commutative 54.9%

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

   6. Simplified 54.9%

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

   if -2.5499999999999999e-172 < t < -6.99999999999999966e-248

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   5. Taylor expanded in a around inf 40.3%

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

   6. Taylor expanded in y around inf 51.3%

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

   if -6.99999999999999966e-248 < t < 1.69999999999999992e-238

   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 x around inf 33.0%

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

   4. Taylor expanded in i around -inf 46.7%

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

      1. mul-1-neg 46.7%

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

   6. Simplified 46.7%

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

   if 1.69999999999999992e-238 < t < 4.5e43

   1. Initial program 26.0%

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

   3. Taylor expanded in y0 around inf 49.0%

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

   4. Taylor expanded in x around inf 49.3%

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

   if 4.5e43 < t

   1. Initial program 22.8%

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

   3. Simplified 22.8%

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

   5. Taylor expanded in a around inf 52.8%

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

   6. Taylor expanded in t around -inf 57.0%

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

      1. mul-1-neg 57.0%

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

   8. Simplified 57.0%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot \left(b \cdot z - y2 \cdot y5\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+70}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -3000000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-132}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(y \cdot y4 - z \cdot y0\right)\right)\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-172}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-248}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1 - y \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 21.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y3\right)\\ t_2 := a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;y2 \leq -2.8 \cdot 10^{+138}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -170000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.6 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(y0 \cdot t\_1\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+171}:\\ \;\;\;\;y0 \cdot \left(c \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (- y3))) (t_2 (* a (* y (* x b)))))
   (if (<= y2 -2.8e+138)
     (* k (* y1 (* y2 y4)))
     (if (<= y2 -170000000.0)
       t_2
       (if (<= y2 -3.8e-58)
         (* i (* x (* c (- y))))
         (if (<= y2 -5.6e-194)
           (* a (* (* x y) b))
           (if (<= y2 1.2e-149)
             (* c (* y0 t_1))
             (if (<= y2 2e-68)
               t_2
               (if (<= y2 1.9e+171)
                 (* y0 (* c t_1))
                 (* y0 (* c (* x y2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * -y3;
	double t_2 = a * (y * (x * b));
	double tmp;
	if (y2 <= -2.8e+138) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -170000000.0) {
		tmp = t_2;
	} else if (y2 <= -3.8e-58) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -5.6e-194) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 1.2e-149) {
		tmp = c * (y0 * t_1);
	} else if (y2 <= 2e-68) {
		tmp = t_2;
	} else if (y2 <= 1.9e+171) {
		tmp = y0 * (c * t_1);
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -y3
    t_2 = a * (y * (x * b))
    if (y2 <= (-2.8d+138)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-170000000.0d0)) then
        tmp = t_2
    else if (y2 <= (-3.8d-58)) then
        tmp = i * (x * (c * -y))
    else if (y2 <= (-5.6d-194)) then
        tmp = a * ((x * y) * b)
    else if (y2 <= 1.2d-149) then
        tmp = c * (y0 * t_1)
    else if (y2 <= 2d-68) then
        tmp = t_2
    else if (y2 <= 1.9d+171) then
        tmp = y0 * (c * t_1)
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * -y3;
	double t_2 = a * (y * (x * b));
	double tmp;
	if (y2 <= -2.8e+138) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -170000000.0) {
		tmp = t_2;
	} else if (y2 <= -3.8e-58) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -5.6e-194) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 1.2e-149) {
		tmp = c * (y0 * t_1);
	} else if (y2 <= 2e-68) {
		tmp = t_2;
	} else if (y2 <= 1.9e+171) {
		tmp = y0 * (c * t_1);
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * -y3
	t_2 = a * (y * (x * b))
	tmp = 0
	if y2 <= -2.8e+138:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -170000000.0:
		tmp = t_2
	elif y2 <= -3.8e-58:
		tmp = i * (x * (c * -y))
	elif y2 <= -5.6e-194:
		tmp = a * ((x * y) * b)
	elif y2 <= 1.2e-149:
		tmp = c * (y0 * t_1)
	elif y2 <= 2e-68:
		tmp = t_2
	elif y2 <= 1.9e+171:
		tmp = y0 * (c * t_1)
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(-y3))
	t_2 = Float64(a * Float64(y * Float64(x * b)))
	tmp = 0.0
	if (y2 <= -2.8e+138)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -170000000.0)
		tmp = t_2;
	elseif (y2 <= -3.8e-58)
		tmp = Float64(i * Float64(x * Float64(c * Float64(-y))));
	elseif (y2 <= -5.6e-194)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y2 <= 1.2e-149)
		tmp = Float64(c * Float64(y0 * t_1));
	elseif (y2 <= 2e-68)
		tmp = t_2;
	elseif (y2 <= 1.9e+171)
		tmp = Float64(y0 * Float64(c * t_1));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * -y3;
	t_2 = a * (y * (x * b));
	tmp = 0.0;
	if (y2 <= -2.8e+138)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -170000000.0)
		tmp = t_2;
	elseif (y2 <= -3.8e-58)
		tmp = i * (x * (c * -y));
	elseif (y2 <= -5.6e-194)
		tmp = a * ((x * y) * b);
	elseif (y2 <= 1.2e-149)
		tmp = c * (y0 * t_1);
	elseif (y2 <= 2e-68)
		tmp = t_2;
	elseif (y2 <= 1.9e+171)
		tmp = y0 * (c * t_1);
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * (-y3)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.8e+138], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -170000000.0], t$95$2, If[LessEqual[y2, -3.8e-58], N[(i * N[(x * N[(c * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.6e-194], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.2e-149], N[(c * N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2e-68], t$95$2, If[LessEqual[y2, 1.9e+171], N[(y0 * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -2.8000000000000001e138

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 42.2%

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

   4. Taylor expanded in y1 around inf 36.2%

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

   5. Taylor expanded in k around inf 45.0%

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

   if -2.8000000000000001e138 < y2 < -1.7e8 or 1.2000000000000001e-149 < y2 < 2.00000000000000013e-68

   1. Initial program 18.1%

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

   3. Simplified 18.1%

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

   5. Taylor expanded in a around inf 57.2%

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

   6. Taylor expanded in y around inf 49.1%

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

   7. Taylor expanded in b around inf 42.2%

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

      1. associate-*r* 44.5%

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

   9. Simplified 44.5%

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

   if -1.7e8 < y2 < -3.7999999999999997e-58

   1. Initial program 17.8%

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

   3. Taylor expanded in x around inf 33.7%

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

   4. Taylor expanded in i around -inf 58.9%

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

      1. mul-1-neg 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in c around inf 50.7%

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

   if -3.7999999999999997e-58 < y2 < -5.60000000000000022e-194

   1. Initial program 24.4%

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

   3. Simplified 24.4%

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

   5. Taylor expanded in a around inf 45.3%

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

   6. Taylor expanded in y around inf 28.6%

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

   7. Taylor expanded in b around inf 28.8%

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

   if -5.60000000000000022e-194 < y2 < 1.2000000000000001e-149

   1. Initial program 26.4%

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

   3. Taylor expanded in y0 around inf 39.8%

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

   4. Taylor expanded in c around inf 29.5%

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

   5. Taylor expanded in x around 0 33.6%

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

      1. associate-*r* 33.6%

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

      2. mul-1-neg 33.6%

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

   7. Simplified 33.6%

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

   if 2.00000000000000013e-68 < y2 < 1.9000000000000001e171

   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 y0 around inf 39.4%

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

   4. Taylor expanded in c around inf 28.5%

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

   5. Taylor expanded in x around 0 27.0%

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

      1. neg-mul-1 27.0%

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

      2. distribute-lft-neg-in 27.0%

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

      3. *-commutative 27.0%

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

   7. Simplified 27.0%

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

   if 1.9000000000000001e171 < y2

   1. Initial program 19.6%

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

   3. Taylor expanded in y0 around inf 27.5%

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

   4. Taylor expanded in c around inf 39.1%

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

   5. Taylor expanded in x around inf 46.7%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.8 \cdot 10^{+138}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -170000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.6 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 1.2 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2 \cdot 10^{-68}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+171}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -21000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{-53}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.6 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{+173}:\\ \;\;\;\;\left(-c\right) \cdot \left(y3 \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.8e+140)
   (* k (* y1 (* y2 y4)))
   (if (<= y2 -21000000.0)
     (* a (* y (* x b)))
     (if (<= y2 -3.2e-53)
       (* i (* x (* c (- y))))
       (if (<= y2 -1.6e-193)
         (* a (* (* x y) b))
         (if (<= y2 3.5e-265)
           (* c (* y0 (* z (- y3))))
           (if (<= y2 3.6e+31)
             (* j (* y1 (* y3 (- y4))))
             (if (<= y2 1.5e+173)
               (* (- c) (* y3 (* z y0)))
               (* y0 (* c (* x y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.8e+140) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -21000000.0) {
		tmp = a * (y * (x * b));
	} else if (y2 <= -3.2e-53) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -1.6e-193) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 3.5e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 3.6e+31) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 1.5e+173) {
		tmp = -c * (y3 * (z * y0));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.8d+140)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-21000000.0d0)) then
        tmp = a * (y * (x * b))
    else if (y2 <= (-3.2d-53)) then
        tmp = i * (x * (c * -y))
    else if (y2 <= (-1.6d-193)) then
        tmp = a * ((x * y) * b)
    else if (y2 <= 3.5d-265) then
        tmp = c * (y0 * (z * -y3))
    else if (y2 <= 3.6d+31) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y2 <= 1.5d+173) then
        tmp = -c * (y3 * (z * y0))
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.8e+140) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -21000000.0) {
		tmp = a * (y * (x * b));
	} else if (y2 <= -3.2e-53) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -1.6e-193) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 3.5e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 3.6e+31) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 1.5e+173) {
		tmp = -c * (y3 * (z * y0));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.8e+140:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -21000000.0:
		tmp = a * (y * (x * b))
	elif y2 <= -3.2e-53:
		tmp = i * (x * (c * -y))
	elif y2 <= -1.6e-193:
		tmp = a * ((x * y) * b)
	elif y2 <= 3.5e-265:
		tmp = c * (y0 * (z * -y3))
	elif y2 <= 3.6e+31:
		tmp = j * (y1 * (y3 * -y4))
	elif y2 <= 1.5e+173:
		tmp = -c * (y3 * (z * y0))
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.8e+140)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -21000000.0)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y2 <= -3.2e-53)
		tmp = Float64(i * Float64(x * Float64(c * Float64(-y))));
	elseif (y2 <= -1.6e-193)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y2 <= 3.5e-265)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y2 <= 3.6e+31)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 1.5e+173)
		tmp = Float64(Float64(-c) * Float64(y3 * Float64(z * y0)));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.8e+140)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -21000000.0)
		tmp = a * (y * (x * b));
	elseif (y2 <= -3.2e-53)
		tmp = i * (x * (c * -y));
	elseif (y2 <= -1.6e-193)
		tmp = a * ((x * y) * b);
	elseif (y2 <= 3.5e-265)
		tmp = c * (y0 * (z * -y3));
	elseif (y2 <= 3.6e+31)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y2 <= 1.5e+173)
		tmp = -c * (y3 * (z * y0));
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.8e+140], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -21000000.0], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -3.2e-53], N[(i * N[(x * N[(c * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.6e-193], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.5e-265], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.6e+31], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.5e+173], N[((-c) * N[(y3 * N[(z * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -1.8e140

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 42.2%

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

   4. Taylor expanded in y1 around inf 36.2%

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

   5. Taylor expanded in k around inf 45.0%

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

   if -1.8e140 < y2 < -2.1e7

   1. Initial program 22.7%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in a around inf 59.1%

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

   6. Taylor expanded in y around inf 46.7%

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

   7. Taylor expanded in b around inf 46.4%

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

      1. associate-*r* 46.7%

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

   9. Simplified 46.7%

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

   if -2.1e7 < y2 < -3.2000000000000001e-53

   1. Initial program 17.8%

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

   3. Taylor expanded in x around inf 33.7%

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

   4. Taylor expanded in i around -inf 58.9%

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

      1. mul-1-neg 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in c around inf 50.7%

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

   if -3.2000000000000001e-53 < y2 < -1.60000000000000003e-193

   1. Initial program 24.4%

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

   3. Simplified 24.4%

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

   5. Taylor expanded in a around inf 45.3%

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

   6. Taylor expanded in y around inf 28.6%

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

   7. Taylor expanded in b around inf 28.8%

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

   if -1.60000000000000003e-193 < y2 < 3.50000000000000015e-265

   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 y0 around inf 40.9%

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

   4. Taylor expanded in c around inf 51.2%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. associate-*r* 56.0%

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

      2. mul-1-neg 56.0%

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

   7. Simplified 56.0%

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

   if 3.50000000000000015e-265 < y2 < 3.59999999999999996e31

   1. Initial program 16.8%

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

   3. Taylor expanded in x around inf 39.5%

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

   4. Taylor expanded in y1 around inf 35.8%

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

   5. Taylor expanded in y3 around inf 26.6%

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

      1. associate-*r* 26.6%

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

      2. neg-mul-1 26.6%

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

   7. Simplified 26.6%

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

   if 3.59999999999999996e31 < y2 < 1.4999999999999999e173

   1. Initial program 22.9%

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

   3. Taylor expanded in y3 around -inf 54.9%

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

   4. Taylor expanded in c around inf 43.7%

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

   5. Taylor expanded in y0 around inf 35.4%

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

   if 1.4999999999999999e173 < y2

   1. Initial program 19.6%

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

   3. Taylor expanded in y0 around inf 27.5%

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

   4. Taylor expanded in c around inf 39.1%

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

   5. Taylor expanded in x around inf 46.7%

      \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -21000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -3.2 \cdot 10^{-53}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.6 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 3.5 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 1.5 \cdot 10^{+173}:\\ \;\;\;\;\left(-c\right) \cdot \left(y3 \cdot \left(z \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -5.5 \cdot 10^{+140}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1800000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.15 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.85 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.55 \cdot 10^{+175}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot y3\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -5.5e+140)
   (* k (* y1 (* y2 y4)))
   (if (<= y2 -1800000000.0)
     (* a (* y (* x b)))
     (if (<= y2 -2.5e-55)
       (* i (* x (* c (- y))))
       (if (<= y2 -2.15e-193)
         (* a (* (* x y) b))
         (if (<= y2 3.2e-265)
           (* c (* y0 (* z (- y3))))
           (if (<= y2 2.85e+31)
             (* j (* y1 (* y3 (- y4))))
             (if (<= y2 2.55e+175)
               (* c (* (* y0 y3) (- z)))
               (* y0 (* c (* x y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.5e+140) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -1800000000.0) {
		tmp = a * (y * (x * b));
	} else if (y2 <= -2.5e-55) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -2.15e-193) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 3.2e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 2.85e+31) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 2.55e+175) {
		tmp = c * ((y0 * y3) * -z);
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-5.5d+140)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-1800000000.0d0)) then
        tmp = a * (y * (x * b))
    else if (y2 <= (-2.5d-55)) then
        tmp = i * (x * (c * -y))
    else if (y2 <= (-2.15d-193)) then
        tmp = a * ((x * y) * b)
    else if (y2 <= 3.2d-265) then
        tmp = c * (y0 * (z * -y3))
    else if (y2 <= 2.85d+31) then
        tmp = j * (y1 * (y3 * -y4))
    else if (y2 <= 2.55d+175) then
        tmp = c * ((y0 * y3) * -z)
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -5.5e+140) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -1800000000.0) {
		tmp = a * (y * (x * b));
	} else if (y2 <= -2.5e-55) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -2.15e-193) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 3.2e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 2.85e+31) {
		tmp = j * (y1 * (y3 * -y4));
	} else if (y2 <= 2.55e+175) {
		tmp = c * ((y0 * y3) * -z);
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -5.5e+140:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -1800000000.0:
		tmp = a * (y * (x * b))
	elif y2 <= -2.5e-55:
		tmp = i * (x * (c * -y))
	elif y2 <= -2.15e-193:
		tmp = a * ((x * y) * b)
	elif y2 <= 3.2e-265:
		tmp = c * (y0 * (z * -y3))
	elif y2 <= 2.85e+31:
		tmp = j * (y1 * (y3 * -y4))
	elif y2 <= 2.55e+175:
		tmp = c * ((y0 * y3) * -z)
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -5.5e+140)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -1800000000.0)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y2 <= -2.5e-55)
		tmp = Float64(i * Float64(x * Float64(c * Float64(-y))));
	elseif (y2 <= -2.15e-193)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y2 <= 3.2e-265)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y2 <= 2.85e+31)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	elseif (y2 <= 2.55e+175)
		tmp = Float64(c * Float64(Float64(y0 * y3) * Float64(-z)));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -5.5e+140)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -1800000000.0)
		tmp = a * (y * (x * b));
	elseif (y2 <= -2.5e-55)
		tmp = i * (x * (c * -y));
	elseif (y2 <= -2.15e-193)
		tmp = a * ((x * y) * b);
	elseif (y2 <= 3.2e-265)
		tmp = c * (y0 * (z * -y3));
	elseif (y2 <= 2.85e+31)
		tmp = j * (y1 * (y3 * -y4));
	elseif (y2 <= 2.55e+175)
		tmp = c * ((y0 * y3) * -z);
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -5.5e+140], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1800000000.0], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.5e-55], N[(i * N[(x * N[(c * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -2.15e-193], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.2e-265], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.85e+31], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.55e+175], N[(c * N[(N[(y0 * y3), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y2 < -5.5e140

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 42.2%

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

   4. Taylor expanded in y1 around inf 36.2%

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

   5. Taylor expanded in k around inf 45.0%

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

   if -5.5e140 < y2 < -1.8e9

   1. Initial program 22.7%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in a around inf 59.1%

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

   6. Taylor expanded in y around inf 46.7%

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

   7. Taylor expanded in b around inf 46.4%

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

      1. associate-*r* 46.7%

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

   9. Simplified 46.7%

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

   if -1.8e9 < y2 < -2.5000000000000001e-55

   1. Initial program 17.8%

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

   3. Taylor expanded in x around inf 33.7%

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

   4. Taylor expanded in i around -inf 58.9%

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

      1. mul-1-neg 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in c around inf 50.7%

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

   if -2.5000000000000001e-55 < y2 < -2.1500000000000001e-193

   1. Initial program 24.4%

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

   3. Simplified 24.4%

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

   5. Taylor expanded in a around inf 45.3%

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

   6. Taylor expanded in y around inf 28.6%

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

   7. Taylor expanded in b around inf 28.8%

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

   if -2.1500000000000001e-193 < y2 < 3.2e-265

   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 y0 around inf 40.9%

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

   4. Taylor expanded in c around inf 51.2%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. associate-*r* 56.0%

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

      2. mul-1-neg 56.0%

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

   7. Simplified 56.0%

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

   if 3.2e-265 < y2 < 2.85e31

   1. Initial program 16.8%

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

   3. Taylor expanded in x around inf 39.5%

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

   4. Taylor expanded in y1 around inf 35.8%

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

   5. Taylor expanded in y3 around inf 26.6%

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

      1. associate-*r* 26.6%

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

      2. neg-mul-1 26.6%

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

   7. Simplified 26.6%

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

   if 2.85e31 < y2 < 2.55000000000000003e175

   1. Initial program 21.6%

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

   3. Taylor expanded in y3 around -inf 52.0%

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

   4. Taylor expanded in c around inf 41.4%

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

   5. Taylor expanded in y0 around inf 31.0%

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

      1. associate-*r* 36.2%

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

      2. *-commutative 36.2%

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

   7. Simplified 36.2%

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

   if 2.55000000000000003e175 < y2

   1. Initial program 21.2%

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

   3. Taylor expanded in y0 around inf 29.8%

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

   4. Taylor expanded in c around inf 38.2%

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

   5. Taylor expanded in x around inf 46.4%

      \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]
3. Recombined 8 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -5.5 \cdot 10^{+140}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -1800000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -2.15 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 3.2 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.85 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 2.55 \cdot 10^{+175}:\\ \;\;\;\;c \cdot \left(\left(y0 \cdot y3\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+140}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -100000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.22 \cdot 10^{-61}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 7.1 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -8.5e+140)
   (* k (* y1 (* y2 y4)))
   (if (<= y2 -100000000.0)
     (* a (* y (* x b)))
     (if (<= y2 -1.22e-61)
       (* i (* x (* c (- y))))
       (if (<= y2 -5.2e-194)
         (* a (* (* x y) b))
         (if (<= y2 3.1e-265)
           (* c (* y0 (* z (- y3))))
           (if (<= y2 7.1e+43)
             (* j (* y1 (* y3 (- y4))))
             (* y0 (* c (* x y2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.5e+140) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -100000000.0) {
		tmp = a * (y * (x * b));
	} else if (y2 <= -1.22e-61) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -5.2e-194) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 3.1e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 7.1e+43) {
		tmp = j * (y1 * (y3 * -y4));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-8.5d+140)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= (-100000000.0d0)) then
        tmp = a * (y * (x * b))
    else if (y2 <= (-1.22d-61)) then
        tmp = i * (x * (c * -y))
    else if (y2 <= (-5.2d-194)) then
        tmp = a * ((x * y) * b)
    else if (y2 <= 3.1d-265) then
        tmp = c * (y0 * (z * -y3))
    else if (y2 <= 7.1d+43) then
        tmp = j * (y1 * (y3 * -y4))
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -8.5e+140) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= -100000000.0) {
		tmp = a * (y * (x * b));
	} else if (y2 <= -1.22e-61) {
		tmp = i * (x * (c * -y));
	} else if (y2 <= -5.2e-194) {
		tmp = a * ((x * y) * b);
	} else if (y2 <= 3.1e-265) {
		tmp = c * (y0 * (z * -y3));
	} else if (y2 <= 7.1e+43) {
		tmp = j * (y1 * (y3 * -y4));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -8.5e+140:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= -100000000.0:
		tmp = a * (y * (x * b))
	elif y2 <= -1.22e-61:
		tmp = i * (x * (c * -y))
	elif y2 <= -5.2e-194:
		tmp = a * ((x * y) * b)
	elif y2 <= 3.1e-265:
		tmp = c * (y0 * (z * -y3))
	elif y2 <= 7.1e+43:
		tmp = j * (y1 * (y3 * -y4))
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -8.5e+140)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= -100000000.0)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y2 <= -1.22e-61)
		tmp = Float64(i * Float64(x * Float64(c * Float64(-y))));
	elseif (y2 <= -5.2e-194)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (y2 <= 3.1e-265)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif (y2 <= 7.1e+43)
		tmp = Float64(j * Float64(y1 * Float64(y3 * Float64(-y4))));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -8.5e+140)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= -100000000.0)
		tmp = a * (y * (x * b));
	elseif (y2 <= -1.22e-61)
		tmp = i * (x * (c * -y));
	elseif (y2 <= -5.2e-194)
		tmp = a * ((x * y) * b);
	elseif (y2 <= 3.1e-265)
		tmp = c * (y0 * (z * -y3));
	elseif (y2 <= 7.1e+43)
		tmp = j * (y1 * (y3 * -y4));
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -8.5e+140], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -100000000.0], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -1.22e-61], N[(i * N[(x * N[(c * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, -5.2e-194], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.1e-265], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 7.1e+43], N[(j * N[(y1 * N[(y3 * (-y4)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y2 < -8.4999999999999996e140

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 42.2%

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

   4. Taylor expanded in y1 around inf 36.2%

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

   5. Taylor expanded in k around inf 45.0%

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

   if -8.4999999999999996e140 < y2 < -1e8

   1. Initial program 22.7%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in a around inf 59.1%

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

   6. Taylor expanded in y around inf 46.7%

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

   7. Taylor expanded in b around inf 46.4%

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

      1. associate-*r* 46.7%

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

   9. Simplified 46.7%

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

   if -1e8 < y2 < -1.22e-61

   1. Initial program 17.8%

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

   3. Taylor expanded in x around inf 33.7%

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

   4. Taylor expanded in i around -inf 58.9%

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

      1. mul-1-neg 58.9%

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

   6. Simplified 58.9%

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

   7. Taylor expanded in c around inf 50.7%

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

   if -1.22e-61 < y2 < -5.20000000000000003e-194

   1. Initial program 24.4%

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

   3. Simplified 24.4%

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

   5. Taylor expanded in a around inf 45.3%

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

   6. Taylor expanded in y around inf 28.6%

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

   7. Taylor expanded in b around inf 28.8%

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

   if -5.20000000000000003e-194 < y2 < 3.09999999999999988e-265

   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 y0 around inf 40.9%

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

   4. Taylor expanded in c around inf 51.2%

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

   5. Taylor expanded in x around 0 56.0%

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

      1. associate-*r* 56.0%

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

      2. mul-1-neg 56.0%

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

   7. Simplified 56.0%

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

   if 3.09999999999999988e-265 < y2 < 7.09999999999999972e43

   1. Initial program 17.7%

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

   3. Taylor expanded in x around inf 41.2%

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

   4. Taylor expanded in y1 around inf 34.8%

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

   5. Taylor expanded in y3 around inf 27.3%

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

      1. associate-*r* 27.3%

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

      2. neg-mul-1 27.3%

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

   7. Simplified 27.3%

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

   if 7.09999999999999972e43 < y2

   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 y0 around inf 32.6%

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

   4. Taylor expanded in c around inf 36.2%

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

   5. Taylor expanded in x around inf 32.9%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -8.5 \cdot 10^{+140}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq -100000000:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq -1.22 \cdot 10^{-61}:\\ \;\;\;\;i \cdot \left(x \cdot \left(c \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;y2 \leq 3.1 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 7.1 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(y1 \cdot \left(y3 \cdot \left(-y4\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-283}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= a -1.8e+102)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= a -4.2e-55)
       (* b (* x (- (* y a) (* j y0))))
       (if (<= a -2.6e-161)
         t_1
         (if (<= a -1.5e-283)
           (* i (* x (* j y1)))
           (if (<= a 1.1e+181) (* c (* t (- (* z i) (* y2 y4)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (a <= -1.8e+102) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -4.2e-55) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -2.6e-161) {
		tmp = t_1;
	} else if (a <= -1.5e-283) {
		tmp = i * (x * (j * y1));
	} else if (a <= 1.1e+181) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    if (a <= (-1.8d+102)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= (-4.2d-55)) then
        tmp = b * (x * ((y * a) - (j * y0)))
    else if (a <= (-2.6d-161)) then
        tmp = t_1
    else if (a <= (-1.5d-283)) then
        tmp = i * (x * (j * y1))
    else if (a <= 1.1d+181) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (a <= -1.8e+102) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -4.2e-55) {
		tmp = b * (x * ((y * a) - (j * y0)));
	} else if (a <= -2.6e-161) {
		tmp = t_1;
	} else if (a <= -1.5e-283) {
		tmp = i * (x * (j * y1));
	} else if (a <= 1.1e+181) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if a <= -1.8e+102:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= -4.2e-55:
		tmp = b * (x * ((y * a) - (j * y0)))
	elif a <= -2.6e-161:
		tmp = t_1
	elif a <= -1.5e-283:
		tmp = i * (x * (j * y1))
	elif a <= 1.1e+181:
		tmp = c * (t * ((z * i) - (y2 * 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(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (a <= -1.8e+102)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= -4.2e-55)
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (a <= -2.6e-161)
		tmp = t_1;
	elseif (a <= -1.5e-283)
		tmp = Float64(i * Float64(x * Float64(j * y1)));
	elseif (a <= 1.1e+181)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (a <= -1.8e+102)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= -4.2e-55)
		tmp = b * (x * ((y * a) - (j * y0)));
	elseif (a <= -2.6e-161)
		tmp = t_1;
	elseif (a <= -1.5e-283)
		tmp = i * (x * (j * y1));
	elseif (a <= 1.1e+181)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+102], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-55], N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-161], t$95$1, If[LessEqual[a, -1.5e-283], N[(i * N[(x * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+181], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.8000000000000001e102

   1. Initial program 22.8%

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

   3. Simplified 22.8%

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

   5. Taylor expanded in a around inf 64.6%

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

   6. Taylor expanded in y around inf 44.0%

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

   if -1.8000000000000001e102 < a < -4.2000000000000003e-55

   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 x around inf 36.3%

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

   4. Taylor expanded in b around inf 37.6%

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

   if -4.2000000000000003e-55 < a < -2.59999999999999995e-161 or 1.1000000000000001e181 < a

   1. Initial program 17.8%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in a around inf 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 y3 around inf 60.8%

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

   if -2.59999999999999995e-161 < a < -1.49999999999999998e-283

   1. Initial program 19.4%

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

   3. Taylor expanded in x around inf 57.9%

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

   4. Taylor expanded in i around -inf 43.4%

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

      1. mul-1-neg 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in c around 0 32.1%

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

      1. neg-mul-1 32.1%

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

      2. distribute-rgt-neg-in 32.1%

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

   9. Simplified 32.1%

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

   if -1.49999999999999998e-283 < a < 1.1000000000000001e181

   1. Initial program 21.1%

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

   3. Taylor expanded in t around inf 41.0%

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

   4. Taylor expanded in c around inf 38.6%

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

      1. *-commutative 38.6%

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

   6. Simplified 38.6%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-283}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-100}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-277}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= a -1.95e+109)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= a -1.22e-100)
       (* c (* y2 (- (* x y0) (* t y4))))
       (if (<= a -2.1e-161)
         t_1
         (if (<= a -1e-277)
           (* i (* x (* j y1)))
           (if (<= a 9.5e+181) (* c (* t (- (* z i) (* y2 y4)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (a <= -1.95e+109) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -1.22e-100) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (a <= -2.1e-161) {
		tmp = t_1;
	} else if (a <= -1e-277) {
		tmp = i * (x * (j * y1));
	} else if (a <= 9.5e+181) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y3 * ((z * y1) - (y * y5)))
    if (a <= (-1.95d+109)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= (-1.22d-100)) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (a <= (-2.1d-161)) then
        tmp = t_1
    else if (a <= (-1d-277)) then
        tmp = i * (x * (j * y1))
    else if (a <= 9.5d+181) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (a <= -1.95e+109) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -1.22e-100) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (a <= -2.1e-161) {
		tmp = t_1;
	} else if (a <= -1e-277) {
		tmp = i * (x * (j * y1));
	} else if (a <= 9.5e+181) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if a <= -1.95e+109:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= -1.22e-100:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif a <= -2.1e-161:
		tmp = t_1
	elif a <= -1e-277:
		tmp = i * (x * (j * y1))
	elif a <= 9.5e+181:
		tmp = c * (t * ((z * i) - (y2 * 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(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (a <= -1.95e+109)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= -1.22e-100)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (a <= -2.1e-161)
		tmp = t_1;
	elseif (a <= -1e-277)
		tmp = Float64(i * Float64(x * Float64(j * y1)));
	elseif (a <= 9.5e+181)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (a <= -1.95e+109)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= -1.22e-100)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (a <= -2.1e-161)
		tmp = t_1;
	elseif (a <= -1e-277)
		tmp = i * (x * (j * y1));
	elseif (a <= 9.5e+181)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e+109], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.22e-100], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-161], t$95$1, If[LessEqual[a, -1e-277], N[(i * N[(x * N[(j * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+181], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.95000000000000008e109

   1. Initial program 22.8%

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

   3. Simplified 22.8%

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

   5. Taylor expanded in a around inf 64.6%

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

   6. Taylor expanded in y around inf 44.0%

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

   if -1.95000000000000008e109 < a < -1.2199999999999999e-100

   1. Initial program 29.1%

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

   3. Taylor expanded in y2 around inf 34.1%

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

   4. Taylor expanded in c around inf 38.8%

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

   if -1.2199999999999999e-100 < a < -2.1e-161 or 9.50000000000000032e181 < a

   1. Initial program 13.9%

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

   3. Simplified 16.7%

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

   5. Taylor expanded in a around inf 53.1%

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

   6. Taylor expanded in y3 around inf 67.3%

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

   if -2.1e-161 < a < -9.99999999999999969e-278

   1. Initial program 21.0%

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

   3. Taylor expanded in x around inf 62.8%

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

   4. Taylor expanded in i around -inf 42.9%

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

      1. mul-1-neg 42.9%

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

   6. Simplified 42.9%

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

   7. Taylor expanded in c around 0 34.6%

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

      1. neg-mul-1 34.6%

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

      2. distribute-rgt-neg-in 34.6%

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

   9. Simplified 34.6%

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

   if -9.99999999999999969e-278 < a < 9.50000000000000032e181

   1. Initial program 20.7%

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

   3. Taylor expanded in t around inf 40.2%

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

   4. Taylor expanded in c around inf 37.8%

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

      1. *-commutative 37.8%

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

   6. Simplified 37.8%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+109}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-100}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-277}:\\ \;\;\;\;i \cdot \left(x \cdot \left(j \cdot y1\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_2 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-161}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+183}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* y0 (- (* y3 y5) (* x b)))))
        (t_2 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= a -3.2e+53)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= a -3.6e-55)
       t_1
       (if (<= a -6.5e-161)
         t_2
         (if (<= a -1.65e-278)
           t_1
           (if (<= a 6.2e+183) (* c (* t (- (* z i) (* y2 y4)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * ((y3 * y5) - (x * b)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (a <= -3.2e+53) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -3.6e-55) {
		tmp = t_1;
	} else if (a <= -6.5e-161) {
		tmp = t_2;
	} else if (a <= -1.65e-278) {
		tmp = t_1;
	} else if (a <= 6.2e+183) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (y0 * ((y3 * y5) - (x * b)))
    t_2 = a * (y3 * ((z * y1) - (y * y5)))
    if (a <= (-3.2d+53)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (a <= (-3.6d-55)) then
        tmp = t_1
    else if (a <= (-6.5d-161)) then
        tmp = t_2
    else if (a <= (-1.65d-278)) then
        tmp = t_1
    else if (a <= 6.2d+183) then
        tmp = c * (t * ((z * i) - (y2 * y4)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = j * (y0 * ((y3 * y5) - (x * b)));
	double t_2 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (a <= -3.2e+53) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (a <= -3.6e-55) {
		tmp = t_1;
	} else if (a <= -6.5e-161) {
		tmp = t_2;
	} else if (a <= -1.65e-278) {
		tmp = t_1;
	} else if (a <= 6.2e+183) {
		tmp = c * (t * ((z * i) - (y2 * y4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = j * (y0 * ((y3 * y5) - (x * b)))
	t_2 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if a <= -3.2e+53:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif a <= -3.6e-55:
		tmp = t_1
	elif a <= -6.5e-161:
		tmp = t_2
	elif a <= -1.65e-278:
		tmp = t_1
	elif a <= 6.2e+183:
		tmp = c * (t * ((z * i) - (y2 * y4)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_2 = Float64(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (a <= -3.2e+53)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (a <= -3.6e-55)
		tmp = t_1;
	elseif (a <= -6.5e-161)
		tmp = t_2;
	elseif (a <= -1.65e-278)
		tmp = t_1;
	elseif (a <= 6.2e+183)
		tmp = Float64(c * Float64(t * Float64(Float64(z * i) - Float64(y2 * y4))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = j * (y0 * ((y3 * y5) - (x * b)));
	t_2 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (a <= -3.2e+53)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (a <= -3.6e-55)
		tmp = t_1;
	elseif (a <= -6.5e-161)
		tmp = t_2;
	elseif (a <= -1.65e-278)
		tmp = t_1;
	elseif (a <= 6.2e+183)
		tmp = c * (t * ((z * i) - (y2 * y4)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+53], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.6e-55], t$95$1, If[LessEqual[a, -6.5e-161], t$95$2, If[LessEqual[a, -1.65e-278], t$95$1, If[LessEqual[a, 6.2e+183], N[(c * N[(t * N[(N[(z * i), $MachinePrecision] - N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2e53

   1. Initial program 22.7%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in a around inf 61.7%

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

   6. Taylor expanded in y around inf 41.1%

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

   if -3.2e53 < a < -3.6000000000000001e-55 or -6.50000000000000008e-161 < a < -1.6499999999999999e-278

   1. Initial program 25.3%

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

   3. Taylor expanded in y0 around inf 37.4%

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

   4. Taylor expanded in j around inf 47.6%

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

   if -3.6000000000000001e-55 < a < -6.50000000000000008e-161 or 6.1999999999999997e183 < a

   1. Initial program 17.8%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in a around inf 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 y3 around inf 60.8%

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

   if -1.6499999999999999e-278 < a < 6.1999999999999997e183

   1. Initial program 20.9%

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

   3. Taylor expanded in t around inf 40.6%

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

   4. Taylor expanded in c around inf 38.2%

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

      1. *-commutative 38.2%

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

   6. Simplified 38.2%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-278}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+183}:\\ \;\;\;\;c \cdot \left(t \cdot \left(z \cdot i - y2 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 27.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{if}\;y0 \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{+127}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (- (* x b) (* y3 y5))))))
   (if (<= y0 -3.2e+164)
     (* c (* y2 (* x y0)))
     (if (<= y0 2.05e-5)
       t_1
       (if (<= y0 1.8e+16)
         (* c (* i (* x (- y))))
         (if (<= y0 2.4e+53)
           t_1
           (if (<= y0 5.2e+127)
             (* (* c y0) (* z (- y3)))
             (* c (* x (* y0 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 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y0 <= -3.2e+164) {
		tmp = c * (y2 * (x * y0));
	} else if (y0 <= 2.05e-5) {
		tmp = t_1;
	} else if (y0 <= 1.8e+16) {
		tmp = c * (i * (x * -y));
	} else if (y0 <= 2.4e+53) {
		tmp = t_1;
	} else if (y0 <= 5.2e+127) {
		tmp = (c * y0) * (z * -y3);
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * ((x * b) - (y3 * y5)))
    if (y0 <= (-3.2d+164)) then
        tmp = c * (y2 * (x * y0))
    else if (y0 <= 2.05d-5) then
        tmp = t_1
    else if (y0 <= 1.8d+16) then
        tmp = c * (i * (x * -y))
    else if (y0 <= 2.4d+53) then
        tmp = t_1
    else if (y0 <= 5.2d+127) then
        tmp = (c * y0) * (z * -y3)
    else
        tmp = c * (x * (y0 * 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 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y0 <= -3.2e+164) {
		tmp = c * (y2 * (x * y0));
	} else if (y0 <= 2.05e-5) {
		tmp = t_1;
	} else if (y0 <= 1.8e+16) {
		tmp = c * (i * (x * -y));
	} else if (y0 <= 2.4e+53) {
		tmp = t_1;
	} else if (y0 <= 5.2e+127) {
		tmp = (c * y0) * (z * -y3);
	} else {
		tmp = c * (x * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * ((x * b) - (y3 * y5)))
	tmp = 0
	if y0 <= -3.2e+164:
		tmp = c * (y2 * (x * y0))
	elif y0 <= 2.05e-5:
		tmp = t_1
	elif y0 <= 1.8e+16:
		tmp = c * (i * (x * -y))
	elif y0 <= 2.4e+53:
		tmp = t_1
	elif y0 <= 5.2e+127:
		tmp = (c * y0) * (z * -y3)
	else:
		tmp = c * (x * (y0 * 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(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))))
	tmp = 0.0
	if (y0 <= -3.2e+164)
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	elseif (y0 <= 2.05e-5)
		tmp = t_1;
	elseif (y0 <= 1.8e+16)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (y0 <= 2.4e+53)
		tmp = t_1;
	elseif (y0 <= 5.2e+127)
		tmp = Float64(Float64(c * y0) * Float64(z * Float64(-y3)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * 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 = a * (y * ((x * b) - (y3 * y5)));
	tmp = 0.0;
	if (y0 <= -3.2e+164)
		tmp = c * (y2 * (x * y0));
	elseif (y0 <= 2.05e-5)
		tmp = t_1;
	elseif (y0 <= 1.8e+16)
		tmp = c * (i * (x * -y));
	elseif (y0 <= 2.4e+53)
		tmp = t_1;
	elseif (y0 <= 5.2e+127)
		tmp = (c * y0) * (z * -y3);
	else
		tmp = c * (x * (y0 * 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[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3.2e+164], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.05e-5], t$95$1, If[LessEqual[y0, 1.8e+16], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.4e+53], t$95$1, If[LessEqual[y0, 5.2e+127], N[(N[(c * y0), $MachinePrecision] * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -3.1999999999999998e164

   1. Initial program 18.2%

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

   3. Taylor expanded in y0 around inf 54.7%

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

   4. Taylor expanded in c around inf 49.0%

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

   5. Taylor expanded in x around inf 42.8%

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

      1. associate-*r* 45.8%

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

      2. *-commutative 45.8%

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

   7. Simplified 45.8%

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

   if -3.1999999999999998e164 < y0 < 2.05000000000000002e-5 or 1.8e16 < y0 < 2.4e53

   1. Initial program 23.3%

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

   3. Simplified 23.9%

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

   5. Taylor expanded in a around inf 39.8%

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

   6. Taylor expanded in y around inf 35.7%

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

   if 2.05000000000000002e-5 < y0 < 1.8e16

   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 x around inf 22.9%

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

   4. Taylor expanded in i around -inf 45.5%

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

      1. mul-1-neg 45.5%

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

   6. Simplified 45.5%

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

   7. Taylor expanded in c around inf 44.9%

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

   if 2.4e53 < y0 < 5.2000000000000004e127

   1. Initial program 21.1%

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

   3. Taylor expanded in y0 around inf 26.9%

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

   4. Taylor expanded in c around inf 37.5%

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

   5. Taylor expanded in x around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-*r* 48.5%

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

      3. distribute-rgt-neg-in 48.5%

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

      4. *-commutative 48.5%

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

      5. distribute-lft-neg-in 48.5%

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

      6. *-commutative 48.5%

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

   7. Simplified 48.5%

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

   if 5.2000000000000004e127 < y0

   1. Initial program 16.7%

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

   3. Taylor expanded in y0 around inf 53.8%

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

   4. Taylor expanded in c around inf 34.4%

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

   5. Taylor expanded in x around inf 47.1%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{+127}:\\ \;\;\;\;\left(c \cdot y0\right) \cdot \left(z \cdot \left(-y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ t_2 := c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{if}\;y4 \leq -1.35 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -3200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -2.85 \cdot 10^{-220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq 6.8 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))) (t_2 (* c (* i (* x (- y))))))
   (if (<= y4 -1.35e+127)
     t_1
     (if (<= y4 -1.02e+91)
       t_2
       (if (<= y4 -3200.0)
         t_1
         (if (<= y4 -2.85e-220)
           t_2
           (if (<= y4 6.8e+138) (* i (* j (* x y1))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double t_2 = c * (i * (x * -y));
	double tmp;
	if (y4 <= -1.35e+127) {
		tmp = t_1;
	} else if (y4 <= -1.02e+91) {
		tmp = t_2;
	} else if (y4 <= -3200.0) {
		tmp = t_1;
	} else if (y4 <= -2.85e-220) {
		tmp = t_2;
	} else if (y4 <= 6.8e+138) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    t_2 = c * (i * (x * -y))
    if (y4 <= (-1.35d+127)) then
        tmp = t_1
    else if (y4 <= (-1.02d+91)) then
        tmp = t_2
    else if (y4 <= (-3200.0d0)) then
        tmp = t_1
    else if (y4 <= (-2.85d-220)) then
        tmp = t_2
    else if (y4 <= 6.8d+138) then
        tmp = i * (j * (x * y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double t_2 = c * (i * (x * -y));
	double tmp;
	if (y4 <= -1.35e+127) {
		tmp = t_1;
	} else if (y4 <= -1.02e+91) {
		tmp = t_2;
	} else if (y4 <= -3200.0) {
		tmp = t_1;
	} else if (y4 <= -2.85e-220) {
		tmp = t_2;
	} else if (y4 <= 6.8e+138) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	t_2 = c * (i * (x * -y))
	tmp = 0
	if y4 <= -1.35e+127:
		tmp = t_1
	elif y4 <= -1.02e+91:
		tmp = t_2
	elif y4 <= -3200.0:
		tmp = t_1
	elif y4 <= -2.85e-220:
		tmp = t_2
	elif y4 <= 6.8e+138:
		tmp = i * (j * (x * y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(y2 * y4)))
	t_2 = Float64(c * Float64(i * Float64(x * Float64(-y))))
	tmp = 0.0
	if (y4 <= -1.35e+127)
		tmp = t_1;
	elseif (y4 <= -1.02e+91)
		tmp = t_2;
	elseif (y4 <= -3200.0)
		tmp = t_1;
	elseif (y4 <= -2.85e-220)
		tmp = t_2;
	elseif (y4 <= 6.8e+138)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	t_2 = c * (i * (x * -y));
	tmp = 0.0;
	if (y4 <= -1.35e+127)
		tmp = t_1;
	elseif (y4 <= -1.02e+91)
		tmp = t_2;
	elseif (y4 <= -3200.0)
		tmp = t_1;
	elseif (y4 <= -2.85e-220)
		tmp = t_2;
	elseif (y4 <= 6.8e+138)
		tmp = i * (j * (x * y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -1.35e+127], t$95$1, If[LessEqual[y4, -1.02e+91], t$95$2, If[LessEqual[y4, -3200.0], t$95$1, If[LessEqual[y4, -2.85e-220], t$95$2, If[LessEqual[y4, 6.8e+138], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -1.3500000000000001e127 or -1.01999999999999992e91 < y4 < -3200 or 6.80000000000000022e138 < y4

   1. Initial program 20.0%

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

   3. Taylor expanded in x around inf 40.8%

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

   4. Taylor expanded in y1 around inf 44.4%

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

   5. Taylor expanded in k around inf 39.5%

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

   if -1.3500000000000001e127 < y4 < -1.01999999999999992e91 or -3200 < y4 < -2.8499999999999999e-220

   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 x around inf 40.0%

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

   4. Taylor expanded in i around -inf 37.4%

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

      1. mul-1-neg 37.4%

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

   6. Simplified 37.4%

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

   7. Taylor expanded in c around inf 38.7%

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

   if -2.8499999999999999e-220 < y4 < 6.80000000000000022e138

   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 x around inf 30.5%

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

   4. Taylor expanded in y1 around inf 25.4%

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

   5. Taylor expanded in i around inf 25.7%

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

      1. *-commutative 25.7%

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

   7. Simplified 25.7%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -1.35 \cdot 10^{+127}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -1.02 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -3200:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -2.85 \cdot 10^{-220}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6.8 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ t_2 := c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{if}\;y4 \leq -9.8 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -33000:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -2.05 \cdot 10^{-215}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq 4.3 \cdot 10^{+142}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y1 (* y2 y4)))) (t_2 (* c (* i (* x (- y))))))
   (if (<= y4 -9.8e+123)
     t_1
     (if (<= y4 -4.2e+87)
       t_2
       (if (<= y4 -33000.0)
         (* (- a) (* x (* y1 y2)))
         (if (<= y4 -2.05e-215)
           t_2
           (if (<= y4 4.3e+142) (* i (* j (* x y1))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double t_2 = c * (i * (x * -y));
	double tmp;
	if (y4 <= -9.8e+123) {
		tmp = t_1;
	} else if (y4 <= -4.2e+87) {
		tmp = t_2;
	} else if (y4 <= -33000.0) {
		tmp = -a * (x * (y1 * y2));
	} else if (y4 <= -2.05e-215) {
		tmp = t_2;
	} else if (y4 <= 4.3e+142) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = k * (y1 * (y2 * y4))
    t_2 = c * (i * (x * -y))
    if (y4 <= (-9.8d+123)) then
        tmp = t_1
    else if (y4 <= (-4.2d+87)) then
        tmp = t_2
    else if (y4 <= (-33000.0d0)) then
        tmp = -a * (x * (y1 * y2))
    else if (y4 <= (-2.05d-215)) then
        tmp = t_2
    else if (y4 <= 4.3d+142) then
        tmp = i * (j * (x * y1))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y1 * (y2 * y4));
	double t_2 = c * (i * (x * -y));
	double tmp;
	if (y4 <= -9.8e+123) {
		tmp = t_1;
	} else if (y4 <= -4.2e+87) {
		tmp = t_2;
	} else if (y4 <= -33000.0) {
		tmp = -a * (x * (y1 * y2));
	} else if (y4 <= -2.05e-215) {
		tmp = t_2;
	} else if (y4 <= 4.3e+142) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y1 * (y2 * y4))
	t_2 = c * (i * (x * -y))
	tmp = 0
	if y4 <= -9.8e+123:
		tmp = t_1
	elif y4 <= -4.2e+87:
		tmp = t_2
	elif y4 <= -33000.0:
		tmp = -a * (x * (y1 * y2))
	elif y4 <= -2.05e-215:
		tmp = t_2
	elif y4 <= 4.3e+142:
		tmp = i * (j * (x * y1))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y1 * Float64(y2 * y4)))
	t_2 = Float64(c * Float64(i * Float64(x * Float64(-y))))
	tmp = 0.0
	if (y4 <= -9.8e+123)
		tmp = t_1;
	elseif (y4 <= -4.2e+87)
		tmp = t_2;
	elseif (y4 <= -33000.0)
		tmp = Float64(Float64(-a) * Float64(x * Float64(y1 * y2)));
	elseif (y4 <= -2.05e-215)
		tmp = t_2;
	elseif (y4 <= 4.3e+142)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y1 * (y2 * y4));
	t_2 = c * (i * (x * -y));
	tmp = 0.0;
	if (y4 <= -9.8e+123)
		tmp = t_1;
	elseif (y4 <= -4.2e+87)
		tmp = t_2;
	elseif (y4 <= -33000.0)
		tmp = -a * (x * (y1 * y2));
	elseif (y4 <= -2.05e-215)
		tmp = t_2;
	elseif (y4 <= 4.3e+142)
		tmp = i * (j * (x * y1));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -9.8e+123], t$95$1, If[LessEqual[y4, -4.2e+87], t$95$2, If[LessEqual[y4, -33000.0], N[((-a) * N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, -2.05e-215], t$95$2, If[LessEqual[y4, 4.3e+142], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -9.79999999999999952e123 or 4.30000000000000012e142 < y4

   1. Initial program 16.4%

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

   3. Taylor expanded in x around inf 35.2%

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

   4. Taylor expanded in y1 around inf 43.3%

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

   5. Taylor expanded in k around inf 39.7%

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

   if -9.79999999999999952e123 < y4 < -4.2e87 or -33000 < y4 < -2.04999999999999992e-215

   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 x around inf 40.0%

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

   4. Taylor expanded in i around -inf 37.4%

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

      1. mul-1-neg 37.4%

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

   6. Simplified 37.4%

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

   7. Taylor expanded in c around inf 38.7%

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

   if -4.2e87 < y4 < -33000

   1. Initial program 37.9%

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

   3. Taylor expanded in x around inf 68.8%

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

   4. Taylor expanded in y1 around inf 50.1%

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

   5. Taylor expanded in a around inf 38.6%

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

      1. mul-1-neg 38.6%

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

      2. distribute-rgt-neg-in 38.6%

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

      3. mul-1-neg 38.6%

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

      4. associate-*r* 38.6%

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

      5. mul-1-neg 38.6%

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

   7. Simplified 38.6%

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

   if -2.04999999999999992e-215 < y4 < 4.30000000000000012e142

   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 x around inf 30.5%

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

   4. Taylor expanded in y1 around inf 25.4%

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

   5. Taylor expanded in i around inf 25.7%

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

      1. *-commutative 25.7%

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

   7. Simplified 25.7%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -9.8 \cdot 10^{+123}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -4.2 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y4 \leq -33000:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y4 \leq -2.05 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 4.3 \cdot 10^{+142}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 27.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= b -4.5e-126)
     (* a (* y (- (* x b) (* y3 y5))))
     (if (<= b 5.4e-283)
       t_1
       (if (<= b 6.8e-133)
         (* c (* i (* x (- y))))
         (if (<= b 1.12e+217) t_1 (* b (* x (- (* y a) (* j 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 * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (b <= -4.5e-126) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (b <= 5.4e-283) {
		tmp = t_1;
	} else if (b <= 6.8e-133) {
		tmp = c * (i * (x * -y));
	} else if (b <= 1.12e+217) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * 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 * (y3 * ((z * y1) - (y * y5)))
    if (b <= (-4.5d-126)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (b <= 5.4d-283) then
        tmp = t_1
    else if (b <= 6.8d-133) then
        tmp = c * (i * (x * -y))
    else if (b <= 1.12d+217) then
        tmp = t_1
    else
        tmp = b * (x * ((y * a) - (j * 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 * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (b <= -4.5e-126) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (b <= 5.4e-283) {
		tmp = t_1;
	} else if (b <= 6.8e-133) {
		tmp = c * (i * (x * -y));
	} else if (b <= 1.12e+217) {
		tmp = t_1;
	} else {
		tmp = b * (x * ((y * a) - (j * 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 * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if b <= -4.5e-126:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif b <= 5.4e-283:
		tmp = t_1
	elif b <= 6.8e-133:
		tmp = c * (i * (x * -y))
	elif b <= 1.12e+217:
		tmp = t_1
	else:
		tmp = b * (x * ((y * a) - (j * 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(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (b <= -4.5e-126)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (b <= 5.4e-283)
		tmp = t_1;
	elseif (b <= 6.8e-133)
		tmp = Float64(c * Float64(i * Float64(x * Float64(-y))));
	elseif (b <= 1.12e+217)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(y * a) - Float64(j * 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 * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (b <= -4.5e-126)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (b <= 5.4e-283)
		tmp = t_1;
	elseif (b <= 6.8e-133)
		tmp = c * (i * (x * -y));
	elseif (b <= 1.12e+217)
		tmp = t_1;
	else
		tmp = b * (x * ((y * a) - (j * 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[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e-126], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.4e-283], t$95$1, If[LessEqual[b, 6.8e-133], N[(c * N[(i * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+217], t$95$1, N[(b * N[(x * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.50000000000000025e-126

   1. Initial program 25.0%

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

   3. Simplified 26.0%

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

   5. Taylor expanded in a around inf 45.2%

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

   6. Taylor expanded in y around inf 41.9%

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

   if -4.50000000000000025e-126 < b < 5.4e-283 or 6.80000000000000012e-133 < b < 1.11999999999999993e217

   1. Initial program 20.6%

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

   3. Simplified 20.6%

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

   5. Taylor expanded in a around inf 36.5%

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

   6. Taylor expanded in y3 around inf 38.1%

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

   if 5.4e-283 < b < 6.80000000000000012e-133

   1. Initial program 10.4%

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

   3. Taylor expanded in x around inf 42.4%

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

   4. Taylor expanded in i around -inf 40.2%

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

      1. mul-1-neg 40.2%

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

   6. Simplified 40.2%

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

   7. Taylor expanded in c around inf 33.2%

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

   if 1.11999999999999993e217 < b

   1. Initial program 27.7%

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

   3. Taylor expanded in x around inf 36.8%

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

   4. Taylor expanded in b around inf 60.7%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-283}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(i \cdot \left(x \cdot \left(-y\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 26.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{if}\;y5 \leq -3.9 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-200}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y3 (- (* z y1) (* y y5))))))
   (if (<= y5 -3.9e+108)
     t_1
     (if (<= y5 -5e-208)
       (* a (* y (- (* x b) (* y3 y5))))
       (if (<= y5 6e-200) (* y0 (* c (* x 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 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y5 <= -3.9e+108) {
		tmp = t_1;
	} else if (y5 <= -5e-208) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y5 <= 6e-200) {
		tmp = y0 * (c * (x * 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 = a * (y3 * ((z * y1) - (y * y5)))
    if (y5 <= (-3.9d+108)) then
        tmp = t_1
    else if (y5 <= (-5d-208)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y5 <= 6d-200) then
        tmp = y0 * (c * (x * 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 = a * (y3 * ((z * y1) - (y * y5)));
	double tmp;
	if (y5 <= -3.9e+108) {
		tmp = t_1;
	} else if (y5 <= -5e-208) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y5 <= 6e-200) {
		tmp = y0 * (c * (x * 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 = a * (y3 * ((z * y1) - (y * y5)))
	tmp = 0
	if y5 <= -3.9e+108:
		tmp = t_1
	elif y5 <= -5e-208:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y5 <= 6e-200:
		tmp = y0 * (c * (x * 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(a * Float64(y3 * Float64(Float64(z * y1) - Float64(y * y5))))
	tmp = 0.0
	if (y5 <= -3.9e+108)
		tmp = t_1;
	elseif (y5 <= -5e-208)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y5 <= 6e-200)
		tmp = Float64(y0 * Float64(c * Float64(x * 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 = a * (y3 * ((z * y1) - (y * y5)));
	tmp = 0.0;
	if (y5 <= -3.9e+108)
		tmp = t_1;
	elseif (y5 <= -5e-208)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y5 <= 6e-200)
		tmp = y0 * (c * (x * 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[(a * N[(y3 * N[(N[(z * y1), $MachinePrecision] - N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.9e+108], t$95$1, If[LessEqual[y5, -5e-208], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 6e-200], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -3.89999999999999985e108 or 5.99999999999999989e-200 < y5

   1. Initial program 19.9%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in a around inf 36.1%

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

   6. Taylor expanded in y3 around inf 40.3%

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

   if -3.89999999999999985e108 < y5 < -4.99999999999999963e-208

   1. Initial program 28.2%

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

   3. Simplified 28.2%

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

   5. Taylor expanded in a around inf 49.0%

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

   6. Taylor expanded in y around inf 39.2%

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

   if -4.99999999999999963e-208 < y5 < 5.99999999999999989e-200

   1. Initial program 18.1%

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

   3. Taylor expanded in y0 around inf 36.3%

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

   4. Taylor expanded in c around inf 36.6%

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

   5. Taylor expanded in x around inf 35.0%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.9 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq -5 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y5 \leq 6 \cdot 10^{-200}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1 - y \cdot y5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 22.2% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -6 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{+22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -6e+139)
   (* k (* y1 (* y2 y4)))
   (if (<= y2 4.2e-73)
     (* a (* y (* x b)))
     (if (<= y2 1.45e+22) (* i (* j (* x y1))) (* c (* x (* y0 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 <= -6e+139) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= 4.2e-73) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 1.45e+22) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = c * (x * (y0 * 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 <= (-6d+139)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= 4.2d-73) then
        tmp = a * (y * (x * b))
    else if (y2 <= 1.45d+22) then
        tmp = i * (j * (x * y1))
    else
        tmp = c * (x * (y0 * 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 <= -6e+139) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= 4.2e-73) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 1.45e+22) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = c * (x * (y0 * 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 <= -6e+139:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= 4.2e-73:
		tmp = a * (y * (x * b))
	elif y2 <= 1.45e+22:
		tmp = i * (j * (x * y1))
	else:
		tmp = c * (x * (y0 * 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 <= -6e+139)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= 4.2e-73)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y2 <= 1.45e+22)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * 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 <= -6e+139)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= 4.2e-73)
		tmp = a * (y * (x * b));
	elseif (y2 <= 1.45e+22)
		tmp = i * (j * (x * y1));
	else
		tmp = c * (x * (y0 * 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, -6e+139], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.2e-73], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.45e+22], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -5.9999999999999999e139

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 42.2%

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

   4. Taylor expanded in y1 around inf 36.2%

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

   5. Taylor expanded in k around inf 45.0%

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

   if -5.9999999999999999e139 < y2 < 4.1999999999999997e-73

   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 23.2%

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

   5. Taylor expanded in a around inf 41.8%

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

   6. Taylor expanded in y around inf 31.7%

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

   7. Taylor expanded in b around inf 25.1%

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

      1. associate-*r* 27.3%

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

   9. Simplified 27.3%

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

   if 4.1999999999999997e-73 < y2 < 1.45e22

   1. Initial program 6.8%

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

   3. Taylor expanded in x around inf 38.5%

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

   4. Taylor expanded in y1 around inf 50.3%

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

   5. Taylor expanded in i around inf 32.7%

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

      1. *-commutative 32.7%

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

   7. Simplified 32.7%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if 1.45e22 < y2

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 33.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in c around inf 36.6%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 32.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -6 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 4.2 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 1.45 \cdot 10^{+22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.2% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -1.1 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.15 \cdot 10^{+22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -1.1e+139)
   (* k (* y1 (* y2 y4)))
   (if (<= y2 8.5e-71)
     (* a (* y (* x b)))
     (if (<= y2 3.15e+22) (* i (* j (* x y1))) (* y0 (* c (* x y2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.1e+139) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= 8.5e-71) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 3.15e+22) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-1.1d+139)) then
        tmp = k * (y1 * (y2 * y4))
    else if (y2 <= 8.5d-71) then
        tmp = a * (y * (x * b))
    else if (y2 <= 3.15d+22) then
        tmp = i * (j * (x * y1))
    else
        tmp = y0 * (c * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -1.1e+139) {
		tmp = k * (y1 * (y2 * y4));
	} else if (y2 <= 8.5e-71) {
		tmp = a * (y * (x * b));
	} else if (y2 <= 3.15e+22) {
		tmp = i * (j * (x * y1));
	} else {
		tmp = y0 * (c * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -1.1e+139:
		tmp = k * (y1 * (y2 * y4))
	elif y2 <= 8.5e-71:
		tmp = a * (y * (x * b))
	elif y2 <= 3.15e+22:
		tmp = i * (j * (x * y1))
	else:
		tmp = y0 * (c * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -1.1e+139)
		tmp = Float64(k * Float64(y1 * Float64(y2 * y4)));
	elseif (y2 <= 8.5e-71)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y2 <= 3.15e+22)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	else
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -1.1e+139)
		tmp = k * (y1 * (y2 * y4));
	elseif (y2 <= 8.5e-71)
		tmp = a * (y * (x * b));
	elseif (y2 <= 3.15e+22)
		tmp = i * (j * (x * y1));
	else
		tmp = y0 * (c * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -1.1e+139], N[(k * N[(y1 * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 8.5e-71], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 3.15e+22], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.1e139

   1. Initial program 24.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 42.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y1 around inf 36.2%

      \[\leadsto \color{blue}{y1 \cdot \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 45.0%

      \[\leadsto \color{blue}{k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)} \]

   if -1.1e139 < y2 < 8.49999999999999988e-71

   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 23.2%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 41.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 31.7%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around inf 25.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 27.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   9. Simplified 27.3%

      \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   if 8.49999999999999988e-71 < y2 < 3.1500000000000001e22

   1. Initial program 6.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 38.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Taylor expanded in y1 around inf 50.3%

      \[\leadsto \color{blue}{y1 \cdot \left(x \cdot \left(-1 \cdot \left(a \cdot y2\right) - -1 \cdot \left(i \cdot j\right)\right) + y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)} \]

   5. Taylor expanded in i around inf 32.7%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(x \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.7%

         \[\leadsto i \cdot \left(j \cdot \color{blue}{\left(y1 \cdot x\right)}\right) \]

   7. Simplified 32.7%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if 3.1500000000000001e22 < y2

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 33.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in c around inf 36.6%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 33.5%

      \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.1 \cdot 10^{+139}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 8.5 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y2 \leq 3.15 \cdot 10^{+22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 21.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-9} \lor \neg \left(b \leq 1.65 \cdot 10^{+128}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -1.75e-9) (not (<= b 1.65e+128)))
   (* a (* y (* x b)))
   (* c (* x (* y0 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 ((b <= -1.75e-9) || !(b <= 1.65e+128)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (x * (y0 * 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 ((b <= (-1.75d-9)) .or. (.not. (b <= 1.65d+128))) then
        tmp = a * (y * (x * b))
    else
        tmp = c * (x * (y0 * 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 ((b <= -1.75e-9) || !(b <= 1.65e+128)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (x * (y0 * 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 (b <= -1.75e-9) or not (b <= 1.65e+128):
		tmp = a * (y * (x * b))
	else:
		tmp = c * (x * (y0 * 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 ((b <= -1.75e-9) || !(b <= 1.65e+128))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(c * Float64(x * Float64(y0 * 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 ((b <= -1.75e-9) || ~((b <= 1.65e+128)))
		tmp = a * (y * (x * b));
	else
		tmp = c * (x * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[b, -1.75e-9], N[Not[LessEqual[b, 1.65e+128]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(x * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.75e-9 or 1.65e128 < b

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 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 a around inf 44.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 42.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around inf 32.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   9. Simplified 39.7%

      \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   if -1.75e-9 < b < 1.65e128

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 33.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in c around inf 27.2%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 19.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-9} \lor \neg \left(b \leq 1.65 \cdot 10^{+128}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-9} \lor \neg \left(b \leq 2.6 \cdot 10^{+132}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -2.1e-9) (not (<= b 2.6e+132)))
   (* a (* y (* x b)))
   (* c (* y2 (* 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 ((b <= -2.1e-9) || !(b <= 2.6e+132)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y2 * (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 ((b <= (-2.1d-9)) .or. (.not. (b <= 2.6d+132))) then
        tmp = a * (y * (x * b))
    else
        tmp = c * (y2 * (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 ((b <= -2.1e-9) || !(b <= 2.6e+132)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = c * (y2 * (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 (b <= -2.1e-9) or not (b <= 2.6e+132):
		tmp = a * (y * (x * b))
	else:
		tmp = c * (y2 * (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 ((b <= -2.1e-9) || !(b <= 2.6e+132))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(c * Float64(y2 * 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 ((b <= -2.1e-9) || ~((b <= 2.6e+132)))
		tmp = a * (y * (x * b));
	else
		tmp = c * (y2 * (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[Or[LessEqual[b, -2.1e-9], N[Not[LessEqual[b, 2.6e+132]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.10000000000000019e-9 or 2.6e132 < b

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 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 a around inf 44.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   6. Taylor expanded in y around inf 42.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   7. Taylor expanded in b around inf 32.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   9. Simplified 39.7%

      \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

   if -2.10000000000000019e-9 < b < 2.6e132

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y0 around inf 33.9%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   4. Taylor expanded in c around inf 27.2%

      \[\leadsto y0 \cdot \color{blue}{\left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf 19.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(y0 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 21.0%

         \[\leadsto c \cdot \color{blue}{\left(\left(x \cdot y0\right) \cdot y2\right)} \]

      2. *-commutative 21.0%

         \[\leadsto c \cdot \left(\color{blue}{\left(y0 \cdot x\right)} \cdot y2\right) \]

   7. Simplified 21.0%

      \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x\right) \cdot y2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-9} \lor \neg \left(b \leq 2.6 \cdot 10^{+132}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 17.0% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 21.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 22.5%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 38.7%

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

6. Taylor expanded in y around inf 30.4%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

7. Taylor expanded in b around inf 18.6%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

8. Final simplification 18.6%

   \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]
9. Add Preprocessing

Alternative 34: 16.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y \cdot \left(x \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y (* x b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y * (x * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y * (x * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y * Float64(x * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y * (x * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 21.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 22.5%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \mathsf{fma}\left(c, y0, y1 \cdot \left(-a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \mathsf{fma}\left(b, y4, -i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 38.7%

   \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + b \cdot \left(-1 \cdot \left(t \cdot z\right) + x \cdot y\right)\right) - -1 \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

6. Taylor expanded in y around inf 30.4%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

7. Taylor expanded in b around inf 18.6%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]
8. Step-by-step derivation

   1. associate-*r* 20.5%

      \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

9. Simplified 20.5%

   \[\leadsto a \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot y\right)} \]

10. Final simplification 20.5%

    \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]
11. Add Preprocessing

Developer target: 26.8% 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 2024076 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))