Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.6% → 36.8%

Time: 1.9min

Alternatives: 38

Speedup: 3.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 30.6% 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: 36.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_2\right) + y4 \cdot t_1\right)\\ t_4 := t \cdot j - y \cdot k\\ t_5 := k \cdot y2 - j \cdot y3\\ t_6 := j \cdot y3 - k \cdot y2\\ t_7 := y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot t_6\right)\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+154}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_4 + y1 \cdot t_5\right) + c \cdot t_1\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-228}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-273}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_5 - a \cdot t_2\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-299}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;c \leq 10^{-225}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-180}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{-165}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot t_6\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(y4 \cdot t_4 + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-11}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+90} \lor \neg \left(c \leq 9.2 \cdot 10^{+167}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \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 (- (* y y3) (* t y2)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (* c (+ (+ (* i (- (* z t) (* x y))) (* y0 t_2)) (* y4 t_1))))
        (t_4 (- (* t j) (* y k)))
        (t_5 (- (* k y2) (* j y3)))
        (t_6 (- (* j y3) (* k y2)))
        (t_7
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (+ (* a (- (* t y2) (* y y3))) (* y0 t_6))))))
   (if (<= c -1.2e+154)
     (* (* y0 y3) (- (* j y5) (* z c)))
     (if (<= c -1.05e+78)
       t_3
       (if (<= c -3.5e-67)
         (* y4 (+ (+ (* b t_4) (* y1 t_5)) (* c t_1)))
         (if (<= c -4.5e-228)
           t_7
           (if (<= c -2.5e-273)
             (* y1 (- (* y4 t_5) (* a t_2)))
             (if (<= c -6.2e-299)
               t_7
               (if (<= c 1e-225)
                 (* x (* y1 (- (* i j) (* a y2))))
                 (if (<= c 1.45e-180)
                   (* k (* y4 (- (* y1 y2) (* y b))))
                   (if (<= c 8.6e-165)
                     (* y0 (* y5 t_6))
                     (if (<= c 3.9e-98)
                       (*
                        b
                        (+
                         (* a (- (* x y) (* z t)))
                         (+ (* y4 t_4) (* y0 (- (* z k) (* x j))))))
                       (if (<= c 1.65e-11)
                         (* (* j y1) (- (* x i) (* y3 y4)))
                         (if (<= c 3.5e+59)
                           (*
                            y2
                            (+
                             (+
                              (* x (- (* c y0) (* a y1)))
                              (* k (- (* y1 y4) (* y0 y5))))
                             (* t (- (* a y5) (* c y4)))))
                           (if (or (<= c 2.15e+90) (not (<= c 9.2e+167)))
                             t_3
                             (* y2 (* y0 (- (* x c) (* k 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 = (y * y3) - (t * y2);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_1));
	double t_4 = (t * j) - (y * k);
	double t_5 = (k * y2) - (j * y3);
	double t_6 = (j * y3) - (k * y2);
	double t_7 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_6)));
	double tmp;
	if (c <= -1.2e+154) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (c <= -1.05e+78) {
		tmp = t_3;
	} else if (c <= -3.5e-67) {
		tmp = y4 * (((b * t_4) + (y1 * t_5)) + (c * t_1));
	} else if (c <= -4.5e-228) {
		tmp = t_7;
	} else if (c <= -2.5e-273) {
		tmp = y1 * ((y4 * t_5) - (a * t_2));
	} else if (c <= -6.2e-299) {
		tmp = t_7;
	} else if (c <= 1e-225) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (c <= 1.45e-180) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (c <= 8.6e-165) {
		tmp = y0 * (y5 * t_6);
	} else if (c <= 3.9e-98) {
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * t_4) + (y0 * ((z * k) - (x * j)))));
	} else if (c <= 1.65e-11) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (c <= 3.5e+59) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if ((c <= 2.15e+90) || !(c <= 9.2e+167)) {
		tmp = t_3;
	} else {
		tmp = y2 * (y0 * ((x * c) - (k * 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 = (y * y3) - (t * y2)
    t_2 = (x * y2) - (z * y3)
    t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_1))
    t_4 = (t * j) - (y * k)
    t_5 = (k * y2) - (j * y3)
    t_6 = (j * y3) - (k * y2)
    t_7 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_6)))
    if (c <= (-1.2d+154)) then
        tmp = (y0 * y3) * ((j * y5) - (z * c))
    else if (c <= (-1.05d+78)) then
        tmp = t_3
    else if (c <= (-3.5d-67)) then
        tmp = y4 * (((b * t_4) + (y1 * t_5)) + (c * t_1))
    else if (c <= (-4.5d-228)) then
        tmp = t_7
    else if (c <= (-2.5d-273)) then
        tmp = y1 * ((y4 * t_5) - (a * t_2))
    else if (c <= (-6.2d-299)) then
        tmp = t_7
    else if (c <= 1d-225) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else if (c <= 1.45d-180) then
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    else if (c <= 8.6d-165) then
        tmp = y0 * (y5 * t_6)
    else if (c <= 3.9d-98) then
        tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * t_4) + (y0 * ((z * k) - (x * j)))))
    else if (c <= 1.65d-11) then
        tmp = (j * y1) * ((x * i) - (y3 * y4))
    else if (c <= 3.5d+59) then
        tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if ((c <= 2.15d+90) .or. (.not. (c <= 9.2d+167))) then
        tmp = t_3
    else
        tmp = y2 * (y0 * ((x * c) - (k * 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 = (y * y3) - (t * y2);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_1));
	double t_4 = (t * j) - (y * k);
	double t_5 = (k * y2) - (j * y3);
	double t_6 = (j * y3) - (k * y2);
	double t_7 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_6)));
	double tmp;
	if (c <= -1.2e+154) {
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	} else if (c <= -1.05e+78) {
		tmp = t_3;
	} else if (c <= -3.5e-67) {
		tmp = y4 * (((b * t_4) + (y1 * t_5)) + (c * t_1));
	} else if (c <= -4.5e-228) {
		tmp = t_7;
	} else if (c <= -2.5e-273) {
		tmp = y1 * ((y4 * t_5) - (a * t_2));
	} else if (c <= -6.2e-299) {
		tmp = t_7;
	} else if (c <= 1e-225) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else if (c <= 1.45e-180) {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	} else if (c <= 8.6e-165) {
		tmp = y0 * (y5 * t_6);
	} else if (c <= 3.9e-98) {
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * t_4) + (y0 * ((z * k) - (x * j)))));
	} else if (c <= 1.65e-11) {
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	} else if (c <= 3.5e+59) {
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if ((c <= 2.15e+90) || !(c <= 9.2e+167)) {
		tmp = t_3;
	} else {
		tmp = y2 * (y0 * ((x * c) - (k * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * y3) - (t * y2)
	t_2 = (x * y2) - (z * y3)
	t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_1))
	t_4 = (t * j) - (y * k)
	t_5 = (k * y2) - (j * y3)
	t_6 = (j * y3) - (k * y2)
	t_7 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_6)))
	tmp = 0
	if c <= -1.2e+154:
		tmp = (y0 * y3) * ((j * y5) - (z * c))
	elif c <= -1.05e+78:
		tmp = t_3
	elif c <= -3.5e-67:
		tmp = y4 * (((b * t_4) + (y1 * t_5)) + (c * t_1))
	elif c <= -4.5e-228:
		tmp = t_7
	elif c <= -2.5e-273:
		tmp = y1 * ((y4 * t_5) - (a * t_2))
	elif c <= -6.2e-299:
		tmp = t_7
	elif c <= 1e-225:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	elif c <= 1.45e-180:
		tmp = k * (y4 * ((y1 * y2) - (y * b)))
	elif c <= 8.6e-165:
		tmp = y0 * (y5 * t_6)
	elif c <= 3.9e-98:
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * t_4) + (y0 * ((z * k) - (x * j)))))
	elif c <= 1.65e-11:
		tmp = (j * y1) * ((x * i) - (y3 * y4))
	elif c <= 3.5e+59:
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif (c <= 2.15e+90) or not (c <= 9.2e+167):
		tmp = t_3
	else:
		tmp = y2 * (y0 * ((x * c) - (k * 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(y * y3) - Float64(t * y2))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_2)) + Float64(y4 * t_1)))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(Float64(k * y2) - Float64(j * y3))
	t_6 = Float64(Float64(j * y3) - Float64(k * y2))
	t_7 = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * t_6))))
	tmp = 0.0
	if (c <= -1.2e+154)
		tmp = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)));
	elseif (c <= -1.05e+78)
		tmp = t_3;
	elseif (c <= -3.5e-67)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_4) + Float64(y1 * t_5)) + Float64(c * t_1)));
	elseif (c <= -4.5e-228)
		tmp = t_7;
	elseif (c <= -2.5e-273)
		tmp = Float64(y1 * Float64(Float64(y4 * t_5) - Float64(a * t_2)));
	elseif (c <= -6.2e-299)
		tmp = t_7;
	elseif (c <= 1e-225)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	elseif (c <= 1.45e-180)
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (c <= 8.6e-165)
		tmp = Float64(y0 * Float64(y5 * t_6));
	elseif (c <= 3.9e-98)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(y4 * t_4) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))));
	elseif (c <= 1.65e-11)
		tmp = Float64(Float64(j * y1) * Float64(Float64(x * i) - Float64(y3 * y4)));
	elseif (c <= 3.5e+59)
		tmp = Float64(y2 * Float64(Float64(Float64(x * Float64(Float64(c * y0) - Float64(a * y1))) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif ((c <= 2.15e+90) || !(c <= 9.2e+167))
		tmp = t_3;
	else
		tmp = Float64(y2 * Float64(y0 * Float64(Float64(x * c) - Float64(k * 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 = (y * y3) - (t * y2);
	t_2 = (x * y2) - (z * y3);
	t_3 = c * (((i * ((z * t) - (x * y))) + (y0 * t_2)) + (y4 * t_1));
	t_4 = (t * j) - (y * k);
	t_5 = (k * y2) - (j * y3);
	t_6 = (j * y3) - (k * y2);
	t_7 = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_6)));
	tmp = 0.0;
	if (c <= -1.2e+154)
		tmp = (y0 * y3) * ((j * y5) - (z * c));
	elseif (c <= -1.05e+78)
		tmp = t_3;
	elseif (c <= -3.5e-67)
		tmp = y4 * (((b * t_4) + (y1 * t_5)) + (c * t_1));
	elseif (c <= -4.5e-228)
		tmp = t_7;
	elseif (c <= -2.5e-273)
		tmp = y1 * ((y4 * t_5) - (a * t_2));
	elseif (c <= -6.2e-299)
		tmp = t_7;
	elseif (c <= 1e-225)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	elseif (c <= 1.45e-180)
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	elseif (c <= 8.6e-165)
		tmp = y0 * (y5 * t_6);
	elseif (c <= 3.9e-98)
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * t_4) + (y0 * ((z * k) - (x * j)))));
	elseif (c <= 1.65e-11)
		tmp = (j * y1) * ((x * i) - (y3 * y4));
	elseif (c <= 3.5e+59)
		tmp = y2 * (((x * ((c * y0) - (a * y1))) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif ((c <= 2.15e+90) || ~((c <= 9.2e+167)))
		tmp = t_3;
	else
		tmp = y2 * (y0 * ((x * c) - (k * 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[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+154], N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e+78], t$95$3, If[LessEqual[c, -3.5e-67], N[(y4 * N[(N[(N[(b * t$95$4), $MachinePrecision] + N[(y1 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.5e-228], t$95$7, If[LessEqual[c, -2.5e-273], N[(y1 * N[(N[(y4 * t$95$5), $MachinePrecision] - N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.2e-299], t$95$7, If[LessEqual[c, 1e-225], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e-180], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.6e-165], N[(y0 * N[(y5 * t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.9e-98], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * t$95$4), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e-11], N[(N[(j * y1), $MachinePrecision] * N[(N[(x * i), $MachinePrecision] - N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+59], N[(y2 * N[(N[(N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 2.15e+90], N[Not[LessEqual[c, 9.2e+167]], $MachinePrecision]], t$95$3, N[(y2 * N[(y0 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if c < -1.20000000000000007e154

   1. Initial program 9.7%

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

   3. Simplified 9.7%

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

   4. Taylor expanded in y0 around inf 41.2%

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

      1. mul-1-neg 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in y3 around inf 66.3%

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

      1. distribute-lft-out-- 66.3%

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

      2. associate-*r* 66.3%

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

      3. mul-1-neg 66.3%

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

      4. *-commutative 66.3%

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

      5. *-commutative 66.3%

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

      6. *-commutative 66.3%

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

   9. Simplified 66.3%

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

   if -1.20000000000000007e154 < c < -1.05e78 or 3.5e59 < c < 2.1499999999999999e90 or 9.19999999999999952e167 < c

   1. Initial program 26.2%

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

   3. Simplified 26.2%

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

   4. Taylor expanded in c around inf 69.7%

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

      1. mul-1-neg 69.7%

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

   6. Simplified 69.7%

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

   if -1.05e78 < c < -3.5e-67

   1. Initial program 27.0%

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

   3. Simplified 27.0%

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

   4. Taylor expanded in y4 around inf 57.0%

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

   if -3.5e-67 < c < -4.4999999999999999e-228 or -2.49999999999999983e-273 < c < -6.1999999999999999e-299

   1. Initial program 41.0%

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

   3. Simplified 47.1%

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

   4. Taylor expanded in y5 around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

   6. Simplified 61.6%

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

   if -4.4999999999999999e-228 < c < -2.49999999999999983e-273

   1. Initial program 23.1%

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

   3. Simplified 23.1%

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

   4. Taylor expanded in y1 around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. mul-1-neg 61.5%

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

      3. sub-neg 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in i around 0 92.3%

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

   if -6.1999999999999999e-299 < c < 9.9999999999999996e-226

   1. Initial program 22.2%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y1 around inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. mul-1-neg 88.9%

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

      3. sub-neg 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in x around inf 88.9%

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

      1. associate-*r* 88.9%

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

      2. *-commutative 88.9%

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

      3. *-commutative 88.9%

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

   9. Simplified 88.9%

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

   if 9.9999999999999996e-226 < c < 1.4499999999999999e-180

   1. Initial program 28.6%

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

   3. Simplified 28.6%

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

   4. Taylor expanded in y4 around inf 42.9%

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

   5. Taylor expanded in k around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

   7. Simplified 71.5%

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

   if 1.4499999999999999e-180 < c < 8.60000000000000013e-165

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y0 around inf 57.1%

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

      1. mul-1-neg 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in y5 around inf 100.0%

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

   if 8.60000000000000013e-165 < c < 3.89999999999999971e-98

   1. Initial program 24.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in b around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. mul-1-neg 63.3%

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

   6. Simplified 63.3%

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

   if 3.89999999999999971e-98 < c < 1.6500000000000001e-11

   1. Initial program 22.5%

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

   3. Simplified 26.9%

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

   4. Taylor expanded in y1 around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. mul-1-neg 48.0%

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

      3. sub-neg 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in j around inf 65.5%

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

      1. associate-*r* 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

   9. Simplified 61.5%

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

   if 1.6500000000000001e-11 < c < 3.5e59

   1. Initial program 17.1%

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

   3. Simplified 17.1%

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

   4. Taylor expanded in y2 around inf 67.3%

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

   if 2.1499999999999999e90 < c < 9.19999999999999952e167

   1. Initial program 23.1%

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

   3. Simplified 23.1%

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

   4. Taylor expanded in y0 around inf 61.4%

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

      1. mul-1-neg 61.4%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in y2 around inf 62.3%

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

      1. associate-*r* 62.4%

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

      2. *-commutative 62.4%

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

   9. Simplified 62.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+154}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{+78}:\\ \;\;\;\;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 -3.5 \cdot 10^{-67}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-228}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-273}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-299}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;c \leq 10^{-225}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-180}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{-165}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(y4 \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-11}:\\ \;\;\;\;\left(j \cdot y1\right) \cdot \left(x \cdot i - y3 \cdot y4\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;c \leq 2.15 \cdot 10^{+90} \lor \neg \left(c \leq 9.2 \cdot 10^{+167}\right):\\ \;\;\;\;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}:\\ \;\;\;\;y2 \cdot \left(y0 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \end{array} \]

Alternative 2: 52.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* b y0) (* i y1)) (- (* z k) (* x j))))
             (* t_2 (- (* c y0) (* a y1))))
            (* (- (* b y4) (* i y5)) (- (* t j) (* y k))))
           (* (- (* t y2) (* y y3)) (- (* a y5) (* c y4))))
          (* t_1 (- (* y1 y4) (* y0 y5))))))
   (if (<= t_3 INFINITY) t_3 (* y1 (- (* y4 t_1) (* a 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 = (k * y2) - (j * y3);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_1 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y1 * ((y4 * t_1) - (a * t_2));
	}
	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 = (k * y2) - (j * y3);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_1 * ((y1 * y4) - (y0 * y5)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = y1 * ((y4 * t_1) - (a * 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 = (k * y2) - (j * y3)
	t_2 = (x * y2) - (z * y3)
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_1 * ((y1 * y4) - (y0 * y5)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = y1 * ((y4 * t_1) - (a * t_2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(a * b) - Float64(c * i)) * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * Float64(Float64(z * k) - Float64(x * j)))) + Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(Float64(Float64(b * y4) - Float64(i * y5)) * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(a * y5) - Float64(c * y4)))) + Float64(t_1 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y1 * Float64(Float64(y4 * t_1) - Float64(a * 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 = (k * y2) - (j * y3);
	t_2 = (x * y2) - (z * y3);
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (t_2 * ((c * y0) - (a * y1)))) + (((b * y4) - (i * y5)) * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * ((a * y5) - (c * y4)))) + (t_1 * ((y1 * y4) - (y0 * y5)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = y1 * ((y4 * t_1) - (a * t_2));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.5%

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

   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 7.7%

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

   4. Taylor expanded in y1 around inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. mul-1-neg 40.3%

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

      3. sub-neg 40.3%

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

   6. Simplified 40.3%

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

   7. Taylor expanded in i around 0 40.5%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

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

Alternative 3: 35.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_4 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_5 := y1 \cdot t_2\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5500000:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_2 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-204}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-216}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-13}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + t_5\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+130}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+180}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+251}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+268}:\\ \;\;\;\;y4 \cdot \left(t_5 - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* a (- (* y2 y5) (* z b)))))
        (t_2 (- (* k y2) (* j y3)))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0))))))
        (t_4 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_5 (* y1 t_2)))
   (if (<= x -2.9e+92)
     t_3
     (if (<= x -5500000.0)
       (* y1 (- (* y4 t_2) (* a (- (* x y2) (* z y3)))))
       (if (<= x -1.8e-125)
         t_1
         (if (<= x -7e-204)
           t_4
           (if (<= x -7.5e-297)
             t_1
             (if (<= x 5.4e-216)
               t_4
               (if (<= x 7.5e-13)
                 (*
                  y4
                  (+
                   (+ (* b (- (* t j) (* y k))) t_5)
                   (* c (- (* y y3) (* t y2)))))
                 (if (<= x 6.4e+130)
                   (* y1 (* a (- (* z y3) (* x y2))))
                   (if (<= x 2.15e+180)
                     (* (* k y0) (- (* z b) (* y2 y5)))
                     (if (<= x 1.55e+251)
                       (* (- (* y a) (* j y0)) (* x b))
                       (if (<= x 6e+268)
                         (* y4 (- t_5 (* c (- (* t y2) (* y y3)))))
                         t_3)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (a * ((y2 * y5) - (z * b)));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_5 = y1 * t_2;
	double tmp;
	if (x <= -2.9e+92) {
		tmp = t_3;
	} else if (x <= -5500000.0) {
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	} else if (x <= -1.8e-125) {
		tmp = t_1;
	} else if (x <= -7e-204) {
		tmp = t_4;
	} else if (x <= -7.5e-297) {
		tmp = t_1;
	} else if (x <= 5.4e-216) {
		tmp = t_4;
	} else if (x <= 7.5e-13) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_5) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 6.4e+130) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 2.15e+180) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (x <= 1.55e+251) {
		tmp = ((y * a) - (j * y0)) * (x * b);
	} else if (x <= 6e+268) {
		tmp = y4 * (t_5 - (c * ((t * y2) - (y * y3))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = t * (a * ((y2 * y5) - (z * b)))
    t_2 = (k * y2) - (j * y3)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    t_4 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_5 = y1 * t_2
    if (x <= (-2.9d+92)) then
        tmp = t_3
    else if (x <= (-5500000.0d0)) then
        tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
    else if (x <= (-1.8d-125)) then
        tmp = t_1
    else if (x <= (-7d-204)) then
        tmp = t_4
    else if (x <= (-7.5d-297)) then
        tmp = t_1
    else if (x <= 5.4d-216) then
        tmp = t_4
    else if (x <= 7.5d-13) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + t_5) + (c * ((y * y3) - (t * y2))))
    else if (x <= 6.4d+130) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (x <= 2.15d+180) then
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    else if (x <= 1.55d+251) then
        tmp = ((y * a) - (j * y0)) * (x * b)
    else if (x <= 6d+268) then
        tmp = y4 * (t_5 - (c * ((t * y2) - (y * y3))))
    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 = t * (a * ((y2 * y5) - (z * b)));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double t_4 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_5 = y1 * t_2;
	double tmp;
	if (x <= -2.9e+92) {
		tmp = t_3;
	} else if (x <= -5500000.0) {
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	} else if (x <= -1.8e-125) {
		tmp = t_1;
	} else if (x <= -7e-204) {
		tmp = t_4;
	} else if (x <= -7.5e-297) {
		tmp = t_1;
	} else if (x <= 5.4e-216) {
		tmp = t_4;
	} else if (x <= 7.5e-13) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_5) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 6.4e+130) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 2.15e+180) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (x <= 1.55e+251) {
		tmp = ((y * a) - (j * y0)) * (x * b);
	} else if (x <= 6e+268) {
		tmp = y4 * (t_5 - (c * ((t * y2) - (y * y3))));
	} 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 = t * (a * ((y2 * y5) - (z * b)))
	t_2 = (k * y2) - (j * y3)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	t_4 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_5 = y1 * t_2
	tmp = 0
	if x <= -2.9e+92:
		tmp = t_3
	elif x <= -5500000.0:
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
	elif x <= -1.8e-125:
		tmp = t_1
	elif x <= -7e-204:
		tmp = t_4
	elif x <= -7.5e-297:
		tmp = t_1
	elif x <= 5.4e-216:
		tmp = t_4
	elif x <= 7.5e-13:
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_5) + (c * ((y * y3) - (t * y2))))
	elif x <= 6.4e+130:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif x <= 2.15e+180:
		tmp = (k * y0) * ((z * b) - (y2 * y5))
	elif x <= 1.55e+251:
		tmp = ((y * a) - (j * y0)) * (x * b)
	elif x <= 6e+268:
		tmp = y4 * (t_5 - (c * ((t * y2) - (y * y3))))
	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(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_4 = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_5 = Float64(y1 * t_2)
	tmp = 0.0
	if (x <= -2.9e+92)
		tmp = t_3;
	elseif (x <= -5500000.0)
		tmp = Float64(y1 * Float64(Float64(y4 * t_2) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))));
	elseif (x <= -1.8e-125)
		tmp = t_1;
	elseif (x <= -7e-204)
		tmp = t_4;
	elseif (x <= -7.5e-297)
		tmp = t_1;
	elseif (x <= 5.4e-216)
		tmp = t_4;
	elseif (x <= 7.5e-13)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + t_5) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= 6.4e+130)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (x <= 2.15e+180)
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	elseif (x <= 1.55e+251)
		tmp = Float64(Float64(Float64(y * a) - Float64(j * y0)) * Float64(x * b));
	elseif (x <= 6e+268)
		tmp = Float64(y4 * Float64(t_5 - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	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 = t * (a * ((y2 * y5) - (z * b)));
	t_2 = (k * y2) - (j * y3);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	t_4 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_5 = y1 * t_2;
	tmp = 0.0;
	if (x <= -2.9e+92)
		tmp = t_3;
	elseif (x <= -5500000.0)
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	elseif (x <= -1.8e-125)
		tmp = t_1;
	elseif (x <= -7e-204)
		tmp = t_4;
	elseif (x <= -7.5e-297)
		tmp = t_1;
	elseif (x <= 5.4e-216)
		tmp = t_4;
	elseif (x <= 7.5e-13)
		tmp = y4 * (((b * ((t * j) - (y * k))) + t_5) + (c * ((y * y3) - (t * y2))));
	elseif (x <= 6.4e+130)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (x <= 2.15e+180)
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	elseif (x <= 1.55e+251)
		tmp = ((y * a) - (j * y0)) * (x * b);
	elseif (x <= 6e+268)
		tmp = y4 * (t_5 - (c * ((t * y2) - (y * y3))));
	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[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y1 * t$95$2), $MachinePrecision]}, If[LessEqual[x, -2.9e+92], t$95$3, If[LessEqual[x, -5500000.0], N[(y1 * N[(N[(y4 * t$95$2), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.8e-125], t$95$1, If[LessEqual[x, -7e-204], t$95$4, If[LessEqual[x, -7.5e-297], t$95$1, If[LessEqual[x, 5.4e-216], t$95$4, If[LessEqual[x, 7.5e-13], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e+130], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+180], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+251], N[(N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+268], N[(y4 * N[(t$95$5 - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -2.9000000000000001e92 or 5.99999999999999984e268 < x

   1. Initial program 21.5%

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

   3. Simplified 21.5%

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

   4. Taylor expanded in x around inf 72.0%

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

   if -2.9000000000000001e92 < x < -5.5e6

   1. Initial program 14.3%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in y1 around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. mul-1-neg 76.2%

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

      3. sub-neg 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in i around 0 76.2%

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

   if -5.5e6 < x < -1.8000000000000001e-125 or -7.00000000000000054e-204 < x < -7.4999999999999994e-297

   1. Initial program 33.8%

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

   3. Simplified 33.8%

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

   4. Taylor expanded in t around inf 45.5%

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

      1. associate--l+ 45.5%

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

      2. mul-1-neg 45.5%

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

   6. Simplified 45.5%

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

   7. Taylor expanded in a around -inf 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-*l* 48.1%

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

      3. *-commutative 48.1%

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

      4. +-commutative 48.1%

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

      5. mul-1-neg 48.1%

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

      6. unsub-neg 48.1%

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

   9. Simplified 48.1%

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

   if -1.8000000000000001e-125 < x < -7.00000000000000054e-204 or -7.4999999999999994e-297 < x < 5.3999999999999998e-216

   1. Initial program 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in y0 around inf 73.6%

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

      1. mul-1-neg 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in y5 around inf 67.3%

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

   if 5.3999999999999998e-216 < x < 7.5000000000000004e-13

   1. Initial program 32.1%

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

   3. Simplified 32.1%

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

   4. Taylor expanded in y4 around inf 51.0%

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

   if 7.5000000000000004e-13 < x < 6.4e130

   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%

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

   4. Taylor expanded in y1 around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. mul-1-neg 37.1%

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

      3. sub-neg 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in a around inf 64.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 59.9%

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

      2. *-commutative 59.9%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if 6.4e130 < x < 2.14999999999999995e180

   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%

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

   4. Taylor expanded in y0 around inf 25.0%

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

      1. mul-1-neg 25.0%

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

   6. Simplified 25.0%

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

   7. Taylor expanded in k around -inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. mul-1-neg 66.9%

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

      3. unsub-neg 66.9%

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

      4. *-commutative 66.9%

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

   9. Simplified 66.9%

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

   if 2.14999999999999995e180 < x < 1.5499999999999999e251

   1. Initial program 19.0%

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

   3. Simplified 19.0%

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

   4. Taylor expanded in b around inf 38.5%

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

      1. associate--l+ 38.5%

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

      2. mul-1-neg 38.5%

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

   6. Simplified 38.5%

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

   7. Taylor expanded in x around inf 53.3%

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

   if 1.5499999999999999e251 < x < 5.99999999999999984e268

   1. Initial program 42.1%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in y4 around inf 60.9%

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

   5. Taylor expanded in b around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -5500000:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-204}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-216}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-13}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+130}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+180}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+251}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+268}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 4: 36.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_5 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -80000000:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_3 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-219}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_3\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+131}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+169}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+233}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{+263}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* t (* a (- (* y2 y5) (* z b)))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3 (- (* k y2) (* j y3)))
        (t_4
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_2))
           (* j (- (* i y1) (* b y0))))))
        (t_5 (* y0 (* y5 (- (* j y3) (* k y2))))))
   (if (<= x -1.3e+92)
     t_4
     (if (<= x -80000000.0)
       (* y1 (- (* y4 t_3) (* a (- (* x y2) (* z y3)))))
       (if (<= x -2.5e-126)
         t_1
         (if (<= x -1.5e-203)
           t_5
           (if (<= x -6.2e-298)
             t_1
             (if (<= x 1.05e-219)
               t_5
               (if (<= x 2.8e-12)
                 (*
                  y4
                  (+
                   (+ (* b (- (* t j) (* y k))) (* y1 t_3))
                   (* c (- (* y y3) (* t y2)))))
                 (if (<= x 2.85e+131)
                   (* y1 (* a (- (* z y3) (* x y2))))
                   (if (<= x 3.2e+169)
                     (* (* k y0) (- (* z b) (* y2 y5)))
                     (if (<= x 1.05e+233)
                       (*
                        y2
                        (+
                         (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
                         (* t (- (* a y5) (* c y4)))))
                       (if (<= x 1.14e+263)
                         (* b (* j (- (* t y4) (* x y0))))
                         t_4)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (a * ((y2 * y5) - (z * b)));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double t_5 = y0 * (y5 * ((j * y3) - (k * y2)));
	double tmp;
	if (x <= -1.3e+92) {
		tmp = t_4;
	} else if (x <= -80000000.0) {
		tmp = y1 * ((y4 * t_3) - (a * ((x * y2) - (z * y3))));
	} else if (x <= -2.5e-126) {
		tmp = t_1;
	} else if (x <= -1.5e-203) {
		tmp = t_5;
	} else if (x <= -6.2e-298) {
		tmp = t_1;
	} else if (x <= 1.05e-219) {
		tmp = t_5;
	} else if (x <= 2.8e-12) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 2.85e+131) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 3.2e+169) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (x <= 1.05e+233) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (x <= 1.14e+263) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = t * (a * ((y2 * y5) - (z * b)))
    t_2 = (c * y0) - (a * y1)
    t_3 = (k * y2) - (j * y3)
    t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    t_5 = y0 * (y5 * ((j * y3) - (k * y2)))
    if (x <= (-1.3d+92)) then
        tmp = t_4
    else if (x <= (-80000000.0d0)) then
        tmp = y1 * ((y4 * t_3) - (a * ((x * y2) - (z * y3))))
    else if (x <= (-2.5d-126)) then
        tmp = t_1
    else if (x <= (-1.5d-203)) then
        tmp = t_5
    else if (x <= (-6.2d-298)) then
        tmp = t_1
    else if (x <= 1.05d-219) then
        tmp = t_5
    else if (x <= 2.8d-12) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
    else if (x <= 2.85d+131) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (x <= 3.2d+169) then
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    else if (x <= 1.05d+233) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (x <= 1.14d+263) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = t * (a * ((y2 * y5) - (z * b)));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = (k * y2) - (j * y3);
	double t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double t_5 = y0 * (y5 * ((j * y3) - (k * y2)));
	double tmp;
	if (x <= -1.3e+92) {
		tmp = t_4;
	} else if (x <= -80000000.0) {
		tmp = y1 * ((y4 * t_3) - (a * ((x * y2) - (z * y3))));
	} else if (x <= -2.5e-126) {
		tmp = t_1;
	} else if (x <= -1.5e-203) {
		tmp = t_5;
	} else if (x <= -6.2e-298) {
		tmp = t_1;
	} else if (x <= 1.05e-219) {
		tmp = t_5;
	} else if (x <= 2.8e-12) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 2.85e+131) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 3.2e+169) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (x <= 1.05e+233) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (x <= 1.14e+263) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = t * (a * ((y2 * y5) - (z * b)))
	t_2 = (c * y0) - (a * y1)
	t_3 = (k * y2) - (j * y3)
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	t_5 = y0 * (y5 * ((j * y3) - (k * y2)))
	tmp = 0
	if x <= -1.3e+92:
		tmp = t_4
	elif x <= -80000000.0:
		tmp = y1 * ((y4 * t_3) - (a * ((x * y2) - (z * y3))))
	elif x <= -2.5e-126:
		tmp = t_1
	elif x <= -1.5e-203:
		tmp = t_5
	elif x <= -6.2e-298:
		tmp = t_1
	elif x <= 1.05e-219:
		tmp = t_5
	elif x <= 2.8e-12:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))))
	elif x <= 2.85e+131:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif x <= 3.2e+169:
		tmp = (k * y0) * ((z * b) - (y2 * y5))
	elif x <= 1.05e+233:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif x <= 1.14e+263:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_5 = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	tmp = 0.0
	if (x <= -1.3e+92)
		tmp = t_4;
	elseif (x <= -80000000.0)
		tmp = Float64(y1 * Float64(Float64(y4 * t_3) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))));
	elseif (x <= -2.5e-126)
		tmp = t_1;
	elseif (x <= -1.5e-203)
		tmp = t_5;
	elseif (x <= -6.2e-298)
		tmp = t_1;
	elseif (x <= 1.05e-219)
		tmp = t_5;
	elseif (x <= 2.8e-12)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_3)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= 2.85e+131)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (x <= 3.2e+169)
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	elseif (x <= 1.05e+233)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (x <= 1.14e+263)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = t * (a * ((y2 * y5) - (z * b)));
	t_2 = (c * y0) - (a * y1);
	t_3 = (k * y2) - (j * y3);
	t_4 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	t_5 = y0 * (y5 * ((j * y3) - (k * y2)));
	tmp = 0.0;
	if (x <= -1.3e+92)
		tmp = t_4;
	elseif (x <= -80000000.0)
		tmp = y1 * ((y4 * t_3) - (a * ((x * y2) - (z * y3))));
	elseif (x <= -2.5e-126)
		tmp = t_1;
	elseif (x <= -1.5e-203)
		tmp = t_5;
	elseif (x <= -6.2e-298)
		tmp = t_1;
	elseif (x <= 1.05e-219)
		tmp = t_5;
	elseif (x <= 2.8e-12)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_3)) + (c * ((y * y3) - (t * y2))));
	elseif (x <= 2.85e+131)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (x <= 3.2e+169)
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	elseif (x <= 1.05e+233)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (x <= 1.14e+263)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+92], t$95$4, If[LessEqual[x, -80000000.0], N[(y1 * N[(N[(y4 * t$95$3), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-126], t$95$1, If[LessEqual[x, -1.5e-203], t$95$5, If[LessEqual[x, -6.2e-298], t$95$1, If[LessEqual[x, 1.05e-219], t$95$5, If[LessEqual[x, 2.8e-12], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.85e+131], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+169], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+233], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.14e+263], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -1.2999999999999999e92 or 1.14e263 < x

   1. Initial program 21.1%

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

   3. Simplified 21.1%

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

   4. Taylor expanded in x around inf 70.7%

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

   if -1.2999999999999999e92 < x < -8e7

   1. Initial program 14.3%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in y1 around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. mul-1-neg 76.2%

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

      3. sub-neg 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in i around 0 76.2%

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

   if -8e7 < x < -2.50000000000000003e-126 or -1.5000000000000001e-203 < x < -6.2000000000000003e-298

   1. Initial program 33.8%

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

   3. Simplified 33.8%

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

   4. Taylor expanded in t around inf 45.5%

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

      1. associate--l+ 45.5%

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

      2. mul-1-neg 45.5%

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

   6. Simplified 45.5%

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

   7. Taylor expanded in a around -inf 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-*l* 48.1%

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

      3. *-commutative 48.1%

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

      4. +-commutative 48.1%

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

      5. mul-1-neg 48.1%

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

      6. unsub-neg 48.1%

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

   9. Simplified 48.1%

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

   if -2.50000000000000003e-126 < x < -1.5000000000000001e-203 or -6.2000000000000003e-298 < x < 1.05e-219

   1. Initial program 30.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in y0 around inf 73.6%

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

      1. mul-1-neg 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in y5 around inf 67.3%

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

   if 1.05e-219 < x < 2.8000000000000002e-12

   1. Initial program 32.1%

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

   3. Simplified 32.1%

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

   4. Taylor expanded in y4 around inf 51.0%

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

   if 2.8000000000000002e-12 < x < 2.85e131

   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%

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

   4. Taylor expanded in y1 around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. mul-1-neg 37.1%

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

      3. sub-neg 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in a around inf 64.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 59.9%

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

      2. *-commutative 59.9%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if 2.85e131 < x < 3.1999999999999998e169

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y0 around inf 22.2%

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

      1. mul-1-neg 22.2%

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

   6. Simplified 22.2%

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

   7. Taylor expanded in k around -inf 66.8%

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

      1. associate-*r* 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

   9. Simplified 66.8%

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

   if 3.1999999999999998e169 < x < 1.04999999999999998e233

   1. Initial program 11.8%

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

   3. Simplified 11.8%

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

   4. Taylor expanded in y2 around inf 70.6%

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

   if 1.04999999999999998e233 < x < 1.14e263

   1. Initial program 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in b around inf 19.1%

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

      1. associate--l+ 19.1%

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

      2. mul-1-neg 19.1%

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

   6. Simplified 19.1%

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

   7. Taylor expanded in j around inf 64.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -80000000:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-219}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+131}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+169}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+233}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{+263}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 5: 37.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -30000000:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_2 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(y4 \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-13}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot t_2 - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+130}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+170}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+230}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_1 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+263}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2 (- (* k y2) (* j y3)))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_1))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= x -1.4e+93)
     t_3
     (if (<= x -30000000.0)
       (* y1 (- (* y4 t_2) (* a (- (* x y2) (* z y3)))))
       (if (<= x -3.6e-137)
         (* t (* a (- (* y2 y5) (* z b))))
         (if (<= x -6.2e-203)
           (* y0 (* y5 (- (* j y3) (* k y2))))
           (if (<= x 1.8e-167)
             (*
              b
              (+
               (* a (- (* x y) (* z t)))
               (+ (* y4 (- (* t j) (* y k))) (* y0 (- (* z k) (* x j))))))
             (if (<= x 6.1e-13)
               (* y4 (- (* y1 t_2) (* c (- (* t y2) (* y y3)))))
               (if (<= x 5.7e+130)
                 (* y1 (* a (- (* z y3) (* x y2))))
                 (if (<= x 1.55e+170)
                   (* (* k y0) (- (* z b) (* y2 y5)))
                   (if (<= x 3.15e+230)
                     (*
                      y2
                      (+
                       (+ (* x t_1) (* k (- (* y1 y4) (* y0 y5))))
                       (* t (- (* a y5) (* c y4)))))
                     (if (<= x 1.65e+263)
                       (* b (* j (- (* t y4) (* x 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 = (c * y0) - (a * y1);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -1.4e+93) {
		tmp = t_3;
	} else if (x <= -30000000.0) {
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	} else if (x <= -3.6e-137) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (x <= -6.2e-203) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (x <= 1.8e-167) {
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * ((t * j) - (y * k))) + (y0 * ((z * k) - (x * j)))));
	} else if (x <= 6.1e-13) {
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))));
	} else if (x <= 5.7e+130) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 1.55e+170) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (x <= 3.15e+230) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (x <= 1.65e+263) {
		tmp = b * (j * ((t * y4) - (x * 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 = (c * y0) - (a * y1)
    t_2 = (k * y2) - (j * y3)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    if (x <= (-1.4d+93)) then
        tmp = t_3
    else if (x <= (-30000000.0d0)) then
        tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
    else if (x <= (-3.6d-137)) then
        tmp = t * (a * ((y2 * y5) - (z * b)))
    else if (x <= (-6.2d-203)) then
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    else if (x <= 1.8d-167) then
        tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * ((t * j) - (y * k))) + (y0 * ((z * k) - (x * j)))))
    else if (x <= 6.1d-13) then
        tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))))
    else if (x <= 5.7d+130) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (x <= 1.55d+170) then
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    else if (x <= 3.15d+230) then
        tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (x <= 1.65d+263) then
        tmp = b * (j * ((t * y4) - (x * 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 = (c * y0) - (a * y1);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -1.4e+93) {
		tmp = t_3;
	} else if (x <= -30000000.0) {
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	} else if (x <= -3.6e-137) {
		tmp = t * (a * ((y2 * y5) - (z * b)));
	} else if (x <= -6.2e-203) {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	} else if (x <= 1.8e-167) {
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * ((t * j) - (y * k))) + (y0 * ((z * k) - (x * j)))));
	} else if (x <= 6.1e-13) {
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))));
	} else if (x <= 5.7e+130) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (x <= 1.55e+170) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else if (x <= 3.15e+230) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (x <= 1.65e+263) {
		tmp = b * (j * ((t * y4) - (x * 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 = (c * y0) - (a * y1)
	t_2 = (k * y2) - (j * y3)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if x <= -1.4e+93:
		tmp = t_3
	elif x <= -30000000.0:
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
	elif x <= -3.6e-137:
		tmp = t * (a * ((y2 * y5) - (z * b)))
	elif x <= -6.2e-203:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	elif x <= 1.8e-167:
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * ((t * j) - (y * k))) + (y0 * ((z * k) - (x * j)))))
	elif x <= 6.1e-13:
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))))
	elif x <= 5.7e+130:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif x <= 1.55e+170:
		tmp = (k * y0) * ((z * b) - (y2 * y5))
	elif x <= 3.15e+230:
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif x <= 1.65e+263:
		tmp = b * (j * ((t * y4) - (x * 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(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	tmp = 0.0
	if (x <= -1.4e+93)
		tmp = t_3;
	elseif (x <= -30000000.0)
		tmp = Float64(y1 * Float64(Float64(y4 * t_2) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))));
	elseif (x <= -3.6e-137)
		tmp = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (x <= -6.2e-203)
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	elseif (x <= 1.8e-167)
		tmp = Float64(b * Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(y4 * Float64(Float64(t * j) - Float64(y * k))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j))))));
	elseif (x <= 6.1e-13)
		tmp = Float64(y4 * Float64(Float64(y1 * t_2) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (x <= 5.7e+130)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (x <= 1.55e+170)
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	elseif (x <= 3.15e+230)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_1) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (x <= 1.65e+263)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * 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 = (c * y0) - (a * y1);
	t_2 = (k * y2) - (j * y3);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (x <= -1.4e+93)
		tmp = t_3;
	elseif (x <= -30000000.0)
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	elseif (x <= -3.6e-137)
		tmp = t * (a * ((y2 * y5) - (z * b)));
	elseif (x <= -6.2e-203)
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	elseif (x <= 1.8e-167)
		tmp = b * ((a * ((x * y) - (z * t))) + ((y4 * ((t * j) - (y * k))) + (y0 * ((z * k) - (x * j)))));
	elseif (x <= 6.1e-13)
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))));
	elseif (x <= 5.7e+130)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (x <= 1.55e+170)
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	elseif (x <= 3.15e+230)
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (x <= 1.65e+263)
		tmp = b * (j * ((t * y4) - (x * 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[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+93], t$95$3, If[LessEqual[x, -30000000.0], N[(y1 * N[(N[(y4 * t$95$2), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e-137], N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-203], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-167], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.1e-13], N[(y4 * N[(N[(y1 * t$95$2), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.7e+130], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+170], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.15e+230], N[(y2 * N[(N[(N[(x * t$95$1), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+263], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if x < -1.39999999999999994e93 or 1.65e263 < x

   1. Initial program 21.1%

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

   3. Simplified 21.1%

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

   4. Taylor expanded in x around inf 70.7%

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

   if -1.39999999999999994e93 < x < -3e7

   1. Initial program 14.3%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in y1 around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. mul-1-neg 76.2%

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

      3. sub-neg 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in i around 0 76.2%

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

   if -3e7 < x < -3.60000000000000006e-137

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in t around inf 43.7%

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

      1. associate--l+ 43.7%

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

      2. mul-1-neg 43.7%

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

   6. Simplified 43.7%

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

   7. Taylor expanded in a around -inf 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-*l* 53.8%

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

      3. *-commutative 53.8%

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

      4. +-commutative 53.8%

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

      5. mul-1-neg 53.8%

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

      6. unsub-neg 53.8%

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

   9. Simplified 53.8%

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

   if -3.60000000000000006e-137 < x < -6.19999999999999955e-203

   1. Initial program 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in y0 around inf 65.2%

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

      1. mul-1-neg 65.2%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in y5 around inf 65.6%

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

   if -6.19999999999999955e-203 < x < 1.8e-167

   1. Initial program 34.5%

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

   3. Simplified 34.5%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate--l+ 50.8%

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

      2. mul-1-neg 50.8%

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

   6. Simplified 50.8%

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

   if 1.8e-167 < x < 6.1000000000000003e-13

   1. Initial program 32.5%

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

   3. Simplified 32.5%

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

   4. Taylor expanded in y4 around inf 55.8%

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

   5. Taylor expanded in b around 0 56.0%

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

      1. *-commutative 56.0%

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

      2. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if 6.1000000000000003e-13 < x < 5.7e130

   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%

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

   4. Taylor expanded in y1 around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. mul-1-neg 37.1%

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

      3. sub-neg 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in a around inf 64.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 59.9%

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

      2. *-commutative 59.9%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

   9. Simplified 60.3%

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

   if 5.7e130 < x < 1.55e170

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y0 around inf 22.2%

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

      1. mul-1-neg 22.2%

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

   6. Simplified 22.2%

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

   7. Taylor expanded in k around -inf 66.8%

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

      1. associate-*r* 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

   9. Simplified 66.8%

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

   if 1.55e170 < x < 3.1500000000000001e230

   1. Initial program 11.8%

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

   3. Simplified 11.8%

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

   4. Taylor expanded in y2 around inf 70.6%

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

   if 3.1500000000000001e230 < x < 1.65e263

   1. Initial program 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in b around inf 19.1%

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

      1. associate--l+ 19.1%

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

      2. mul-1-neg 19.1%

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

   6. Simplified 19.1%

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

   7. Taylor expanded in j around inf 64.1%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -30000000:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot \left(x \cdot y - z \cdot t\right) + \left(y4 \cdot \left(t \cdot j - y \cdot k\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-13}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+130}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+170}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+230}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+263}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

Alternative 6: 37.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_2 := x \cdot j - z \cdot k\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := a \cdot t_3\\ t_5 := z \cdot t - x \cdot y\\ t_6 := i \cdot t_2\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot t_3\right)\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(\left(i \cdot t_5 + y0 \cdot t_3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-206}:\\ \;\;\;\;y1 \cdot \left(\left(t_1 + t_6\right) - t_4\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-177}:\\ \;\;\;\;i \cdot \left(c \cdot t_5 + \left(y1 \cdot t_2 + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-47}:\\ \;\;\;\;y1 \cdot \left(t_1 - t_4\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+80}:\\ \;\;\;\;y1 \cdot t_6\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+267}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (- (* k y2) (* j y3))))
        (t_2 (- (* x j) (* z k)))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (* a t_3))
        (t_5 (- (* z t) (* x y)))
        (t_6 (* i t_2)))
   (if (<= y -2.7e+136)
     (*
      y
      (+
       (+ (* k (- (* i y5) (* b y4))) (* x (- (* a b) (* c i))))
       (* y3 (- (* c y4) (* a y5)))))
     (if (<= y -7.2e+53)
       (*
        a
        (+
         (* b (- (* x y) (* z t)))
         (- (* y5 (- (* t y2) (* y y3))) (* y1 t_3))))
       (if (<= y -4.5e-226)
         (* c (+ (+ (* i t_5) (* y0 t_3)) (* y4 (- (* y y3) (* t y2)))))
         (if (<= y 3.3e-206)
           (* y1 (- (+ t_1 t_6) t_4))
           (if (<= y 1.75e-177)
             (* i (+ (* c t_5) (+ (* y1 t_2) (* y5 (- (* y k) (* t j))))))
             (if (<= y 9e-47)
               (* y1 (- t_1 t_4))
               (if (<= y 2.15e+80)
                 (* y1 t_6)
                 (if (<= y 1.15e+267)
                   (*
                    y0
                    (+
                     (+ (* y5 (- (* j y3) (* k y2))) (* c t_3))
                     (* b (- (* z k) (* x j)))))
                   (* k (* y4 (- (* y1 y2) (* y b))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * ((k * y2) - (j * y3));
	double t_2 = (x * j) - (z * k);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = a * t_3;
	double t_5 = (z * t) - (x * y);
	double t_6 = i * t_2;
	double tmp;
	if (y <= -2.7e+136) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y <= -7.2e+53) {
		tmp = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_3)));
	} else if (y <= -4.5e-226) {
		tmp = c * (((i * t_5) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y <= 3.3e-206) {
		tmp = y1 * ((t_1 + t_6) - t_4);
	} else if (y <= 1.75e-177) {
		tmp = i * ((c * t_5) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= 9e-47) {
		tmp = y1 * (t_1 - t_4);
	} else if (y <= 2.15e+80) {
		tmp = y1 * t_6;
	} else if (y <= 1.15e+267) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	} else {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = y4 * ((k * y2) - (j * y3))
    t_2 = (x * j) - (z * k)
    t_3 = (x * y2) - (z * y3)
    t_4 = a * t_3
    t_5 = (z * t) - (x * y)
    t_6 = i * t_2
    if (y <= (-2.7d+136)) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
    else if (y <= (-7.2d+53)) then
        tmp = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_3)))
    else if (y <= (-4.5d-226)) then
        tmp = c * (((i * t_5) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
    else if (y <= 3.3d-206) then
        tmp = y1 * ((t_1 + t_6) - t_4)
    else if (y <= 1.75d-177) then
        tmp = i * ((c * t_5) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))))
    else if (y <= 9d-47) then
        tmp = y1 * (t_1 - t_4)
    else if (y <= 2.15d+80) then
        tmp = y1 * t_6
    else if (y <= 1.15d+267) then
        tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
    else
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * ((k * y2) - (j * y3));
	double t_2 = (x * j) - (z * k);
	double t_3 = (x * y2) - (z * y3);
	double t_4 = a * t_3;
	double t_5 = (z * t) - (x * y);
	double t_6 = i * t_2;
	double tmp;
	if (y <= -2.7e+136) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y <= -7.2e+53) {
		tmp = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_3)));
	} else if (y <= -4.5e-226) {
		tmp = c * (((i * t_5) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y <= 3.3e-206) {
		tmp = y1 * ((t_1 + t_6) - t_4);
	} else if (y <= 1.75e-177) {
		tmp = i * ((c * t_5) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= 9e-47) {
		tmp = y1 * (t_1 - t_4);
	} else if (y <= 2.15e+80) {
		tmp = y1 * t_6;
	} else if (y <= 1.15e+267) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	} else {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * ((k * y2) - (j * y3))
	t_2 = (x * j) - (z * k)
	t_3 = (x * y2) - (z * y3)
	t_4 = a * t_3
	t_5 = (z * t) - (x * y)
	t_6 = i * t_2
	tmp = 0
	if y <= -2.7e+136:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
	elif y <= -7.2e+53:
		tmp = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_3)))
	elif y <= -4.5e-226:
		tmp = c * (((i * t_5) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
	elif y <= 3.3e-206:
		tmp = y1 * ((t_1 + t_6) - t_4)
	elif y <= 1.75e-177:
		tmp = i * ((c * t_5) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))))
	elif y <= 9e-47:
		tmp = y1 * (t_1 - t_4)
	elif y <= 2.15e+80:
		tmp = y1 * t_6
	elif y <= 1.15e+267:
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
	else:
		tmp = k * (y4 * ((y1 * y2) - (y * 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(y4 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_2 = Float64(Float64(x * j) - Float64(z * k))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(a * t_3)
	t_5 = Float64(Float64(z * t) - Float64(x * y))
	t_6 = Float64(i * t_2)
	tmp = 0.0
	if (y <= -2.7e+136)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y <= -7.2e+53)
		tmp = Float64(a * Float64(Float64(b * Float64(Float64(x * y) - Float64(z * t))) + Float64(Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))) - Float64(y1 * t_3))));
	elseif (y <= -4.5e-226)
		tmp = Float64(c * Float64(Float64(Float64(i * t_5) + Float64(y0 * t_3)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 3.3e-206)
		tmp = Float64(y1 * Float64(Float64(t_1 + t_6) - t_4));
	elseif (y <= 1.75e-177)
		tmp = Float64(i * Float64(Float64(c * t_5) + Float64(Float64(y1 * t_2) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y <= 9e-47)
		tmp = Float64(y1 * Float64(t_1 - t_4));
	elseif (y <= 2.15e+80)
		tmp = Float64(y1 * t_6);
	elseif (y <= 1.15e+267)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * t_3)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * ((k * y2) - (j * y3));
	t_2 = (x * j) - (z * k);
	t_3 = (x * y2) - (z * y3);
	t_4 = a * t_3;
	t_5 = (z * t) - (x * y);
	t_6 = i * t_2;
	tmp = 0.0;
	if (y <= -2.7e+136)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	elseif (y <= -7.2e+53)
		tmp = a * ((b * ((x * y) - (z * t))) + ((y5 * ((t * y2) - (y * y3))) - (y1 * t_3)));
	elseif (y <= -4.5e-226)
		tmp = c * (((i * t_5) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y <= 3.3e-206)
		tmp = y1 * ((t_1 + t_6) - t_4);
	elseif (y <= 1.75e-177)
		tmp = i * ((c * t_5) + ((y1 * t_2) + (y5 * ((y * k) - (t * j)))));
	elseif (y <= 9e-47)
		tmp = y1 * (t_1 - t_4);
	elseif (y <= 2.15e+80)
		tmp = y1 * t_6;
	elseif (y <= 1.15e+267)
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	else
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(i * t$95$2), $MachinePrecision]}, If[LessEqual[y, -2.7e+136], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e+53], N[(a * N[(N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-226], N[(c * N[(N[(N[(i * t$95$5), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-206], N[(y1 * N[(N[(t$95$1 + t$95$6), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-177], N[(i * N[(N[(c * t$95$5), $MachinePrecision] + N[(N[(y1 * t$95$2), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-47], N[(y1 * N[(t$95$1 - t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+80], N[(y1 * t$95$6), $MachinePrecision], If[LessEqual[y, 1.15e+267], N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -2.7000000000000002e136

   1. Initial program 22.7%

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

   3. Simplified 22.7%

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

   4. Taylor expanded in y around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. mul-1-neg 68.4%

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

   6. Simplified 68.4%

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

   if -2.7000000000000002e136 < y < -7.2e53

   1. Initial program 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in a around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. mul-1-neg 72.9%

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

      3. mul-1-neg 72.9%

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

   6. Simplified 72.9%

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

   if -7.2e53 < y < -4.50000000000000011e-226

   1. Initial program 22.9%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in c around inf 54.3%

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

      1. mul-1-neg 54.3%

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

   6. Simplified 54.3%

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

   if -4.50000000000000011e-226 < y < 3.2999999999999998e-206

   1. Initial program 32.6%

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

   3. Simplified 41.9%

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

   4. Taylor expanded in y1 around inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. mul-1-neg 58.6%

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

      3. sub-neg 58.6%

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

   6. Simplified 58.6%

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

   if 3.2999999999999998e-206 < y < 1.7500000000000001e-177

   1. Initial program 2.0%

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

   3. Simplified 2.0%

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

   4. Taylor expanded in i around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. associate--l+ 85.7%

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

      3. mul-1-neg 85.7%

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

   6. Simplified 85.7%

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

   if 1.7500000000000001e-177 < y < 9e-47

   1. Initial program 42.8%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in y1 around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. mul-1-neg 51.0%

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

      3. sub-neg 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in i around 0 68.7%

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

   if 9e-47 < y < 2.15000000000000002e80

   1. Initial program 30.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y1 around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. mul-1-neg 36.8%

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

      3. sub-neg 36.8%

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

   6. Simplified 36.8%

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

   7. Taylor expanded in i around inf 55.4%

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

   if 2.15000000000000002e80 < y < 1.15000000000000011e267

   1. Initial program 10.7%

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

   3. Simplified 10.7%

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

   4. Taylor expanded in y0 around inf 61.4%

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

      1. mul-1-neg 61.4%

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

   6. Simplified 61.4%

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

   if 1.15000000000000011e267 < y

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in y4 around inf 60.0%

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

   5. Taylor expanded in k around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

   7. Simplified 70.3%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right) + \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right) - y1 \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-206}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-177}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-47}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+80}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+267}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \end{array} \]

Alternative 7: 37.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := \left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := y1 \cdot \left(\left(y4 \cdot t_1 + i \cdot \left(x \cdot j - z \cdot k\right)\right) - a \cdot t_3\right)\\ t_5 := y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-119}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq -3.9 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 2.25 \cdot 10^{-200}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 65000000000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y3 \leq 3.4 \cdot 10^{+74}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 1.15 \cdot 10^{+104}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y3 \leq 1.55 \cdot 10^{+165}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot t_1 - c \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2 (* (* y0 y3) (- (* j y5) (* z c))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (* y1 (- (+ (* y4 t_1) (* i (- (* x j) (* z k)))) (* a t_3))))
        (t_5
         (*
          y0
          (+
           (+ (* y5 (- (* j y3) (* k y2))) (* c t_3))
           (* b (- (* z k) (* x j)))))))
   (if (<= y3 -1.65e+55)
     t_2
     (if (<= y3 -9.2e-119)
       t_4
       (if (<= y3 -3.9e-241)
         (*
          t
          (+
           (* z (- (* c i) (* a b)))
           (+ (* j (- (* b y4) (* i y5))) (* y2 (- (* a y5) (* c y4))))))
         (if (<= y3 2.25e-200)
           t_4
           (if (<= y3 2.5e-58)
             (*
              k
              (+
               (* y (- (* i y5) (* b y4)))
               (+ (* z (- (* b y0) (* i y1))) (* y2 (- (* y1 y4) (* y0 y5))))))
             (if (<= y3 65000000000.0)
               t_5
               (if (<= y3 3.4e+74)
                 (*
                  c
                  (+
                   (+ (* i (- (* z t) (* x y))) (* y0 t_3))
                   (* y4 (- (* y y3) (* t y2)))))
                 (if (<= y3 1.15e+104)
                   t_5
                   (if (<= y3 1.55e+165)
                     (* y4 (- (* y1 t_1) (* c (* t y2))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y0 * y3) * ((j * y5) - (z * c));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y1 * (((y4 * t_1) + (i * ((x * j) - (z * k)))) - (a * t_3));
	double t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	double tmp;
	if (y3 <= -1.65e+55) {
		tmp = t_2;
	} else if (y3 <= -9.2e-119) {
		tmp = t_4;
	} else if (y3 <= -3.9e-241) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))));
	} else if (y3 <= 2.25e-200) {
		tmp = t_4;
	} else if (y3 <= 2.5e-58) {
		tmp = k * ((y * ((i * y5) - (b * y4))) + ((z * ((b * y0) - (i * y1))) + (y2 * ((y1 * y4) - (y0 * y5)))));
	} else if (y3 <= 65000000000.0) {
		tmp = t_5;
	} else if (y3 <= 3.4e+74) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y3 <= 1.15e+104) {
		tmp = t_5;
	} else if (y3 <= 1.55e+165) {
		tmp = y4 * ((y1 * t_1) - (c * (t * y2)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (k * y2) - (j * y3)
    t_2 = (y0 * y3) * ((j * y5) - (z * c))
    t_3 = (x * y2) - (z * y3)
    t_4 = y1 * (((y4 * t_1) + (i * ((x * j) - (z * k)))) - (a * t_3))
    t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
    if (y3 <= (-1.65d+55)) then
        tmp = t_2
    else if (y3 <= (-9.2d-119)) then
        tmp = t_4
    else if (y3 <= (-3.9d-241)) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))))
    else if (y3 <= 2.25d-200) then
        tmp = t_4
    else if (y3 <= 2.5d-58) then
        tmp = k * ((y * ((i * y5) - (b * y4))) + ((z * ((b * y0) - (i * y1))) + (y2 * ((y1 * y4) - (y0 * y5)))))
    else if (y3 <= 65000000000.0d0) then
        tmp = t_5
    else if (y3 <= 3.4d+74) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
    else if (y3 <= 1.15d+104) then
        tmp = t_5
    else if (y3 <= 1.55d+165) then
        tmp = y4 * ((y1 * t_1) - (c * (t * y2)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (y0 * y3) * ((j * y5) - (z * c));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = y1 * (((y4 * t_1) + (i * ((x * j) - (z * k)))) - (a * t_3));
	double t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	double tmp;
	if (y3 <= -1.65e+55) {
		tmp = t_2;
	} else if (y3 <= -9.2e-119) {
		tmp = t_4;
	} else if (y3 <= -3.9e-241) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))));
	} else if (y3 <= 2.25e-200) {
		tmp = t_4;
	} else if (y3 <= 2.5e-58) {
		tmp = k * ((y * ((i * y5) - (b * y4))) + ((z * ((b * y0) - (i * y1))) + (y2 * ((y1 * y4) - (y0 * y5)))));
	} else if (y3 <= 65000000000.0) {
		tmp = t_5;
	} else if (y3 <= 3.4e+74) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y3 <= 1.15e+104) {
		tmp = t_5;
	} else if (y3 <= 1.55e+165) {
		tmp = y4 * ((y1 * t_1) - (c * (t * y2)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (k * y2) - (j * y3)
	t_2 = (y0 * y3) * ((j * y5) - (z * c))
	t_3 = (x * y2) - (z * y3)
	t_4 = y1 * (((y4 * t_1) + (i * ((x * j) - (z * k)))) - (a * t_3))
	t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
	tmp = 0
	if y3 <= -1.65e+55:
		tmp = t_2
	elif y3 <= -9.2e-119:
		tmp = t_4
	elif y3 <= -3.9e-241:
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))))
	elif y3 <= 2.25e-200:
		tmp = t_4
	elif y3 <= 2.5e-58:
		tmp = k * ((y * ((i * y5) - (b * y4))) + ((z * ((b * y0) - (i * y1))) + (y2 * ((y1 * y4) - (y0 * y5)))))
	elif y3 <= 65000000000.0:
		tmp = t_5
	elif y3 <= 3.4e+74:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
	elif y3 <= 1.15e+104:
		tmp = t_5
	elif y3 <= 1.55e+165:
		tmp = y4 * ((y1 * t_1) - (c * (t * y2)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(y1 * Float64(Float64(Float64(y4 * t_1) + Float64(i * Float64(Float64(x * j) - Float64(z * k)))) - Float64(a * t_3)))
	t_5 = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * t_3)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))))
	tmp = 0.0
	if (y3 <= -1.65e+55)
		tmp = t_2;
	elseif (y3 <= -9.2e-119)
		tmp = t_4;
	elseif (y3 <= -3.9e-241)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(j * Float64(Float64(b * y4) - Float64(i * y5))) + Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))))));
	elseif (y3 <= 2.25e-200)
		tmp = t_4;
	elseif (y3 <= 2.5e-58)
		tmp = Float64(k * Float64(Float64(y * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(Float64(z * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y2 * Float64(Float64(y1 * y4) - Float64(y0 * y5))))));
	elseif (y3 <= 65000000000.0)
		tmp = t_5;
	elseif (y3 <= 3.4e+74)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_3)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y3 <= 1.15e+104)
		tmp = t_5;
	elseif (y3 <= 1.55e+165)
		tmp = Float64(y4 * Float64(Float64(y1 * t_1) - Float64(c * Float64(t * y2))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (k * y2) - (j * y3);
	t_2 = (y0 * y3) * ((j * y5) - (z * c));
	t_3 = (x * y2) - (z * y3);
	t_4 = y1 * (((y4 * t_1) + (i * ((x * j) - (z * k)))) - (a * t_3));
	t_5 = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	tmp = 0.0;
	if (y3 <= -1.65e+55)
		tmp = t_2;
	elseif (y3 <= -9.2e-119)
		tmp = t_4;
	elseif (y3 <= -3.9e-241)
		tmp = t * ((z * ((c * i) - (a * b))) + ((j * ((b * y4) - (i * y5))) + (y2 * ((a * y5) - (c * y4)))));
	elseif (y3 <= 2.25e-200)
		tmp = t_4;
	elseif (y3 <= 2.5e-58)
		tmp = k * ((y * ((i * y5) - (b * y4))) + ((z * ((b * y0) - (i * y1))) + (y2 * ((y1 * y4) - (y0 * y5)))));
	elseif (y3 <= 65000000000.0)
		tmp = t_5;
	elseif (y3 <= 3.4e+74)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y3 <= 1.15e+104)
		tmp = t_5;
	elseif (y3 <= 1.55e+165)
		tmp = y4 * ((y1 * t_1) - (c * (t * y2)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y1 * N[(N[(N[(y4 * t$95$1), $MachinePrecision] + N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.65e+55], t$95$2, If[LessEqual[y3, -9.2e-119], t$95$4, If[LessEqual[y3, -3.9e-241], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.25e-200], t$95$4, If[LessEqual[y3, 2.5e-58], N[(k * N[(N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 65000000000.0], t$95$5, If[LessEqual[y3, 3.4e+74], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.15e+104], t$95$5, If[LessEqual[y3, 1.55e+165], N[(y4 * N[(N[(y1 * t$95$1), $MachinePrecision] - N[(c * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -1.65e55 or 1.5500000000000001e165 < y3

   1. Initial program 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in y0 around inf 43.1%

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

      1. mul-1-neg 43.1%

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

   6. Simplified 43.1%

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

   7. Taylor expanded in y3 around inf 56.9%

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

      1. distribute-lft-out-- 56.9%

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

      2. associate-*r* 56.9%

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

      3. mul-1-neg 56.9%

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

      4. *-commutative 56.9%

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

      5. *-commutative 56.9%

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

      6. *-commutative 56.9%

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

   9. Simplified 56.9%

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

   if -1.65e55 < y3 < -9.19999999999999973e-119 or -3.8999999999999999e-241 < y3 < 2.2500000000000001e-200

   1. Initial program 30.4%

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

   3. Simplified 35.4%

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

   4. Taylor expanded in y1 around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. mul-1-neg 58.9%

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

      3. sub-neg 58.9%

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

   6. Simplified 58.9%

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

   if -9.19999999999999973e-119 < y3 < -3.8999999999999999e-241

   1. Initial program 38.5%

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

   3. Simplified 38.5%

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

   4. Taylor expanded in t around inf 62.6%

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

      1. associate--l+ 62.6%

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

      2. mul-1-neg 62.6%

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

   6. Simplified 62.6%

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

   if 2.2500000000000001e-200 < y3 < 2.49999999999999989e-58

   1. Initial program 32.0%

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

   3. Simplified 36.0%

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

   4. Taylor expanded in k around inf 56.8%

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

      1. mul-1-neg 56.8%

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

   6. Simplified 56.8%

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

   if 2.49999999999999989e-58 < y3 < 6.5e10 or 3.3999999999999999e74 < y3 < 1.14999999999999992e104

   1. Initial program 41.3%

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

   3. Simplified 41.3%

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

   4. Taylor expanded in y0 around inf 67.5%

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

      1. mul-1-neg 67.5%

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

   6. Simplified 67.5%

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

   if 6.5e10 < y3 < 3.3999999999999999e74

   1. Initial program 27.3%

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

   3. Simplified 27.3%

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

   4. Taylor expanded in c around inf 81.8%

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

      1. mul-1-neg 81.8%

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

   6. Simplified 81.8%

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

   if 1.14999999999999992e104 < y3 < 1.5500000000000001e165

   1. Initial program 12.8%

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

   3. Simplified 12.8%

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

   4. Taylor expanded in y4 around inf 57.0%

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

   5. Taylor expanded in b around 0 57.0%

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

      1. *-commutative 57.0%

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

      2. *-commutative 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in y around 0 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

   10. Simplified 69.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.65 \cdot 10^{+55}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y3 \leq -9.2 \cdot 10^{-119}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq -3.9 \cdot 10^{-241}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(j \cdot \left(b \cdot y4 - i \cdot y5\right) + y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 2.25 \cdot 10^{-200}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{-58}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right) + \left(z \cdot \left(b \cdot y0 - i \cdot y1\right) + y2 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 65000000000:\\ \;\;\;\;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}\;y3 \leq 3.4 \cdot 10^{+74}:\\ \;\;\;\;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}\;y3 \leq 1.15 \cdot 10^{+104}:\\ \;\;\;\;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}\;y3 \leq 1.55 \cdot 10^{+165}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \end{array} \]

Alternative 8: 38.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x \cdot y\\ t_2 := y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\\ t_3 := x \cdot y2 - z \cdot y3\\ t_4 := a \cdot t_3\\ t_5 := x \cdot j - z \cdot k\\ t_6 := i \cdot t_5\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-224}:\\ \;\;\;\;c \cdot \left(\left(i \cdot t_1 + y0 \cdot t_3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-205}:\\ \;\;\;\;y1 \cdot \left(\left(t_2 + t_6\right) - t_4\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-176}:\\ \;\;\;\;i \cdot \left(c \cdot t_1 + \left(y1 \cdot t_5 + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-47}:\\ \;\;\;\;y1 \cdot \left(t_2 - t_4\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+80}:\\ \;\;\;\;y1 \cdot t_6\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+264}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z t) (* x y)))
        (t_2 (* y4 (- (* k y2) (* j y3))))
        (t_3 (- (* x y2) (* z y3)))
        (t_4 (* a t_3))
        (t_5 (- (* x j) (* z k)))
        (t_6 (* i t_5)))
   (if (<= y -2.2e+48)
     (*
      y
      (+
       (+ (* k (- (* i y5) (* b y4))) (* x (- (* a b) (* c i))))
       (* y3 (- (* c y4) (* a y5)))))
     (if (<= y -8.2e-224)
       (* c (+ (+ (* i t_1) (* y0 t_3)) (* y4 (- (* y y3) (* t y2)))))
       (if (<= y 6.7e-205)
         (* y1 (- (+ t_2 t_6) t_4))
         (if (<= y 2.85e-176)
           (* i (+ (* c t_1) (+ (* y1 t_5) (* y5 (- (* y k) (* t j))))))
           (if (<= y 9.2e-47)
             (* y1 (- t_2 t_4))
             (if (<= y 1.05e+80)
               (* y1 t_6)
               (if (<= y 6.8e+264)
                 (*
                  y0
                  (+
                   (+ (* y5 (- (* j y3) (* k y2))) (* c t_3))
                   (* b (- (* z k) (* x j)))))
                 (* k (* y4 (- (* y1 y2) (* y b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = y4 * ((k * y2) - (j * y3));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = a * t_3;
	double t_5 = (x * j) - (z * k);
	double t_6 = i * t_5;
	double tmp;
	if (y <= -2.2e+48) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y <= -8.2e-224) {
		tmp = c * (((i * t_1) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y <= 6.7e-205) {
		tmp = y1 * ((t_2 + t_6) - t_4);
	} else if (y <= 2.85e-176) {
		tmp = i * ((c * t_1) + ((y1 * t_5) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= 9.2e-47) {
		tmp = y1 * (t_2 - t_4);
	} else if (y <= 1.05e+80) {
		tmp = y1 * t_6;
	} else if (y <= 6.8e+264) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	} else {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = (z * t) - (x * y)
    t_2 = y4 * ((k * y2) - (j * y3))
    t_3 = (x * y2) - (z * y3)
    t_4 = a * t_3
    t_5 = (x * j) - (z * k)
    t_6 = i * t_5
    if (y <= (-2.2d+48)) then
        tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
    else if (y <= (-8.2d-224)) then
        tmp = c * (((i * t_1) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
    else if (y <= 6.7d-205) then
        tmp = y1 * ((t_2 + t_6) - t_4)
    else if (y <= 2.85d-176) then
        tmp = i * ((c * t_1) + ((y1 * t_5) + (y5 * ((y * k) - (t * j)))))
    else if (y <= 9.2d-47) then
        tmp = y1 * (t_2 - t_4)
    else if (y <= 1.05d+80) then
        tmp = y1 * t_6
    else if (y <= 6.8d+264) then
        tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
    else
        tmp = k * (y4 * ((y1 * y2) - (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (z * t) - (x * y);
	double t_2 = y4 * ((k * y2) - (j * y3));
	double t_3 = (x * y2) - (z * y3);
	double t_4 = a * t_3;
	double t_5 = (x * j) - (z * k);
	double t_6 = i * t_5;
	double tmp;
	if (y <= -2.2e+48) {
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	} else if (y <= -8.2e-224) {
		tmp = c * (((i * t_1) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y <= 6.7e-205) {
		tmp = y1 * ((t_2 + t_6) - t_4);
	} else if (y <= 2.85e-176) {
		tmp = i * ((c * t_1) + ((y1 * t_5) + (y5 * ((y * k) - (t * j)))));
	} else if (y <= 9.2e-47) {
		tmp = y1 * (t_2 - t_4);
	} else if (y <= 1.05e+80) {
		tmp = y1 * t_6;
	} else if (y <= 6.8e+264) {
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	} else {
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	}
	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 = y4 * ((k * y2) - (j * y3))
	t_3 = (x * y2) - (z * y3)
	t_4 = a * t_3
	t_5 = (x * j) - (z * k)
	t_6 = i * t_5
	tmp = 0
	if y <= -2.2e+48:
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))))
	elif y <= -8.2e-224:
		tmp = c * (((i * t_1) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
	elif y <= 6.7e-205:
		tmp = y1 * ((t_2 + t_6) - t_4)
	elif y <= 2.85e-176:
		tmp = i * ((c * t_1) + ((y1 * t_5) + (y5 * ((y * k) - (t * j)))))
	elif y <= 9.2e-47:
		tmp = y1 * (t_2 - t_4)
	elif y <= 1.05e+80:
		tmp = y1 * t_6
	elif y <= 6.8e+264:
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))))
	else:
		tmp = k * (y4 * ((y1 * y2) - (y * 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(Float64(z * t) - Float64(x * y))
	t_2 = Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3)))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	t_4 = Float64(a * t_3)
	t_5 = Float64(Float64(x * j) - Float64(z * k))
	t_6 = Float64(i * t_5)
	tmp = 0.0
	if (y <= -2.2e+48)
		tmp = Float64(y * Float64(Float64(Float64(k * Float64(Float64(i * y5) - Float64(b * y4))) + Float64(x * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y3 * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y <= -8.2e-224)
		tmp = Float64(c * Float64(Float64(Float64(i * t_1) + Float64(y0 * t_3)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 6.7e-205)
		tmp = Float64(y1 * Float64(Float64(t_2 + t_6) - t_4));
	elseif (y <= 2.85e-176)
		tmp = Float64(i * Float64(Float64(c * t_1) + Float64(Float64(y1 * t_5) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))));
	elseif (y <= 9.2e-47)
		tmp = Float64(y1 * Float64(t_2 - t_4));
	elseif (y <= 1.05e+80)
		tmp = Float64(y1 * t_6);
	elseif (y <= 6.8e+264)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))) + Float64(c * t_3)) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	else
		tmp = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (z * t) - (x * y);
	t_2 = y4 * ((k * y2) - (j * y3));
	t_3 = (x * y2) - (z * y3);
	t_4 = a * t_3;
	t_5 = (x * j) - (z * k);
	t_6 = i * t_5;
	tmp = 0.0;
	if (y <= -2.2e+48)
		tmp = y * (((k * ((i * y5) - (b * y4))) + (x * ((a * b) - (c * i)))) + (y3 * ((c * y4) - (a * y5))));
	elseif (y <= -8.2e-224)
		tmp = c * (((i * t_1) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y <= 6.7e-205)
		tmp = y1 * ((t_2 + t_6) - t_4);
	elseif (y <= 2.85e-176)
		tmp = i * ((c * t_1) + ((y1 * t_5) + (y5 * ((y * k) - (t * j)))));
	elseif (y <= 9.2e-47)
		tmp = y1 * (t_2 - t_4);
	elseif (y <= 1.05e+80)
		tmp = y1 * t_6;
	elseif (y <= 6.8e+264)
		tmp = y0 * (((y5 * ((j * y3) - (k * y2))) + (c * t_3)) + (b * ((z * k) - (x * j))));
	else
		tmp = k * (y4 * ((y1 * y2) - (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(i * t$95$5), $MachinePrecision]}, If[LessEqual[y, -2.2e+48], N[(y * N[(N[(N[(k * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-224], N[(c * N[(N[(N[(i * t$95$1), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.7e-205], N[(y1 * N[(N[(t$95$2 + t$95$6), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e-176], N[(i * N[(N[(c * t$95$1), $MachinePrecision] + N[(N[(y1 * t$95$5), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-47], N[(y1 * N[(t$95$2 - t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+80], N[(y1 * t$95$6), $MachinePrecision], If[LessEqual[y, 6.8e+264], N[(y0 * N[(N[(N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -2.1999999999999999e48

   1. Initial program 22.0%

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

   3. Simplified 22.0%

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

   4. Taylor expanded in y around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. mul-1-neg 59.8%

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

   6. Simplified 59.8%

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

   if -2.1999999999999999e48 < y < -8.19999999999999972e-224

   1. Initial program 23.9%

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

   3. Simplified 23.9%

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

   4. Taylor expanded in c around inf 56.7%

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

      1. mul-1-neg 56.7%

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

   6. Simplified 56.7%

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

   if -8.19999999999999972e-224 < y < 6.7000000000000001e-205

   1. Initial program 32.6%

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

   3. Simplified 41.9%

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

   4. Taylor expanded in y1 around inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. mul-1-neg 58.6%

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

      3. sub-neg 58.6%

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

   6. Simplified 58.6%

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

   if 6.7000000000000001e-205 < y < 2.84999999999999992e-176

   1. Initial program 2.0%

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

   3. Simplified 2.0%

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

   4. Taylor expanded in i around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. associate--l+ 85.7%

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

      3. mul-1-neg 85.7%

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

   6. Simplified 85.7%

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

   if 2.84999999999999992e-176 < y < 9.19999999999999928e-47

   1. Initial program 42.8%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in y1 around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. mul-1-neg 51.0%

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

      3. sub-neg 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in i around 0 68.7%

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

   if 9.19999999999999928e-47 < y < 1.05000000000000001e80

   1. Initial program 30.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y1 around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. mul-1-neg 36.8%

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

      3. sub-neg 36.8%

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

   6. Simplified 36.8%

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

   7. Taylor expanded in i around inf 55.4%

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

   if 1.05000000000000001e80 < y < 6.8000000000000002e264

   1. Initial program 10.7%

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

   3. Simplified 10.7%

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

   4. Taylor expanded in y0 around inf 61.4%

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

      1. mul-1-neg 61.4%

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

   6. Simplified 61.4%

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

   if 6.8000000000000002e264 < y

   1. Initial program 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in y4 around inf 60.0%

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

   5. Taylor expanded in k around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

   7. Simplified 70.3%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(\left(k \cdot \left(i \cdot y5 - b \cdot y4\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) + y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-224}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-205}:\\ \;\;\;\;y1 \cdot \left(\left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) + i \cdot \left(x \cdot j - z \cdot k\right)\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-176}:\\ \;\;\;\;i \cdot \left(c \cdot \left(z \cdot t - x \cdot y\right) + \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-47}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+80}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+264}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \end{array} \]

Alternative 9: 33.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ t_2 := j \cdot y3 - k \cdot y2\\ t_3 := x \cdot y2 - z \cdot y3\\ \mathbf{if}\;y \leq -510000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-303}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot t_3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-173}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot t_2\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot t_3\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+80}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+266}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot t_2 + c \cdot t_3\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y4 (- (* y1 y2) (* y b)))))
        (t_2 (- (* j y3) (* k y2)))
        (t_3 (- (* x y2) (* z y3))))
   (if (<= y -510000000000.0)
     t_1
     (if (<= y 4e-303)
       (*
        c
        (+
         (+ (* i (- (* z t) (* x y))) (* y0 t_3))
         (* y4 (- (* y y3) (* t y2)))))
       (if (<= y 3.7e-173)
         (*
          y5
          (+
           (* i (- (* y k) (* t j)))
           (+ (* a (- (* t y2) (* y y3))) (* y0 t_2))))
         (if (<= y 1.4e-46)
           (* y1 (- (* y4 (- (* k y2) (* j y3))) (* a t_3)))
           (if (<= y 3.3e+80)
             (* y1 (* i (- (* x j) (* z k))))
             (if (<= y 2.35e+266)
               (* y0 (+ (+ (* y5 t_2) (* c t_3)) (* 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 * (y4 * ((y1 * y2) - (y * b)));
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -510000000000.0) {
		tmp = t_1;
	} else if (y <= 4e-303) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y <= 3.7e-173) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_2)));
	} else if (y <= 1.4e-46) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (a * t_3));
	} else if (y <= 3.3e+80) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y <= 2.35e+266) {
		tmp = y0 * (((y5 * t_2) + (c * t_3)) + (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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * (y4 * ((y1 * y2) - (y * b)))
    t_2 = (j * y3) - (k * y2)
    t_3 = (x * y2) - (z * y3)
    if (y <= (-510000000000.0d0)) then
        tmp = t_1
    else if (y <= 4d-303) then
        tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
    else if (y <= 3.7d-173) then
        tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_2)))
    else if (y <= 1.4d-46) then
        tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (a * t_3))
    else if (y <= 3.3d+80) then
        tmp = y1 * (i * ((x * j) - (z * k)))
    else if (y <= 2.35d+266) then
        tmp = y0 * (((y5 * t_2) + (c * t_3)) + (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 * (y4 * ((y1 * y2) - (y * b)));
	double t_2 = (j * y3) - (k * y2);
	double t_3 = (x * y2) - (z * y3);
	double tmp;
	if (y <= -510000000000.0) {
		tmp = t_1;
	} else if (y <= 4e-303) {
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	} else if (y <= 3.7e-173) {
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_2)));
	} else if (y <= 1.4e-46) {
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (a * t_3));
	} else if (y <= 3.3e+80) {
		tmp = y1 * (i * ((x * j) - (z * k)));
	} else if (y <= 2.35e+266) {
		tmp = y0 * (((y5 * t_2) + (c * t_3)) + (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 * (y4 * ((y1 * y2) - (y * b)))
	t_2 = (j * y3) - (k * y2)
	t_3 = (x * y2) - (z * y3)
	tmp = 0
	if y <= -510000000000.0:
		tmp = t_1
	elif y <= 4e-303:
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))))
	elif y <= 3.7e-173:
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_2)))
	elif y <= 1.4e-46:
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (a * t_3))
	elif y <= 3.3e+80:
		tmp = y1 * (i * ((x * j) - (z * k)))
	elif y <= 2.35e+266:
		tmp = y0 * (((y5 * t_2) + (c * t_3)) + (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(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))))
	t_2 = Float64(Float64(j * y3) - Float64(k * y2))
	t_3 = Float64(Float64(x * y2) - Float64(z * y3))
	tmp = 0.0
	if (y <= -510000000000.0)
		tmp = t_1;
	elseif (y <= 4e-303)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(y0 * t_3)) + Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (y <= 3.7e-173)
		tmp = Float64(y5 * Float64(Float64(i * Float64(Float64(y * k) - Float64(t * j))) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * t_2))));
	elseif (y <= 1.4e-46)
		tmp = Float64(y1 * Float64(Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(a * t_3)));
	elseif (y <= 3.3e+80)
		tmp = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))));
	elseif (y <= 2.35e+266)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * t_2) + Float64(c * t_3)) + 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 * (y4 * ((y1 * y2) - (y * b)));
	t_2 = (j * y3) - (k * y2);
	t_3 = (x * y2) - (z * y3);
	tmp = 0.0;
	if (y <= -510000000000.0)
		tmp = t_1;
	elseif (y <= 4e-303)
		tmp = c * (((i * ((z * t) - (x * y))) + (y0 * t_3)) + (y4 * ((y * y3) - (t * y2))));
	elseif (y <= 3.7e-173)
		tmp = y5 * ((i * ((y * k) - (t * j))) + ((a * ((t * y2) - (y * y3))) + (y0 * t_2)));
	elseif (y <= 1.4e-46)
		tmp = y1 * ((y4 * ((k * y2) - (j * y3))) - (a * t_3));
	elseif (y <= 3.3e+80)
		tmp = y1 * (i * ((x * j) - (z * k)));
	elseif (y <= 2.35e+266)
		tmp = y0 * (((y5 * t_2) + (c * t_3)) + (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[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -510000000000.0], t$95$1, If[LessEqual[y, 4e-303], N[(c * N[(N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-173], N[(y5 * N[(N[(i * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-46], N[(y1 * N[(N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+80], N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+266], N[(y0 * N[(N[(N[(y5 * t$95$2), $MachinePrecision] + N[(c * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.1e11 or 2.3499999999999999e266 < y

   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%

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

   4. Taylor expanded in y4 around inf 45.2%

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

   5. Taylor expanded in k around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

   7. Simplified 52.1%

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

   if -5.1e11 < y < 3.99999999999999972e-303

   1. Initial program 27.6%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in c around inf 51.7%

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

      1. mul-1-neg 51.7%

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

   6. Simplified 51.7%

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

   if 3.99999999999999972e-303 < y < 3.7e-173

   1. Initial program 27.1%

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

   3. Simplified 33.7%

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

   4. Taylor expanded in y5 around -inf 54.2%

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

      1. mul-1-neg 54.2%

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

   6. Simplified 54.2%

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

   if 3.7e-173 < y < 1.3999999999999999e-46

   1. Initial program 42.8%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in y1 around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. mul-1-neg 51.0%

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

      3. sub-neg 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in i around 0 68.7%

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

   if 1.3999999999999999e-46 < y < 3.29999999999999991e80

   1. Initial program 30.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in y1 around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. mul-1-neg 36.8%

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

      3. sub-neg 36.8%

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

   6. Simplified 36.8%

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

   7. Taylor expanded in i around inf 55.4%

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

   if 3.29999999999999991e80 < y < 2.3499999999999999e266

   1. Initial program 10.7%

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

   3. Simplified 10.7%

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

   4. Taylor expanded in y0 around inf 61.4%

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

      1. mul-1-neg 61.4%

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

   6. Simplified 61.4%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -510000000000:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-303}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \left(z \cdot t - x \cdot y\right) + y0 \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-173}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+80}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+266}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \end{array} \]

Alternative 10: 31.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := \left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-200}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot t_2\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-94}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot t_2 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+278}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* i (- (* x j) (* z k)))))
        (t_2 (- (* k y2) (* j y3)))
        (t_3 (* (* y0 y3) (- (* j y5) (* z c)))))
   (if (<= z -2e+163)
     t_3
     (if (<= z -2.2e-37)
       t_1
       (if (<= z -8.2e-76)
         (* y4 (* y2 (- (* k y1) (* t c))))
         (if (<= z -2.5e-200)
           (*
            y4
            (+
             (+ (* b (- (* t j) (* y k))) (* y1 t_2))
             (* c (- (* y y3) (* t y2)))))
           (if (<= z 2.8e-94)
             (* y1 (- (* y4 t_2) (* a (- (* x y2) (* z y3)))))
             (if (<= z 2.2e+48)
               (* a (* y (- (* x b) (* y3 y5))))
               (if (<= z 7.5e+206)
                 t_1
                 (if (<= z 1.5e+278)
                   t_3
                   (* (* z y1) (- (* a y3) (* i k)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (z <= -2e+163) {
		tmp = t_3;
	} else if (z <= -2.2e-37) {
		tmp = t_1;
	} else if (z <= -8.2e-76) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (z <= -2.5e-200) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	} else if (z <= 2.8e-94) {
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	} else if (z <= 2.2e+48) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (z <= 7.5e+206) {
		tmp = t_1;
	} else if (z <= 1.5e+278) {
		tmp = t_3;
	} else {
		tmp = (z * y1) * ((a * y3) - (i * k));
	}
	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 = y1 * (i * ((x * j) - (z * k)))
    t_2 = (k * y2) - (j * y3)
    t_3 = (y0 * y3) * ((j * y5) - (z * c))
    if (z <= (-2d+163)) then
        tmp = t_3
    else if (z <= (-2.2d-37)) then
        tmp = t_1
    else if (z <= (-8.2d-76)) then
        tmp = y4 * (y2 * ((k * y1) - (t * c)))
    else if (z <= (-2.5d-200)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))))
    else if (z <= 2.8d-94) then
        tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
    else if (z <= 2.2d+48) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (z <= 7.5d+206) then
        tmp = t_1
    else if (z <= 1.5d+278) then
        tmp = t_3
    else
        tmp = (z * y1) * ((a * y3) - (i * k))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y1 * (i * ((x * j) - (z * k)));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (z <= -2e+163) {
		tmp = t_3;
	} else if (z <= -2.2e-37) {
		tmp = t_1;
	} else if (z <= -8.2e-76) {
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	} else if (z <= -2.5e-200) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	} else if (z <= 2.8e-94) {
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	} else if (z <= 2.2e+48) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (z <= 7.5e+206) {
		tmp = t_1;
	} else if (z <= 1.5e+278) {
		tmp = t_3;
	} else {
		tmp = (z * y1) * ((a * y3) - (i * k));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (i * ((x * j) - (z * k)))
	t_2 = (k * y2) - (j * y3)
	t_3 = (y0 * y3) * ((j * y5) - (z * c))
	tmp = 0
	if z <= -2e+163:
		tmp = t_3
	elif z <= -2.2e-37:
		tmp = t_1
	elif z <= -8.2e-76:
		tmp = y4 * (y2 * ((k * y1) - (t * c)))
	elif z <= -2.5e-200:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))))
	elif z <= 2.8e-94:
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
	elif z <= 2.2e+48:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif z <= 7.5e+206:
		tmp = t_1
	elif z <= 1.5e+278:
		tmp = t_3
	else:
		tmp = (z * y1) * ((a * y3) - (i * k))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y1 * Float64(i * Float64(Float64(x * j) - Float64(z * k))))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)))
	tmp = 0.0
	if (z <= -2e+163)
		tmp = t_3;
	elseif (z <= -2.2e-37)
		tmp = t_1;
	elseif (z <= -8.2e-76)
		tmp = Float64(y4 * Float64(y2 * Float64(Float64(k * y1) - Float64(t * c))));
	elseif (z <= -2.5e-200)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * t_2)) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (z <= 2.8e-94)
		tmp = Float64(y1 * Float64(Float64(y4 * t_2) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))));
	elseif (z <= 2.2e+48)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (z <= 7.5e+206)
		tmp = t_1;
	elseif (z <= 1.5e+278)
		tmp = t_3;
	else
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y1 * (i * ((x * j) - (z * k)));
	t_2 = (k * y2) - (j * y3);
	t_3 = (y0 * y3) * ((j * y5) - (z * c));
	tmp = 0.0;
	if (z <= -2e+163)
		tmp = t_3;
	elseif (z <= -2.2e-37)
		tmp = t_1;
	elseif (z <= -8.2e-76)
		tmp = y4 * (y2 * ((k * y1) - (t * c)));
	elseif (z <= -2.5e-200)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * t_2)) + (c * ((y * y3) - (t * y2))));
	elseif (z <= 2.8e-94)
		tmp = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	elseif (z <= 2.2e+48)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (z <= 7.5e+206)
		tmp = t_1;
	elseif (z <= 1.5e+278)
		tmp = t_3;
	else
		tmp = (z * y1) * ((a * y3) - (i * k));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y1 * N[(i * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+163], t$95$3, If[LessEqual[z, -2.2e-37], t$95$1, If[LessEqual[z, -8.2e-76], N[(y4 * N[(y2 * N[(N[(k * y1), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-200], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-94], N[(y1 * N[(N[(y4 * t$95$2), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+48], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+206], t$95$1, If[LessEqual[z, 1.5e+278], t$95$3, N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.9999999999999999e163 or 7.49999999999999958e206 < z < 1.5e278

   1. Initial program 17.4%

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

   3. Simplified 17.4%

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

   4. Taylor expanded in y0 around inf 48.2%

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

      1. mul-1-neg 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in y3 around inf 67.8%

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

      1. distribute-lft-out-- 67.8%

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

      2. associate-*r* 67.8%

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

      3. mul-1-neg 67.8%

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

      4. *-commutative 67.8%

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

      5. *-commutative 67.8%

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

      6. *-commutative 67.8%

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

   9. Simplified 67.8%

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

   if -1.9999999999999999e163 < z < -2.20000000000000002e-37 or 2.1999999999999999e48 < z < 7.49999999999999958e206

   1. Initial program 18.9%

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

   3. Simplified 20.4%

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

   4. Taylor expanded in y1 around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. mul-1-neg 38.1%

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

      3. sub-neg 38.1%

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

   6. Simplified 38.1%

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

   7. Taylor expanded in i around inf 47.9%

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

   if -2.20000000000000002e-37 < z < -8.1999999999999996e-76

   1. Initial program 29.8%

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

   3. Simplified 29.8%

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

   4. Taylor expanded in y4 around inf 30.2%

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

   5. Taylor expanded in y2 around inf 61.0%

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

      1. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   if -8.1999999999999996e-76 < z < -2.49999999999999996e-200

   1. Initial program 34.6%

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

   3. Simplified 34.6%

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

   4. Taylor expanded in y4 around inf 70.2%

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

   if -2.49999999999999996e-200 < z < 2.7999999999999998e-94

   1. Initial program 35.6%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in y1 around inf 53.1%

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

      1. mul-1-neg 53.1%

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

      2. mul-1-neg 53.1%

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

      3. sub-neg 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in i around 0 51.7%

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

   if 2.7999999999999998e-94 < z < 2.1999999999999999e48

   1. Initial program 24.6%

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

   3. Simplified 24.6%

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

   4. Taylor expanded in a around inf 41.5%

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

      1. associate--l+ 41.5%

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

      2. mul-1-neg 41.5%

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

      3. mul-1-neg 41.5%

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

   6. Simplified 41.5%

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

   7. Taylor expanded in y around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   9. Simplified 52.9%

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

   if 1.5e278 < z

   1. Initial program 11.1%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in y1 around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. mul-1-neg 55.6%

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

      3. sub-neg 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in z around inf 69.0%

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

      1. distribute-lft-out-- 69.0%

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

      2. associate-*r* 69.0%

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

      3. mul-1-neg 69.0%

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

      4. *-commutative 69.0%

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

      5. *-commutative 69.0%

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

   9. Simplified 69.0%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+163}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-37}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(k \cdot y1 - t \cdot c\right)\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-200}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-94}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+206}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j - z \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+278}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \end{array} \]

Alternative 11: 29.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ t_3 := y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+266}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-151}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-125}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 0.295:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+131} \lor \neg \left(x \leq 6.7 \cdot 10^{+196}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b)))))
        (t_3 (* y1 (* a (- (* z y3) (* x y2))))))
   (if (<= x -4.3e+266)
     (* i (* j (* x y1)))
     (if (<= x -2.3e+27)
       t_3
       (if (<= x -1.15e-127)
         t_2
         (if (<= x -6e-204)
           t_1
           (if (<= x -8.5e-297)
             t_2
             (if (<= x 6.8e-223)
               t_1
               (if (<= x 1.6e-151)
                 (* y4 (* t (- (* b j) (* c y2))))
                 (if (<= x 3.7e-125)
                   (* y1 (* y4 (- (* k y2) (* j y3))))
                   (if (<= x 0.295)
                     (* c (* y4 (- (* y y3) (* t y2))))
                     (if (or (<= x 2.5e+131) (not (<= x 6.7e+196)))
                       t_3
                       (* (* k y0) (- (* z b) (* y2 y5)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -4.3e+266) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.3e+27) {
		tmp = t_3;
	} else if (x <= -1.15e-127) {
		tmp = t_2;
	} else if (x <= -6e-204) {
		tmp = t_1;
	} else if (x <= -8.5e-297) {
		tmp = t_2;
	} else if (x <= 6.8e-223) {
		tmp = t_1;
	} else if (x <= 1.6e-151) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 3.7e-125) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 0.295) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if ((x <= 2.5e+131) || !(x <= 6.7e+196)) {
		tmp = t_3;
	} else {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    t_3 = y1 * (a * ((z * y3) - (x * y2)))
    if (x <= (-4.3d+266)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-2.3d+27)) then
        tmp = t_3
    else if (x <= (-1.15d-127)) then
        tmp = t_2
    else if (x <= (-6d-204)) then
        tmp = t_1
    else if (x <= (-8.5d-297)) then
        tmp = t_2
    else if (x <= 6.8d-223) then
        tmp = t_1
    else if (x <= 1.6d-151) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (x <= 3.7d-125) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= 0.295d0) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if ((x <= 2.5d+131) .or. (.not. (x <= 6.7d+196))) then
        tmp = t_3
    else
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -4.3e+266) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.3e+27) {
		tmp = t_3;
	} else if (x <= -1.15e-127) {
		tmp = t_2;
	} else if (x <= -6e-204) {
		tmp = t_1;
	} else if (x <= -8.5e-297) {
		tmp = t_2;
	} else if (x <= 6.8e-223) {
		tmp = t_1;
	} else if (x <= 1.6e-151) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 3.7e-125) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 0.295) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if ((x <= 2.5e+131) || !(x <= 6.7e+196)) {
		tmp = t_3;
	} else {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	t_3 = y1 * (a * ((z * y3) - (x * y2)))
	tmp = 0
	if x <= -4.3e+266:
		tmp = i * (j * (x * y1))
	elif x <= -2.3e+27:
		tmp = t_3
	elif x <= -1.15e-127:
		tmp = t_2
	elif x <= -6e-204:
		tmp = t_1
	elif x <= -8.5e-297:
		tmp = t_2
	elif x <= 6.8e-223:
		tmp = t_1
	elif x <= 1.6e-151:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif x <= 3.7e-125:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= 0.295:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif (x <= 2.5e+131) or not (x <= 6.7e+196):
		tmp = t_3
	else:
		tmp = (k * y0) * ((z * b) - (y2 * 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(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	t_3 = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (x <= -4.3e+266)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -2.3e+27)
		tmp = t_3;
	elseif (x <= -1.15e-127)
		tmp = t_2;
	elseif (x <= -6e-204)
		tmp = t_1;
	elseif (x <= -8.5e-297)
		tmp = t_2;
	elseif (x <= 6.8e-223)
		tmp = t_1;
	elseif (x <= 1.6e-151)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (x <= 3.7e-125)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 0.295)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif ((x <= 2.5e+131) || !(x <= 6.7e+196))
		tmp = t_3;
	else
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	t_3 = y1 * (a * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (x <= -4.3e+266)
		tmp = i * (j * (x * y1));
	elseif (x <= -2.3e+27)
		tmp = t_3;
	elseif (x <= -1.15e-127)
		tmp = t_2;
	elseif (x <= -6e-204)
		tmp = t_1;
	elseif (x <= -8.5e-297)
		tmp = t_2;
	elseif (x <= 6.8e-223)
		tmp = t_1;
	elseif (x <= 1.6e-151)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (x <= 3.7e-125)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= 0.295)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif ((x <= 2.5e+131) || ~((x <= 6.7e+196)))
		tmp = t_3;
	else
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+266], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e+27], t$95$3, If[LessEqual[x, -1.15e-127], t$95$2, If[LessEqual[x, -6e-204], t$95$1, If[LessEqual[x, -8.5e-297], t$95$2, If[LessEqual[x, 6.8e-223], t$95$1, If[LessEqual[x, 1.6e-151], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-125], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.295], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.5e+131], N[Not[LessEqual[x, 6.7e+196]], $MachinePrecision]], t$95$3, N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -4.3000000000000002e266

   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 12.5%

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

   4. Taylor expanded in y1 around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. mul-1-neg 87.5%

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

      3. sub-neg 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in j around inf 100.0%

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

       1. *-commutative 100.0%

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

       2. associate-*r* 100.0%

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

   12. Simplified 100.0%

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

   13. Taylor expanded in y1 around 0 100.0%

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

       1. associate-*r* 100.0%

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

       2. *-commutative 100.0%

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

       3. associate-*l* 100.0%

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

   15. Simplified 100.0%

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

   if -4.3000000000000002e266 < x < -2.3000000000000001e27 or 0.294999999999999984 < x < 2.49999999999999998e131 or 6.7000000000000002e196 < x

   1. Initial program 23.5%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in y1 around inf 43.5%

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

      1. mul-1-neg 43.5%

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

      2. mul-1-neg 43.5%

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

      3. sub-neg 43.5%

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

   6. Simplified 43.5%

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

   7. Taylor expanded in a around inf 58.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.1%

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

      2. *-commutative 55.1%

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

      3. associate-*r* 58.7%

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

      4. *-commutative 58.7%

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

   9. Simplified 58.7%

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

   if -2.3000000000000001e27 < x < -1.15000000000000009e-127 or -5.9999999999999997e-204 < x < -8.49999999999999991e-297

   1. Initial program 32.4%

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

   3. Simplified 32.4%

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

   4. Taylor expanded in t around inf 47.0%

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

      1. associate--l+ 47.0%

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

      2. mul-1-neg 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in a around -inf 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l* 43.7%

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

      3. *-commutative 43.7%

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

      4. +-commutative 43.7%

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

      5. mul-1-neg 43.7%

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

      6. unsub-neg 43.7%

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

   9. Simplified 43.7%

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

   if -1.15000000000000009e-127 < x < -5.9999999999999997e-204 or -8.49999999999999991e-297 < x < 6.7999999999999996e-223

   1. Initial program 31.1%

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

   3. Simplified 31.1%

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

   4. Taylor expanded in y0 around inf 76.2%

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

      1. mul-1-neg 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in y5 around inf 69.6%

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

   if 6.7999999999999996e-223 < x < 1.60000000000000011e-151

   1. Initial program 29.8%

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

   3. Simplified 29.8%

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

   4. Taylor expanded in y4 around inf 36.7%

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

   5. Taylor expanded in t around inf 53.7%

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

      1. *-commutative 53.7%

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

   7. Simplified 53.7%

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

   if 1.60000000000000011e-151 < x < 3.6999999999999999e-125

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in y1 around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. mul-1-neg 55.6%

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

      3. sub-neg 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in i around 0 56.3%

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

   8. Taylor expanded in y4 around inf 56.5%

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

      1. *-commutative 56.5%

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

   10. Simplified 56.5%

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

   if 3.6999999999999999e-125 < x < 0.294999999999999984

   1. Initial program 32.0%

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

   3. Simplified 32.0%

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

   4. Taylor expanded in y4 around inf 48.1%

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

   5. Taylor expanded in c around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   7. Simplified 53.5%

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

   if 2.49999999999999998e131 < x < 6.7000000000000002e196

   1. Initial program 6.7%

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

   3. Simplified 6.7%

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

   4. Taylor expanded in y0 around inf 27.3%

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

      1. mul-1-neg 27.3%

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

   6. Simplified 27.3%

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

   7. Taylor expanded in k around -inf 54.4%

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

      1. associate-*r* 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

   9. Simplified 54.4%

      \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+266}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-204}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-223}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-151}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-125}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 0.295:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+131} \lor \neg \left(x \leq 6.7 \cdot 10^{+196}\right):\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \end{array} \]

Alternative 12: 29.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ t_3 := y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+265}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 0.55:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+180}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b)))))
        (t_3 (* y1 (* a (- (* z y3) (* x y2))))))
   (if (<= x -7.2e+265)
     (* i (* j (* x y1)))
     (if (<= x -1.8e+27)
       t_3
       (if (<= x -2.2e-127)
         t_2
         (if (<= x -6.2e-204)
           t_1
           (if (<= x -5.1e-300)
             t_2
             (if (<= x 5.2e-223)
               t_1
               (if (<= x 1.32e-153)
                 (* y4 (* t (- (* b j) (* c y2))))
                 (if (<= x 2.5e-122)
                   (* y1 (* y4 (- (* k y2) (* j y3))))
                   (if (<= x 0.55)
                     (* c (* y4 (- (* y y3) (* t y2))))
                     (if (<= x 2.85e+131)
                       t_3
                       (if (<= x 2.2e+180)
                         (* (* k y0) (- (* z b) (* y2 y5)))
                         (* (- (* y a) (* j y0)) (* 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) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -7.2e+265) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.8e+27) {
		tmp = t_3;
	} else if (x <= -2.2e-127) {
		tmp = t_2;
	} else if (x <= -6.2e-204) {
		tmp = t_1;
	} else if (x <= -5.1e-300) {
		tmp = t_2;
	} else if (x <= 5.2e-223) {
		tmp = t_1;
	} else if (x <= 1.32e-153) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 2.5e-122) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 0.55) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 2.85e+131) {
		tmp = t_3;
	} else if (x <= 2.2e+180) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else {
		tmp = ((y * a) - (j * y0)) * (x * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    t_3 = y1 * (a * ((z * y3) - (x * y2)))
    if (x <= (-7.2d+265)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-1.8d+27)) then
        tmp = t_3
    else if (x <= (-2.2d-127)) then
        tmp = t_2
    else if (x <= (-6.2d-204)) then
        tmp = t_1
    else if (x <= (-5.1d-300)) then
        tmp = t_2
    else if (x <= 5.2d-223) then
        tmp = t_1
    else if (x <= 1.32d-153) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (x <= 2.5d-122) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= 0.55d0) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (x <= 2.85d+131) then
        tmp = t_3
    else if (x <= 2.2d+180) then
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    else
        tmp = ((y * a) - (j * y0)) * (x * 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 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -7.2e+265) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.8e+27) {
		tmp = t_3;
	} else if (x <= -2.2e-127) {
		tmp = t_2;
	} else if (x <= -6.2e-204) {
		tmp = t_1;
	} else if (x <= -5.1e-300) {
		tmp = t_2;
	} else if (x <= 5.2e-223) {
		tmp = t_1;
	} else if (x <= 1.32e-153) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 2.5e-122) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 0.55) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 2.85e+131) {
		tmp = t_3;
	} else if (x <= 2.2e+180) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else {
		tmp = ((y * a) - (j * y0)) * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	t_3 = y1 * (a * ((z * y3) - (x * y2)))
	tmp = 0
	if x <= -7.2e+265:
		tmp = i * (j * (x * y1))
	elif x <= -1.8e+27:
		tmp = t_3
	elif x <= -2.2e-127:
		tmp = t_2
	elif x <= -6.2e-204:
		tmp = t_1
	elif x <= -5.1e-300:
		tmp = t_2
	elif x <= 5.2e-223:
		tmp = t_1
	elif x <= 1.32e-153:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif x <= 2.5e-122:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= 0.55:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif x <= 2.85e+131:
		tmp = t_3
	elif x <= 2.2e+180:
		tmp = (k * y0) * ((z * b) - (y2 * y5))
	else:
		tmp = ((y * a) - (j * y0)) * (x * 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(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	t_3 = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (x <= -7.2e+265)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -1.8e+27)
		tmp = t_3;
	elseif (x <= -2.2e-127)
		tmp = t_2;
	elseif (x <= -6.2e-204)
		tmp = t_1;
	elseif (x <= -5.1e-300)
		tmp = t_2;
	elseif (x <= 5.2e-223)
		tmp = t_1;
	elseif (x <= 1.32e-153)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (x <= 2.5e-122)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 0.55)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 2.85e+131)
		tmp = t_3;
	elseif (x <= 2.2e+180)
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	else
		tmp = Float64(Float64(Float64(y * a) - Float64(j * y0)) * Float64(x * 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 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	t_3 = y1 * (a * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (x <= -7.2e+265)
		tmp = i * (j * (x * y1));
	elseif (x <= -1.8e+27)
		tmp = t_3;
	elseif (x <= -2.2e-127)
		tmp = t_2;
	elseif (x <= -6.2e-204)
		tmp = t_1;
	elseif (x <= -5.1e-300)
		tmp = t_2;
	elseif (x <= 5.2e-223)
		tmp = t_1;
	elseif (x <= 1.32e-153)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (x <= 2.5e-122)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= 0.55)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (x <= 2.85e+131)
		tmp = t_3;
	elseif (x <= 2.2e+180)
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	else
		tmp = ((y * a) - (j * y0)) * (x * 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[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e+265], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.8e+27], t$95$3, If[LessEqual[x, -2.2e-127], t$95$2, If[LessEqual[x, -6.2e-204], t$95$1, If[LessEqual[x, -5.1e-300], t$95$2, If[LessEqual[x, 5.2e-223], t$95$1, If[LessEqual[x, 1.32e-153], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-122], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.55], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.85e+131], t$95$3, If[LessEqual[x, 2.2e+180], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -7.20000000000000005e265

   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 12.5%

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

   4. Taylor expanded in y1 around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. mul-1-neg 87.5%

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

      3. sub-neg 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in j around inf 100.0%

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

       1. *-commutative 100.0%

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

       2. associate-*r* 100.0%

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

   12. Simplified 100.0%

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

   13. Taylor expanded in y1 around 0 100.0%

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

       1. associate-*r* 100.0%

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

       2. *-commutative 100.0%

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

       3. associate-*l* 100.0%

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

   15. Simplified 100.0%

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

   if -7.20000000000000005e265 < x < -1.79999999999999991e27 or 0.55000000000000004 < x < 2.85e131

   1. Initial program 19.5%

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

   3. Simplified 26.4%

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

   4. Taylor expanded in y1 around inf 46.3%

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

      1. mul-1-neg 46.3%

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

      2. mul-1-neg 46.3%

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

      3. sub-neg 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in a around inf 61.9%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 57.7%

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

      2. *-commutative 57.7%

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

      3. associate-*r* 61.9%

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

      4. *-commutative 61.9%

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

   9. Simplified 61.9%

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

   if -1.79999999999999991e27 < x < -2.2000000000000001e-127 or -6.1999999999999998e-204 < x < -5.0999999999999999e-300

   1. Initial program 32.4%

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

   3. Simplified 32.4%

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

   4. Taylor expanded in t around inf 47.0%

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

      1. associate--l+ 47.0%

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

      2. mul-1-neg 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in a around -inf 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l* 43.7%

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

      3. *-commutative 43.7%

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

      4. +-commutative 43.7%

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

      5. mul-1-neg 43.7%

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

      6. unsub-neg 43.7%

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

   9. Simplified 43.7%

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

   if -2.2000000000000001e-127 < x < -6.1999999999999998e-204 or -5.0999999999999999e-300 < x < 5.2e-223

   1. Initial program 31.1%

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

   3. Simplified 31.1%

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

   4. Taylor expanded in y0 around inf 76.2%

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

      1. mul-1-neg 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in y5 around inf 69.6%

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

   if 5.2e-223 < x < 1.32000000000000011e-153

   1. Initial program 29.8%

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

   3. Simplified 29.8%

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

   4. Taylor expanded in y4 around inf 36.7%

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

   5. Taylor expanded in t around inf 53.7%

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

      1. *-commutative 53.7%

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

   7. Simplified 53.7%

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

   if 1.32000000000000011e-153 < x < 2.4999999999999999e-122

   1. Initial program 27.1%

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

   3. Simplified 27.1%

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

   4. Taylor expanded in y1 around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. mul-1-neg 55.6%

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

      3. sub-neg 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in i around 0 56.3%

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

   8. Taylor expanded in y4 around inf 56.5%

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

      1. *-commutative 56.5%

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

   10. Simplified 56.5%

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

   if 2.4999999999999999e-122 < x < 0.55000000000000004

   1. Initial program 32.0%

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

   3. Simplified 32.0%

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

   4. Taylor expanded in y4 around inf 48.1%

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

   5. Taylor expanded in c around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   7. Simplified 53.5%

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

   if 2.85e131 < x < 2.1999999999999999e180

   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%

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

   4. Taylor expanded in y0 around inf 25.0%

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

      1. mul-1-neg 25.0%

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

   6. Simplified 25.0%

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

   7. Taylor expanded in k around -inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. mul-1-neg 66.9%

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

      3. unsub-neg 66.9%

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

      4. *-commutative 66.9%

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

   9. Simplified 66.9%

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

   if 2.1999999999999999e180 < x

   1. Initial program 29.2%

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

   3. Simplified 29.2%

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

   4. Taylor expanded in b around inf 40.1%

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

      1. associate--l+ 40.1%

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

      2. mul-1-neg 40.1%

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

   6. Simplified 40.1%

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

   7. Taylor expanded in x around inf 53.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+265}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-127}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-300}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-223}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 0.55:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+131}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+180}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 13: 30.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ t_2 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_3 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+198}:\\ \;\;\;\;\left(c \cdot y2 - b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1320:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+180}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y1 (* a (- (* z y3) (* x y2)))))
        (t_2 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_3 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= x -4.2e+198)
     (* (- (* c y2) (* b j)) (* x y0))
     (if (<= x -2.4e+27)
       t_1
       (if (<= x -8.5e-126)
         t_3
         (if (<= x -6.2e-204)
           t_2
           (if (<= x -3.2e-296)
             t_3
             (if (<= x 4.6e-222)
               t_2
               (if (<= x 4.6e-153)
                 (* y4 (* t (- (* b j) (* c y2))))
                 (if (<= x 1.6e-123)
                   (* y1 (* y4 (- (* k y2) (* j y3))))
                   (if (<= x 1320.0)
                     (* c (* y4 (- (* y y3) (* t y2))))
                     (if (<= x 6.5e+131)
                       t_1
                       (if (<= x 3.3e+180)
                         (* (* k y0) (- (* z b) (* y2 y5)))
                         (* (- (* y a) (* j y0)) (* 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) {
	double t_1 = y1 * (a * ((z * y3) - (x * y2)));
	double t_2 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_3 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (x <= -4.2e+198) {
		tmp = ((c * y2) - (b * j)) * (x * y0);
	} else if (x <= -2.4e+27) {
		tmp = t_1;
	} else if (x <= -8.5e-126) {
		tmp = t_3;
	} else if (x <= -6.2e-204) {
		tmp = t_2;
	} else if (x <= -3.2e-296) {
		tmp = t_3;
	} else if (x <= 4.6e-222) {
		tmp = t_2;
	} else if (x <= 4.6e-153) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 1.6e-123) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 1320.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 6.5e+131) {
		tmp = t_1;
	} else if (x <= 3.3e+180) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else {
		tmp = ((y * a) - (j * y0)) * (x * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y1 * (a * ((z * y3) - (x * y2)))
    t_2 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_3 = t * (a * ((y2 * y5) - (z * b)))
    if (x <= (-4.2d+198)) then
        tmp = ((c * y2) - (b * j)) * (x * y0)
    else if (x <= (-2.4d+27)) then
        tmp = t_1
    else if (x <= (-8.5d-126)) then
        tmp = t_3
    else if (x <= (-6.2d-204)) then
        tmp = t_2
    else if (x <= (-3.2d-296)) then
        tmp = t_3
    else if (x <= 4.6d-222) then
        tmp = t_2
    else if (x <= 4.6d-153) then
        tmp = y4 * (t * ((b * j) - (c * y2)))
    else if (x <= 1.6d-123) then
        tmp = y1 * (y4 * ((k * y2) - (j * y3)))
    else if (x <= 1320.0d0) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (x <= 6.5d+131) then
        tmp = t_1
    else if (x <= 3.3d+180) then
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    else
        tmp = ((y * a) - (j * y0)) * (x * 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 = y1 * (a * ((z * y3) - (x * y2)));
	double t_2 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_3 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (x <= -4.2e+198) {
		tmp = ((c * y2) - (b * j)) * (x * y0);
	} else if (x <= -2.4e+27) {
		tmp = t_1;
	} else if (x <= -8.5e-126) {
		tmp = t_3;
	} else if (x <= -6.2e-204) {
		tmp = t_2;
	} else if (x <= -3.2e-296) {
		tmp = t_3;
	} else if (x <= 4.6e-222) {
		tmp = t_2;
	} else if (x <= 4.6e-153) {
		tmp = y4 * (t * ((b * j) - (c * y2)));
	} else if (x <= 1.6e-123) {
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	} else if (x <= 1320.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (x <= 6.5e+131) {
		tmp = t_1;
	} else if (x <= 3.3e+180) {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	} else {
		tmp = ((y * a) - (j * y0)) * (x * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y1 * (a * ((z * y3) - (x * y2)))
	t_2 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_3 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if x <= -4.2e+198:
		tmp = ((c * y2) - (b * j)) * (x * y0)
	elif x <= -2.4e+27:
		tmp = t_1
	elif x <= -8.5e-126:
		tmp = t_3
	elif x <= -6.2e-204:
		tmp = t_2
	elif x <= -3.2e-296:
		tmp = t_3
	elif x <= 4.6e-222:
		tmp = t_2
	elif x <= 4.6e-153:
		tmp = y4 * (t * ((b * j) - (c * y2)))
	elif x <= 1.6e-123:
		tmp = y1 * (y4 * ((k * y2) - (j * y3)))
	elif x <= 1320.0:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif x <= 6.5e+131:
		tmp = t_1
	elif x <= 3.3e+180:
		tmp = (k * y0) * ((z * b) - (y2 * y5))
	else:
		tmp = ((y * a) - (j * y0)) * (x * 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(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	t_2 = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_3 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (x <= -4.2e+198)
		tmp = Float64(Float64(Float64(c * y2) - Float64(b * j)) * Float64(x * y0));
	elseif (x <= -2.4e+27)
		tmp = t_1;
	elseif (x <= -8.5e-126)
		tmp = t_3;
	elseif (x <= -6.2e-204)
		tmp = t_2;
	elseif (x <= -3.2e-296)
		tmp = t_3;
	elseif (x <= 4.6e-222)
		tmp = t_2;
	elseif (x <= 4.6e-153)
		tmp = Float64(y4 * Float64(t * Float64(Float64(b * j) - Float64(c * y2))));
	elseif (x <= 1.6e-123)
		tmp = Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3))));
	elseif (x <= 1320.0)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 6.5e+131)
		tmp = t_1;
	elseif (x <= 3.3e+180)
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	else
		tmp = Float64(Float64(Float64(y * a) - Float64(j * y0)) * Float64(x * 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 = y1 * (a * ((z * y3) - (x * y2)));
	t_2 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_3 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (x <= -4.2e+198)
		tmp = ((c * y2) - (b * j)) * (x * y0);
	elseif (x <= -2.4e+27)
		tmp = t_1;
	elseif (x <= -8.5e-126)
		tmp = t_3;
	elseif (x <= -6.2e-204)
		tmp = t_2;
	elseif (x <= -3.2e-296)
		tmp = t_3;
	elseif (x <= 4.6e-222)
		tmp = t_2;
	elseif (x <= 4.6e-153)
		tmp = y4 * (t * ((b * j) - (c * y2)));
	elseif (x <= 1.6e-123)
		tmp = y1 * (y4 * ((k * y2) - (j * y3)));
	elseif (x <= 1320.0)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (x <= 6.5e+131)
		tmp = t_1;
	elseif (x <= 3.3e+180)
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	else
		tmp = ((y * a) - (j * y0)) * (x * 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[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+198], N[(N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e+27], t$95$1, If[LessEqual[x, -8.5e-126], t$95$3, If[LessEqual[x, -6.2e-204], t$95$2, If[LessEqual[x, -3.2e-296], t$95$3, If[LessEqual[x, 4.6e-222], t$95$2, If[LessEqual[x, 4.6e-153], N[(y4 * N[(t * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-123], N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1320.0], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+131], t$95$1, If[LessEqual[x, 3.3e+180], N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if x < -4.20000000000000026e198

   1. Initial program 9.8%

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

   3. Simplified 9.8%

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

   4. Taylor expanded in y0 around inf 52.6%

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

      1. mul-1-neg 52.6%

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

   6. Simplified 52.6%

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

   7. Taylor expanded in x around inf 66.9%

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

   if -4.20000000000000026e198 < x < -2.39999999999999998e27 or 1320 < x < 6.5e131

   1. Initial program 20.3%

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

   3. Simplified 28.8%

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

   4. Taylor expanded in y1 around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. mul-1-neg 49.6%

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

      3. sub-neg 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in a around inf 66.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*r* 66.7%

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

      4. *-commutative 66.7%

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

   9. Simplified 66.7%

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

   if -2.39999999999999998e27 < x < -8.49999999999999938e-126 or -6.1999999999999998e-204 < x < -3.20000000000000013e-296

   1. Initial program 32.4%

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

   3. Simplified 32.4%

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

   4. Taylor expanded in t around inf 47.0%

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

      1. associate--l+ 47.0%

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

      2. mul-1-neg 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in a around -inf 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l* 43.7%

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

      3. *-commutative 43.7%

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

      4. +-commutative 43.7%

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

      5. mul-1-neg 43.7%

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

      6. unsub-neg 43.7%

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

   9. Simplified 43.7%

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

   if -8.49999999999999938e-126 < x < -6.1999999999999998e-204 or -3.20000000000000013e-296 < x < 4.6000000000000003e-222

   1. Initial program 31.1%

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

   3. Simplified 31.1%

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

   4. Taylor expanded in y0 around inf 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.2%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 69.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]

   if 4.6000000000000003e-222 < x < 4.59999999999999994e-153

   1. Initial program 29.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in t around inf 53.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - c \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 53.7%

         \[\leadsto y4 \cdot \left(t \cdot \left(j \cdot b - \color{blue}{y2 \cdot c}\right)\right) \]

   7. Simplified 53.7%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(j \cdot b - y2 \cdot c\right)\right)} \]

   if 4.59999999999999994e-153 < x < 1.59999999999999989e-123

   1. Initial program 27.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 55.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 55.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 55.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 56.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in y4 around inf 56.5%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} \cdot y1 \]
   9. Step-by-step derivation

      1. *-commutative 56.5%

         \[\leadsto \left(y4 \cdot \left(\color{blue}{y2 \cdot k} - y3 \cdot j\right)\right) \cdot y1 \]

   10. Simplified 56.5%

       \[\leadsto \color{blue}{\left(y4 \cdot \left(y2 \cdot k - y3 \cdot j\right)\right)} \cdot y1 \]

   if 1.59999999999999989e-123 < x < 1320

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 48.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 53.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 53.5%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 53.5%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 53.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 6.5e131 < x < 3.29999999999999989e180

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 25.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 25.0%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 25.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in k around -inf 66.9%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(z \cdot b + -1 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 66.9%

         \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(z \cdot b + -1 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. mul-1-neg 66.9%

         \[\leadsto \left(k \cdot y0\right) \cdot \left(z \cdot b + \color{blue}{\left(-y5 \cdot y2\right)}\right) \]

      3. unsub-neg 66.9%

         \[\leadsto \left(k \cdot y0\right) \cdot \color{blue}{\left(z \cdot b - y5 \cdot y2\right)} \]

      4. *-commutative 66.9%

         \[\leadsto \left(k \cdot y0\right) \cdot \left(z \cdot b - \color{blue}{y2 \cdot y5}\right) \]

   9. Simplified 66.9%

      \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)} \]

   if 3.29999999999999989e180 < x

   1. Initial program 29.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 40.1%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 40.1%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 53.2%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+198}:\\ \;\;\;\;\left(c \cdot y2 - b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-222}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-153}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j - c \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq 1320:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+131}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+180}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \end{array} \]

Alternative 14: 35.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := y1 \cdot \left(y4 \cdot t_2 - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{if}\;y0 \leq -1.55 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -5.5 \cdot 10^{+180}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -4.1 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y0 \leq 3 \cdot 10^{-210}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot t_2 - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 10^{-38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{elif}\;y0 \leq 3.2 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y3) (- (* j y5) (* z c))))
        (t_2 (- (* k y2) (* j y3)))
        (t_3 (* y1 (- (* y4 t_2) (* a (- (* x y2) (* z y3)))))))
   (if (<= y0 -1.55e+241)
     t_1
     (if (<= y0 -5.5e+180)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= y0 -2.8e+100)
         t_1
         (if (<= y0 -4.1e-94)
           t_3
           (if (<= y0 3e-210)
             (* y4 (- (* y1 t_2) (* c (- (* t y2) (* y y3)))))
             (if (<= y0 1e-38)
               t_3
               (if (<= y0 5.8e+18)
                 (* (* z y1) (- (* a y3) (* i k)))
                 (if (<= y0 3.2e+151)
                   (* x (* y1 (- (* i j) (* a y2))))
                   (* y0 (* y5 (- (* j y3) (* k y2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	double tmp;
	if (y0 <= -1.55e+241) {
		tmp = t_1;
	} else if (y0 <= -5.5e+180) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y0 <= -2.8e+100) {
		tmp = t_1;
	} else if (y0 <= -4.1e-94) {
		tmp = t_3;
	} else if (y0 <= 3e-210) {
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))));
	} else if (y0 <= 1e-38) {
		tmp = t_3;
	} else if (y0 <= 5.8e+18) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else if (y0 <= 3.2e+151) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y0 * y3) * ((j * y5) - (z * c))
    t_2 = (k * y2) - (j * y3)
    t_3 = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
    if (y0 <= (-1.55d+241)) then
        tmp = t_1
    else if (y0 <= (-5.5d+180)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y0 <= (-2.8d+100)) then
        tmp = t_1
    else if (y0 <= (-4.1d-94)) then
        tmp = t_3
    else if (y0 <= 3d-210) then
        tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))))
    else if (y0 <= 1d-38) then
        tmp = t_3
    else if (y0 <= 5.8d+18) then
        tmp = (z * y1) * ((a * y3) - (i * k))
    else if (y0 <= 3.2d+151) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double t_2 = (k * y2) - (j * y3);
	double t_3 = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	double tmp;
	if (y0 <= -1.55e+241) {
		tmp = t_1;
	} else if (y0 <= -5.5e+180) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y0 <= -2.8e+100) {
		tmp = t_1;
	} else if (y0 <= -4.1e-94) {
		tmp = t_3;
	} else if (y0 <= 3e-210) {
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))));
	} else if (y0 <= 1e-38) {
		tmp = t_3;
	} else if (y0 <= 5.8e+18) {
		tmp = (z * y1) * ((a * y3) - (i * k));
	} else if (y0 <= 3.2e+151) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y3) * ((j * y5) - (z * c))
	t_2 = (k * y2) - (j * y3)
	t_3 = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))))
	tmp = 0
	if y0 <= -1.55e+241:
		tmp = t_1
	elif y0 <= -5.5e+180:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y0 <= -2.8e+100:
		tmp = t_1
	elif y0 <= -4.1e-94:
		tmp = t_3
	elif y0 <= 3e-210:
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))))
	elif y0 <= 1e-38:
		tmp = t_3
	elif y0 <= 5.8e+18:
		tmp = (z * y1) * ((a * y3) - (i * k))
	elif y0 <= 3.2e+151:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(y1 * Float64(Float64(y4 * t_2) - Float64(a * Float64(Float64(x * y2) - Float64(z * y3)))))
	tmp = 0.0
	if (y0 <= -1.55e+241)
		tmp = t_1;
	elseif (y0 <= -5.5e+180)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y0 <= -2.8e+100)
		tmp = t_1;
	elseif (y0 <= -4.1e-94)
		tmp = t_3;
	elseif (y0 <= 3e-210)
		tmp = Float64(y4 * Float64(Float64(y1 * t_2) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y0 <= 1e-38)
		tmp = t_3;
	elseif (y0 <= 5.8e+18)
		tmp = Float64(Float64(z * y1) * Float64(Float64(a * y3) - Float64(i * k)));
	elseif (y0 <= 3.2e+151)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y3) * ((j * y5) - (z * c));
	t_2 = (k * y2) - (j * y3);
	t_3 = y1 * ((y4 * t_2) - (a * ((x * y2) - (z * y3))));
	tmp = 0.0;
	if (y0 <= -1.55e+241)
		tmp = t_1;
	elseif (y0 <= -5.5e+180)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y0 <= -2.8e+100)
		tmp = t_1;
	elseif (y0 <= -4.1e-94)
		tmp = t_3;
	elseif (y0 <= 3e-210)
		tmp = y4 * ((y1 * t_2) - (c * ((t * y2) - (y * y3))));
	elseif (y0 <= 1e-38)
		tmp = t_3;
	elseif (y0 <= 5.8e+18)
		tmp = (z * y1) * ((a * y3) - (i * k));
	elseif (y0 <= 3.2e+151)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	else
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(N[(y4 * t$95$2), $MachinePrecision] - N[(a * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.55e+241], t$95$1, If[LessEqual[y0, -5.5e+180], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.8e+100], t$95$1, If[LessEqual[y0, -4.1e-94], t$95$3, If[LessEqual[y0, 3e-210], N[(y4 * N[(N[(y1 * t$95$2), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1e-38], t$95$3, If[LessEqual[y0, 5.8e+18], N[(N[(z * y1), $MachinePrecision] * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.2e+151], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -1.55e241 or -5.5000000000000003e180 < y0 < -2.7999999999999998e100

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 69.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 69.1%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 69.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y3 around inf 69.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot \left(y0 \cdot y3\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 69.4%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \cdot \left(y0 \cdot y3\right) \]

      2. associate-*r* 69.4%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\right)} \]

      3. mul-1-neg 69.4%

         \[\leadsto \color{blue}{-\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)} \]

      4. *-commutative 69.4%

         \[\leadsto -\color{blue}{\left(y0 \cdot y3\right) \cdot \left(c \cdot z - j \cdot y5\right)} \]

      5. *-commutative 69.4%

         \[\leadsto -\color{blue}{\left(y3 \cdot y0\right)} \cdot \left(c \cdot z - j \cdot y5\right) \]

      6. *-commutative 69.4%

         \[\leadsto -\left(y3 \cdot y0\right) \cdot \left(\color{blue}{z \cdot c} - j \cdot y5\right) \]

   9. Simplified 69.4%

      \[\leadsto \color{blue}{-\left(y3 \cdot y0\right) \cdot \left(z \cdot c - j \cdot y5\right)} \]

   if -1.55e241 < y0 < -5.5000000000000003e180

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.5%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in x around -inf 60.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right)} \]

      2. neg-mul-1 60.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right) \]

      3. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right)\right)} \]

      4. distribute-lft-out-- 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(c \cdot y2 - b \cdot j\right)\right)}\right) \]

      5. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(c \cdot y2 - \color{blue}{j \cdot b}\right)\right)\right) \]

      6. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot c} - j \cdot b\right)\right)\right) \]

   9. Simplified 60.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(y2 \cdot c - j \cdot b\right)\right)\right)} \]

   if -2.7999999999999998e100 < y0 < -4.10000000000000001e-94 or 3.0000000000000001e-210 < y0 < 9.9999999999999996e-39

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 47.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 47.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 47.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 47.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 52.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   if -4.10000000000000001e-94 < y0 < 3.0000000000000001e-210

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 44.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.6%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 44.6%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 44.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 9.9999999999999996e-39 < y0 < 5.8e18

   1. Initial program 46.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 40.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 40.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 40.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 40.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot i\right) - -1 \cdot \left(a \cdot y3\right)\right) \cdot \left(y1 \cdot z\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 54.4%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot i - a \cdot y3\right)\right)} \cdot \left(y1 \cdot z\right) \]

      2. associate-*r* 54.4%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(k \cdot i - a \cdot y3\right) \cdot \left(y1 \cdot z\right)\right)} \]

      3. mul-1-neg 54.4%

         \[\leadsto \color{blue}{-\left(k \cdot i - a \cdot y3\right) \cdot \left(y1 \cdot z\right)} \]

      4. *-commutative 54.4%

         \[\leadsto -\color{blue}{\left(y1 \cdot z\right) \cdot \left(k \cdot i - a \cdot y3\right)} \]

      5. *-commutative 54.4%

         \[\leadsto -\left(y1 \cdot z\right) \cdot \left(k \cdot i - \color{blue}{y3 \cdot a}\right) \]

   9. Simplified 54.4%

      \[\leadsto \color{blue}{-\left(y1 \cdot z\right) \cdot \left(k \cdot i - y3 \cdot a\right)} \]

   if 5.8e18 < y0 < 3.19999999999999994e151

   1. Initial program 19.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 23.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 47.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 47.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 47.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 62.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 62.4%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 62.4%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 62.4%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 62.4%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   if 3.19999999999999994e151 < y0

   1. Initial program 9.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 9.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 64.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.55 \cdot 10^{+241}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -5.5 \cdot 10^{+180}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -4.1 \cdot 10^{-94}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 3 \cdot 10^{-210}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 10^{-38}:\\ \;\;\;\;y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right) - a \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{+18}:\\ \;\;\;\;\left(z \cdot y1\right) \cdot \left(a \cdot y3 - i \cdot k\right)\\ \mathbf{elif}\;y0 \leq 3.2 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]

Alternative 15: 33.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{if}\;y0 \leq -9.2 \cdot 10^{+240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.04 \cdot 10^{+183}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-106}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2.8 \cdot 10^{-133}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 1.04 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y3) (- (* j y5) (* z c)))))
   (if (<= y0 -9.2e+240)
     t_1
     (if (<= y0 -1.04e+183)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= y0 -1.7e+50)
         t_1
         (if (<= y0 -3e-106)
           (* y1 (* a (- (* z y3) (* x y2))))
           (if (<= y0 2.8e-133)
             (*
              y4
              (- (* y1 (- (* k y2) (* j y3))) (* c (- (* t y2) (* y y3)))))
             (if (<= y0 1.04e+154)
               (* x (* y1 (- (* i j) (* a y2))))
               (* y0 (* y5 (- (* j y3) (* k y2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (y0 <= -9.2e+240) {
		tmp = t_1;
	} else if (y0 <= -1.04e+183) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y0 <= -1.7e+50) {
		tmp = t_1;
	} else if (y0 <= -3e-106) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 2.8e-133) {
		tmp = y4 * ((y1 * ((k * y2) - (j * y3))) - (c * ((t * y2) - (y * y3))));
	} else if (y0 <= 1.04e+154) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y0 * y3) * ((j * y5) - (z * c))
    if (y0 <= (-9.2d+240)) then
        tmp = t_1
    else if (y0 <= (-1.04d+183)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y0 <= (-1.7d+50)) then
        tmp = t_1
    else if (y0 <= (-3d-106)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y0 <= 2.8d-133) then
        tmp = y4 * ((y1 * ((k * y2) - (j * y3))) - (c * ((t * y2) - (y * y3))))
    else if (y0 <= 1.04d+154) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (y0 <= -9.2e+240) {
		tmp = t_1;
	} else if (y0 <= -1.04e+183) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y0 <= -1.7e+50) {
		tmp = t_1;
	} else if (y0 <= -3e-106) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 2.8e-133) {
		tmp = y4 * ((y1 * ((k * y2) - (j * y3))) - (c * ((t * y2) - (y * y3))));
	} else if (y0 <= 1.04e+154) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y3) * ((j * y5) - (z * c))
	tmp = 0
	if y0 <= -9.2e+240:
		tmp = t_1
	elif y0 <= -1.04e+183:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y0 <= -1.7e+50:
		tmp = t_1
	elif y0 <= -3e-106:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y0 <= 2.8e-133:
		tmp = y4 * ((y1 * ((k * y2) - (j * y3))) - (c * ((t * y2) - (y * y3))))
	elif y0 <= 1.04e+154:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)))
	tmp = 0.0
	if (y0 <= -9.2e+240)
		tmp = t_1;
	elseif (y0 <= -1.04e+183)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y0 <= -1.7e+50)
		tmp = t_1;
	elseif (y0 <= -3e-106)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y0 <= 2.8e-133)
		tmp = Float64(y4 * Float64(Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y0 <= 1.04e+154)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y3) * ((j * y5) - (z * c));
	tmp = 0.0;
	if (y0 <= -9.2e+240)
		tmp = t_1;
	elseif (y0 <= -1.04e+183)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y0 <= -1.7e+50)
		tmp = t_1;
	elseif (y0 <= -3e-106)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y0 <= 2.8e-133)
		tmp = y4 * ((y1 * ((k * y2) - (j * y3))) - (c * ((t * y2) - (y * y3))));
	elseif (y0 <= 1.04e+154)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	else
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -9.2e+240], t$95$1, If[LessEqual[y0, -1.04e+183], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.7e+50], t$95$1, If[LessEqual[y0, -3e-106], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.8e-133], N[(y4 * N[(N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.04e+154], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -9.20000000000000005e240 or -1.04e183 < y0 < -1.6999999999999999e50

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.3%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y3 around inf 65.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot \left(y0 \cdot y3\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 65.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \cdot \left(y0 \cdot y3\right) \]

      2. associate-*r* 65.3%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\right)} \]

      3. mul-1-neg 65.3%

         \[\leadsto \color{blue}{-\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)} \]

      4. *-commutative 65.3%

         \[\leadsto -\color{blue}{\left(y0 \cdot y3\right) \cdot \left(c \cdot z - j \cdot y5\right)} \]

      5. *-commutative 65.3%

         \[\leadsto -\color{blue}{\left(y3 \cdot y0\right)} \cdot \left(c \cdot z - j \cdot y5\right) \]

      6. *-commutative 65.3%

         \[\leadsto -\left(y3 \cdot y0\right) \cdot \left(\color{blue}{z \cdot c} - j \cdot y5\right) \]

   9. Simplified 65.3%

      \[\leadsto \color{blue}{-\left(y3 \cdot y0\right) \cdot \left(z \cdot c - j \cdot y5\right)} \]

   if -9.20000000000000005e240 < y0 < -1.04e183

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.5%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in x around -inf 60.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right)} \]

      2. neg-mul-1 60.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right) \]

      3. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right)\right)} \]

      4. distribute-lft-out-- 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(c \cdot y2 - b \cdot j\right)\right)}\right) \]

      5. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(c \cdot y2 - \color{blue}{j \cdot b}\right)\right)\right) \]

      6. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot c} - j \cdot b\right)\right)\right) \]

   9. Simplified 60.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(y2 \cdot c - j \cdot b\right)\right)\right)} \]

   if -1.6999999999999999e50 < y0 < -3.00000000000000019e-106

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in a around inf 53.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. *-commutative 50.7%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z - x \cdot y2\right) \]

      3. associate-*r* 53.2%

         \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      4. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot z - \color{blue}{y2 \cdot x}\right)\right) \]

   9. Simplified 53.2%

      \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - y2 \cdot x\right)\right)} \]

   if -3.00000000000000019e-106 < y0 < 2.7999999999999999e-133

   1. Initial program 29.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 46.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 44.8%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 44.8%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 44.8%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   if 2.7999999999999999e-133 < y0 < 1.04e154

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 38.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 46.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 46.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 46.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 46.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.2%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 45.2%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 45.2%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 45.2%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   if 1.04e154 < y0

   1. Initial program 9.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 9.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 64.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -9.2 \cdot 10^{+240}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -1.04 \cdot 10^{+183}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.7 \cdot 10^{+50}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -3 \cdot 10^{-106}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2.8 \cdot 10^{-133}:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 1.04 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]

Alternative 16: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ t_3 := y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -2.75 \cdot 10^{+264}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 96:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{+133} \lor \neg \left(x \leq 6.6 \cdot 10^{+196}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b)))))
        (t_3 (* y1 (* a (- (* z y3) (* x y2))))))
   (if (<= x -2.75e+264)
     (* i (* j (* x y1)))
     (if (<= x -1.6e+27)
       t_3
       (if (<= x -1.6e-129)
         t_2
         (if (<= x -1.3e-203)
           t_1
           (if (<= x -1.45e-296)
             t_2
             (if (<= x 4.8e-222)
               t_1
               (if (<= x 96.0)
                 (* c (* y4 (- (* y y3) (* t y2))))
                 (if (or (<= x 1.04e+133) (not (<= x 6.6e+196)))
                   t_3
                   (* b (* j (- (* t y4) (* x y0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -2.75e+264) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.6e+27) {
		tmp = t_3;
	} else if (x <= -1.6e-129) {
		tmp = t_2;
	} else if (x <= -1.3e-203) {
		tmp = t_1;
	} else if (x <= -1.45e-296) {
		tmp = t_2;
	} else if (x <= 4.8e-222) {
		tmp = t_1;
	} else if (x <= 96.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if ((x <= 1.04e+133) || !(x <= 6.6e+196)) {
		tmp = t_3;
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    t_3 = y1 * (a * ((z * y3) - (x * y2)))
    if (x <= (-2.75d+264)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-1.6d+27)) then
        tmp = t_3
    else if (x <= (-1.6d-129)) then
        tmp = t_2
    else if (x <= (-1.3d-203)) then
        tmp = t_1
    else if (x <= (-1.45d-296)) then
        tmp = t_2
    else if (x <= 4.8d-222) then
        tmp = t_1
    else if (x <= 96.0d0) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if ((x <= 1.04d+133) .or. (.not. (x <= 6.6d+196))) then
        tmp = t_3
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -2.75e+264) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.6e+27) {
		tmp = t_3;
	} else if (x <= -1.6e-129) {
		tmp = t_2;
	} else if (x <= -1.3e-203) {
		tmp = t_1;
	} else if (x <= -1.45e-296) {
		tmp = t_2;
	} else if (x <= 4.8e-222) {
		tmp = t_1;
	} else if (x <= 96.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if ((x <= 1.04e+133) || !(x <= 6.6e+196)) {
		tmp = t_3;
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	t_3 = y1 * (a * ((z * y3) - (x * y2)))
	tmp = 0
	if x <= -2.75e+264:
		tmp = i * (j * (x * y1))
	elif x <= -1.6e+27:
		tmp = t_3
	elif x <= -1.6e-129:
		tmp = t_2
	elif x <= -1.3e-203:
		tmp = t_1
	elif x <= -1.45e-296:
		tmp = t_2
	elif x <= 4.8e-222:
		tmp = t_1
	elif x <= 96.0:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif (x <= 1.04e+133) or not (x <= 6.6e+196):
		tmp = t_3
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	t_3 = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (x <= -2.75e+264)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -1.6e+27)
		tmp = t_3;
	elseif (x <= -1.6e-129)
		tmp = t_2;
	elseif (x <= -1.3e-203)
		tmp = t_1;
	elseif (x <= -1.45e-296)
		tmp = t_2;
	elseif (x <= 4.8e-222)
		tmp = t_1;
	elseif (x <= 96.0)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif ((x <= 1.04e+133) || !(x <= 6.6e+196))
		tmp = t_3;
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	t_3 = y1 * (a * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (x <= -2.75e+264)
		tmp = i * (j * (x * y1));
	elseif (x <= -1.6e+27)
		tmp = t_3;
	elseif (x <= -1.6e-129)
		tmp = t_2;
	elseif (x <= -1.3e-203)
		tmp = t_1;
	elseif (x <= -1.45e-296)
		tmp = t_2;
	elseif (x <= 4.8e-222)
		tmp = t_1;
	elseif (x <= 96.0)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif ((x <= 1.04e+133) || ~((x <= 6.6e+196)))
		tmp = t_3;
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.75e+264], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e+27], t$95$3, If[LessEqual[x, -1.6e-129], t$95$2, If[LessEqual[x, -1.3e-203], t$95$1, If[LessEqual[x, -1.45e-296], t$95$2, If[LessEqual[x, 4.8e-222], t$95$1, If[LessEqual[x, 96.0], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.04e+133], N[Not[LessEqual[x, 6.6e+196]], $MachinePrecision]], t$95$3, N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.7499999999999999e264

   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 12.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 87.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 87.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 87.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 87.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 87.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 100.0%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 100.0%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 100.0%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 100.0%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 100.0%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 100.0%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 100.0%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 100.0%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 100.0%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 100.0%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 100.0%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -2.7499999999999999e264 < x < -1.60000000000000008e27 or 96 < x < 1.04e133 or 6.6000000000000003e196 < x

   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 30.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 44.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 44.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in a around inf 58.3%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 54.6%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. *-commutative 54.6%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z - x \cdot y2\right) \]

      3. associate-*r* 58.2%

         \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      4. *-commutative 58.2%

         \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot z - \color{blue}{y2 \cdot x}\right)\right) \]

   9. Simplified 58.2%

      \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - y2 \cdot x\right)\right)} \]

   if -1.60000000000000008e27 < x < -1.6000000000000001e-129 or -1.29999999999999988e-203 < x < -1.44999999999999991e-296

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 47.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 47.0%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 47.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 47.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in a around -inf 45.8%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.8%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right) \cdot a} \]

      2. associate-*l* 43.7%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right) \cdot a\right)} \]

      3. *-commutative 43.7%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]

      4. +-commutative 43.7%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      5. mul-1-neg 43.7%

         \[\leadsto t \cdot \left(a \cdot \left(y5 \cdot y2 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      6. unsub-neg 43.7%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 - b \cdot z\right)}\right) \]

   9. Simplified 43.7%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(y5 \cdot y2 - b \cdot z\right)\right)} \]

   if -1.6000000000000001e-129 < x < -1.29999999999999988e-203 or -1.44999999999999991e-296 < x < 4.79999999999999986e-222

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.2%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 69.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]

   if 4.79999999999999986e-222 < x < 96

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 41.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 41.5%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 41.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 1.04e133 < x < 6.6000000000000003e196

   1. Initial program 7.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 7.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 21.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 21.4%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 21.4%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 21.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 57.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+264}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-129}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-222}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 96:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.04 \cdot 10^{+133} \lor \neg \left(x \leq 6.6 \cdot 10^{+196}\right):\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 17: 28.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ t_3 := y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+266}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 30000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+131} \lor \neg \left(x \leq 6.6 \cdot 10^{+196}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b)))))
        (t_3 (* y1 (* a (- (* z y3) (* x y2))))))
   (if (<= x -3.8e+266)
     (* i (* j (* x y1)))
     (if (<= x -1.55e+27)
       t_3
       (if (<= x -5.7e-126)
         t_2
         (if (<= x -8.5e-204)
           t_1
           (if (<= x -4e-299)
             t_2
             (if (<= x 2.7e-225)
               t_1
               (if (<= x 30000.0)
                 (* c (* y4 (- (* y y3) (* t y2))))
                 (if (or (<= x 2.5e+131) (not (<= x 6.6e+196)))
                   t_3
                   (* (* k y0) (- (* z b) (* y2 y5)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -3.8e+266) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.55e+27) {
		tmp = t_3;
	} else if (x <= -5.7e-126) {
		tmp = t_2;
	} else if (x <= -8.5e-204) {
		tmp = t_1;
	} else if (x <= -4e-299) {
		tmp = t_2;
	} else if (x <= 2.7e-225) {
		tmp = t_1;
	} else if (x <= 30000.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if ((x <= 2.5e+131) || !(x <= 6.6e+196)) {
		tmp = t_3;
	} else {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    t_3 = y1 * (a * ((z * y3) - (x * y2)))
    if (x <= (-3.8d+266)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-1.55d+27)) then
        tmp = t_3
    else if (x <= (-5.7d-126)) then
        tmp = t_2
    else if (x <= (-8.5d-204)) then
        tmp = t_1
    else if (x <= (-4d-299)) then
        tmp = t_2
    else if (x <= 2.7d-225) then
        tmp = t_1
    else if (x <= 30000.0d0) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if ((x <= 2.5d+131) .or. (.not. (x <= 6.6d+196))) then
        tmp = t_3
    else
        tmp = (k * y0) * ((z * b) - (y2 * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double t_3 = y1 * (a * ((z * y3) - (x * y2)));
	double tmp;
	if (x <= -3.8e+266) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.55e+27) {
		tmp = t_3;
	} else if (x <= -5.7e-126) {
		tmp = t_2;
	} else if (x <= -8.5e-204) {
		tmp = t_1;
	} else if (x <= -4e-299) {
		tmp = t_2;
	} else if (x <= 2.7e-225) {
		tmp = t_1;
	} else if (x <= 30000.0) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if ((x <= 2.5e+131) || !(x <= 6.6e+196)) {
		tmp = t_3;
	} else {
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	t_3 = y1 * (a * ((z * y3) - (x * y2)))
	tmp = 0
	if x <= -3.8e+266:
		tmp = i * (j * (x * y1))
	elif x <= -1.55e+27:
		tmp = t_3
	elif x <= -5.7e-126:
		tmp = t_2
	elif x <= -8.5e-204:
		tmp = t_1
	elif x <= -4e-299:
		tmp = t_2
	elif x <= 2.7e-225:
		tmp = t_1
	elif x <= 30000.0:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif (x <= 2.5e+131) or not (x <= 6.6e+196):
		tmp = t_3
	else:
		tmp = (k * y0) * ((z * b) - (y2 * 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(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	t_3 = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))))
	tmp = 0.0
	if (x <= -3.8e+266)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -1.55e+27)
		tmp = t_3;
	elseif (x <= -5.7e-126)
		tmp = t_2;
	elseif (x <= -8.5e-204)
		tmp = t_1;
	elseif (x <= -4e-299)
		tmp = t_2;
	elseif (x <= 2.7e-225)
		tmp = t_1;
	elseif (x <= 30000.0)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif ((x <= 2.5e+131) || !(x <= 6.6e+196))
		tmp = t_3;
	else
		tmp = Float64(Float64(k * y0) * Float64(Float64(z * b) - Float64(y2 * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	t_3 = y1 * (a * ((z * y3) - (x * y2)));
	tmp = 0.0;
	if (x <= -3.8e+266)
		tmp = i * (j * (x * y1));
	elseif (x <= -1.55e+27)
		tmp = t_3;
	elseif (x <= -5.7e-126)
		tmp = t_2;
	elseif (x <= -8.5e-204)
		tmp = t_1;
	elseif (x <= -4e-299)
		tmp = t_2;
	elseif (x <= 2.7e-225)
		tmp = t_1;
	elseif (x <= 30000.0)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif ((x <= 2.5e+131) || ~((x <= 6.6e+196)))
		tmp = t_3;
	else
		tmp = (k * y0) * ((z * b) - (y2 * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+266], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e+27], t$95$3, If[LessEqual[x, -5.7e-126], t$95$2, If[LessEqual[x, -8.5e-204], t$95$1, If[LessEqual[x, -4e-299], t$95$2, If[LessEqual[x, 2.7e-225], t$95$1, If[LessEqual[x, 30000.0], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.5e+131], N[Not[LessEqual[x, 6.6e+196]], $MachinePrecision]], t$95$3, N[(N[(k * y0), $MachinePrecision] * N[(N[(z * b), $MachinePrecision] - N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.7999999999999997e266

   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 12.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 87.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 87.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 87.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 87.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 87.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 100.0%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 100.0%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 100.0%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 100.0%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 100.0%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 100.0%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 100.0%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 100.0%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 100.0%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 100.0%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 100.0%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -3.7999999999999997e266 < x < -1.54999999999999998e27 or 3e4 < x < 2.49999999999999998e131 or 6.6000000000000003e196 < x

   1. Initial program 23.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 43.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 43.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 43.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in a around inf 58.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.1%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. *-commutative 55.1%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z - x \cdot y2\right) \]

      3. associate-*r* 58.7%

         \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      4. *-commutative 58.7%

         \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot z - \color{blue}{y2 \cdot x}\right)\right) \]

   9. Simplified 58.7%

      \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - y2 \cdot x\right)\right)} \]

   if -1.54999999999999998e27 < x < -5.69999999999999979e-126 or -8.4999999999999997e-204 < x < -3.99999999999999997e-299

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 47.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 47.0%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 47.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 47.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in a around -inf 45.8%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.8%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right) \cdot a} \]

      2. associate-*l* 43.7%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right) \cdot a\right)} \]

      3. *-commutative 43.7%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]

      4. +-commutative 43.7%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      5. mul-1-neg 43.7%

         \[\leadsto t \cdot \left(a \cdot \left(y5 \cdot y2 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      6. unsub-neg 43.7%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 - b \cdot z\right)}\right) \]

   9. Simplified 43.7%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(y5 \cdot y2 - b \cdot z\right)\right)} \]

   if -5.69999999999999979e-126 < x < -8.4999999999999997e-204 or -3.99999999999999997e-299 < x < 2.69999999999999992e-225

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.2%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 69.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]

   if 2.69999999999999992e-225 < x < 3e4

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 47.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 41.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 41.5%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 41.5%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 2.49999999999999998e131 < x < 6.6000000000000003e196

   1. Initial program 6.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 6.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 27.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.3%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 27.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in k around -inf 54.4%

      \[\leadsto \color{blue}{k \cdot \left(y0 \cdot \left(z \cdot b + -1 \cdot \left(y5 \cdot y2\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 54.4%

         \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(z \cdot b + -1 \cdot \left(y5 \cdot y2\right)\right)} \]

      2. mul-1-neg 54.4%

         \[\leadsto \left(k \cdot y0\right) \cdot \left(z \cdot b + \color{blue}{\left(-y5 \cdot y2\right)}\right) \]

      3. unsub-neg 54.4%

         \[\leadsto \left(k \cdot y0\right) \cdot \color{blue}{\left(z \cdot b - y5 \cdot y2\right)} \]

      4. *-commutative 54.4%

         \[\leadsto \left(k \cdot y0\right) \cdot \left(z \cdot b - \color{blue}{y2 \cdot y5}\right) \]

   9. Simplified 54.4%

      \[\leadsto \color{blue}{\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+266}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-204}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-225}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 30000:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+131} \lor \neg \left(x \leq 6.6 \cdot 10^{+196}\right):\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot y0\right) \cdot \left(z \cdot b - y2 \cdot y5\right)\\ \end{array} \]

Alternative 18: 28.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ t_3 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+215}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-295}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-131}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2)))))
        (t_2 (* k (* y4 (- (* y1 y2) (* y b)))))
        (t_3 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= x -1.2e+215)
     (* i (* j (* x y1)))
     (if (<= x -2.1e+27)
       (* y1 (* a (* x (- y2))))
       (if (<= x -8.5e-156)
         t_3
         (if (<= x -1.85e-203)
           t_2
           (if (<= x 1.3e-295)
             t_3
             (if (<= x 3.75e-193)
               t_1
               (if (<= x 2.6e-136)
                 t_2
                 (if (<= x 8.5e-131)
                   (* y4 (* j (* y1 (- y3))))
                   (if (<= x 2.5e+162)
                     t_1
                     (* b (* j (- (* t y4) (* x y0)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = k * (y4 * ((y1 * y2) - (y * b)));
	double t_3 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (x <= -1.2e+215) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.1e+27) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -8.5e-156) {
		tmp = t_3;
	} else if (x <= -1.85e-203) {
		tmp = t_2;
	} else if (x <= 1.3e-295) {
		tmp = t_3;
	} else if (x <= 3.75e-193) {
		tmp = t_1;
	} else if (x <= 2.6e-136) {
		tmp = t_2;
	} else if (x <= 8.5e-131) {
		tmp = y4 * (j * (y1 * -y3));
	} else if (x <= 2.5e+162) {
		tmp = t_1;
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    t_2 = k * (y4 * ((y1 * y2) - (y * b)))
    t_3 = t * (a * ((y2 * y5) - (z * b)))
    if (x <= (-1.2d+215)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-2.1d+27)) then
        tmp = y1 * (a * (x * -y2))
    else if (x <= (-8.5d-156)) then
        tmp = t_3
    else if (x <= (-1.85d-203)) then
        tmp = t_2
    else if (x <= 1.3d-295) then
        tmp = t_3
    else if (x <= 3.75d-193) then
        tmp = t_1
    else if (x <= 2.6d-136) then
        tmp = t_2
    else if (x <= 8.5d-131) then
        tmp = y4 * (j * (y1 * -y3))
    else if (x <= 2.5d+162) then
        tmp = t_1
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = k * (y4 * ((y1 * y2) - (y * b)));
	double t_3 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (x <= -1.2e+215) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.1e+27) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -8.5e-156) {
		tmp = t_3;
	} else if (x <= -1.85e-203) {
		tmp = t_2;
	} else if (x <= 1.3e-295) {
		tmp = t_3;
	} else if (x <= 3.75e-193) {
		tmp = t_1;
	} else if (x <= 2.6e-136) {
		tmp = t_2;
	} else if (x <= 8.5e-131) {
		tmp = y4 * (j * (y1 * -y3));
	} else if (x <= 2.5e+162) {
		tmp = t_1;
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	t_2 = k * (y4 * ((y1 * y2) - (y * b)))
	t_3 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if x <= -1.2e+215:
		tmp = i * (j * (x * y1))
	elif x <= -2.1e+27:
		tmp = y1 * (a * (x * -y2))
	elif x <= -8.5e-156:
		tmp = t_3
	elif x <= -1.85e-203:
		tmp = t_2
	elif x <= 1.3e-295:
		tmp = t_3
	elif x <= 3.75e-193:
		tmp = t_1
	elif x <= 2.6e-136:
		tmp = t_2
	elif x <= 8.5e-131:
		tmp = y4 * (j * (y1 * -y3))
	elif x <= 2.5e+162:
		tmp = t_1
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))))
	t_3 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (x <= -1.2e+215)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -2.1e+27)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (x <= -8.5e-156)
		tmp = t_3;
	elseif (x <= -1.85e-203)
		tmp = t_2;
	elseif (x <= 1.3e-295)
		tmp = t_3;
	elseif (x <= 3.75e-193)
		tmp = t_1;
	elseif (x <= 2.6e-136)
		tmp = t_2;
	elseif (x <= 8.5e-131)
		tmp = Float64(y4 * Float64(j * Float64(y1 * Float64(-y3))));
	elseif (x <= 2.5e+162)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	t_2 = k * (y4 * ((y1 * y2) - (y * b)));
	t_3 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (x <= -1.2e+215)
		tmp = i * (j * (x * y1));
	elseif (x <= -2.1e+27)
		tmp = y1 * (a * (x * -y2));
	elseif (x <= -8.5e-156)
		tmp = t_3;
	elseif (x <= -1.85e-203)
		tmp = t_2;
	elseif (x <= 1.3e-295)
		tmp = t_3;
	elseif (x <= 3.75e-193)
		tmp = t_1;
	elseif (x <= 2.6e-136)
		tmp = t_2;
	elseif (x <= 8.5e-131)
		tmp = y4 * (j * (y1 * -y3));
	elseif (x <= 2.5e+162)
		tmp = t_1;
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+215], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e+27], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-156], t$95$3, If[LessEqual[x, -1.85e-203], t$95$2, If[LessEqual[x, 1.3e-295], t$95$3, If[LessEqual[x, 3.75e-193], t$95$1, If[LessEqual[x, 2.6e-136], t$95$2, If[LessEqual[x, 8.5e-131], N[(y4 * N[(j * N[(y1 * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+162], t$95$1, N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.2e215

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 55.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 55.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 55.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 67.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 67.4%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 67.4%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 67.4%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 56.3%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 56.3%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 56.2%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 56.2%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 61.6%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 61.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 61.6%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 67.0%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 67.0%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.2e215 < x < -2.09999999999999995e27

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 55.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 55.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 55.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 57.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in x around inf 55.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)\right)} \cdot y1 \]
   9. Step-by-step derivation

      1. mul-1-neg 55.7%

         \[\leadsto \color{blue}{\left(-a \cdot \left(y2 \cdot x\right)\right)} \cdot y1 \]

      2. *-commutative 55.7%

         \[\leadsto \left(-\color{blue}{\left(y2 \cdot x\right) \cdot a}\right) \cdot y1 \]

      3. distribute-rgt-neg-in 55.7%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot x\right) \cdot \left(-a\right)\right)} \cdot y1 \]

      4. *-commutative 55.7%

         \[\leadsto \left(\color{blue}{\left(x \cdot y2\right)} \cdot \left(-a\right)\right) \cdot y1 \]

   10. Simplified 55.7%

       \[\leadsto \color{blue}{\left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)} \cdot y1 \]

   if -2.09999999999999995e27 < x < -8.5e-156 or -1.85000000000000001e-203 < x < 1.29999999999999993e-295

   1. Initial program 30.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 46.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 46.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 46.8%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 46.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in a around -inf 42.4%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right) \cdot a} \]

      2. associate-*l* 40.6%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right) \cdot a\right)} \]

      3. *-commutative 40.6%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]

      4. +-commutative 40.6%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      5. mul-1-neg 40.6%

         \[\leadsto t \cdot \left(a \cdot \left(y5 \cdot y2 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      6. unsub-neg 40.6%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 - b \cdot z\right)}\right) \]

   9. Simplified 40.6%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(y5 \cdot y2 - b \cdot z\right)\right)} \]

   if -8.5e-156 < x < -1.85000000000000001e-203 or 3.7499999999999999e-193 < x < 2.59999999999999997e-136

   1. Initial program 30.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 35.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 58.6%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 58.6%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 58.6%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 58.6%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

   7. Simplified 58.6%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]

   if 1.29999999999999993e-295 < x < 3.7499999999999999e-193 or 8.50000000000000013e-131 < x < 2.4999999999999998e162

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 47.9%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 47.9%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 47.9%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 2.59999999999999997e-136 < x < 8.50000000000000013e-131

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 80.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 80.3%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 80.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 80.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 80.3%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 80.4%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in j around inf 80.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 80.4%

         \[\leadsto \color{blue}{-y4 \cdot \left(y1 \cdot \left(y3 \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 80.4%

         \[\leadsto \color{blue}{y4 \cdot \left(-y1 \cdot \left(y3 \cdot j\right)\right)} \]

      3. associate-*r* 80.4%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(y1 \cdot y3\right) \cdot j}\right) \]

      4. distribute-rgt-neg-in 80.4%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot \left(-j\right)\right)} \]

      5. *-commutative 80.4%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot \left(-j\right)\right) \]

   10. Simplified 80.4%

       \[\leadsto \color{blue}{y4 \cdot \left(\left(y3 \cdot y1\right) \cdot \left(-j\right)\right)} \]

   if 2.4999999999999998e162 < x

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 38.7%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+215}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-156}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-203}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-193}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-136}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-131}:\\ \;\;\;\;y4 \cdot \left(j \cdot \left(y1 \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 19: 27.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ t_3 := \left(-a\right) \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{if}\;y1 \leq -6.2 \cdot 10^{+255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq -9.5 \cdot 10^{+193}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y1 \leq -6.4 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-184}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y1 \leq 3.3 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2)))))
        (t_2 (* b (* j (- (* t y4) (* x y0)))))
        (t_3 (* (- a) (* x (* y1 y2)))))
   (if (<= y1 -6.2e+255)
     t_2
     (if (<= y1 -9.5e+193)
       (* y1 (* y2 (* k y4)))
       (if (<= y1 -7.2e+77)
         t_3
         (if (<= y1 -6.4e-25)
           t_1
           (if (<= y1 -5.2e-184)
             (* (* y a) (* x b))
             (if (<= y1 3.3e-94)
               t_1
               (if (<= y1 4.4e-44) t_2 (if (<= y1 3.7e+112) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double t_3 = -a * (x * (y1 * y2));
	double tmp;
	if (y1 <= -6.2e+255) {
		tmp = t_2;
	} else if (y1 <= -9.5e+193) {
		tmp = y1 * (y2 * (k * y4));
	} else if (y1 <= -7.2e+77) {
		tmp = t_3;
	} else if (y1 <= -6.4e-25) {
		tmp = t_1;
	} else if (y1 <= -5.2e-184) {
		tmp = (y * a) * (x * b);
	} else if (y1 <= 3.3e-94) {
		tmp = t_1;
	} else if (y1 <= 4.4e-44) {
		tmp = t_2;
	} else if (y1 <= 3.7e+112) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    t_2 = b * (j * ((t * y4) - (x * y0)))
    t_3 = -a * (x * (y1 * y2))
    if (y1 <= (-6.2d+255)) then
        tmp = t_2
    else if (y1 <= (-9.5d+193)) then
        tmp = y1 * (y2 * (k * y4))
    else if (y1 <= (-7.2d+77)) then
        tmp = t_3
    else if (y1 <= (-6.4d-25)) then
        tmp = t_1
    else if (y1 <= (-5.2d-184)) then
        tmp = (y * a) * (x * b)
    else if (y1 <= 3.3d-94) then
        tmp = t_1
    else if (y1 <= 4.4d-44) then
        tmp = t_2
    else if (y1 <= 3.7d+112) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = b * (j * ((t * y4) - (x * y0)));
	double t_3 = -a * (x * (y1 * y2));
	double tmp;
	if (y1 <= -6.2e+255) {
		tmp = t_2;
	} else if (y1 <= -9.5e+193) {
		tmp = y1 * (y2 * (k * y4));
	} else if (y1 <= -7.2e+77) {
		tmp = t_3;
	} else if (y1 <= -6.4e-25) {
		tmp = t_1;
	} else if (y1 <= -5.2e-184) {
		tmp = (y * a) * (x * b);
	} else if (y1 <= 3.3e-94) {
		tmp = t_1;
	} else if (y1 <= 4.4e-44) {
		tmp = t_2;
	} else if (y1 <= 3.7e+112) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	t_2 = b * (j * ((t * y4) - (x * y0)))
	t_3 = -a * (x * (y1 * y2))
	tmp = 0
	if y1 <= -6.2e+255:
		tmp = t_2
	elif y1 <= -9.5e+193:
		tmp = y1 * (y2 * (k * y4))
	elif y1 <= -7.2e+77:
		tmp = t_3
	elif y1 <= -6.4e-25:
		tmp = t_1
	elif y1 <= -5.2e-184:
		tmp = (y * a) * (x * b)
	elif y1 <= 3.3e-94:
		tmp = t_1
	elif y1 <= 4.4e-44:
		tmp = t_2
	elif y1 <= 3.7e+112:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	t_3 = Float64(Float64(-a) * Float64(x * Float64(y1 * y2)))
	tmp = 0.0
	if (y1 <= -6.2e+255)
		tmp = t_2;
	elseif (y1 <= -9.5e+193)
		tmp = Float64(y1 * Float64(y2 * Float64(k * y4)));
	elseif (y1 <= -7.2e+77)
		tmp = t_3;
	elseif (y1 <= -6.4e-25)
		tmp = t_1;
	elseif (y1 <= -5.2e-184)
		tmp = Float64(Float64(y * a) * Float64(x * b));
	elseif (y1 <= 3.3e-94)
		tmp = t_1;
	elseif (y1 <= 4.4e-44)
		tmp = t_2;
	elseif (y1 <= 3.7e+112)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	t_2 = b * (j * ((t * y4) - (x * y0)));
	t_3 = -a * (x * (y1 * y2));
	tmp = 0.0;
	if (y1 <= -6.2e+255)
		tmp = t_2;
	elseif (y1 <= -9.5e+193)
		tmp = y1 * (y2 * (k * y4));
	elseif (y1 <= -7.2e+77)
		tmp = t_3;
	elseif (y1 <= -6.4e-25)
		tmp = t_1;
	elseif (y1 <= -5.2e-184)
		tmp = (y * a) * (x * b);
	elseif (y1 <= 3.3e-94)
		tmp = t_1;
	elseif (y1 <= 4.4e-44)
		tmp = t_2;
	elseif (y1 <= 3.7e+112)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-a) * N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -6.2e+255], t$95$2, If[LessEqual[y1, -9.5e+193], N[(y1 * N[(y2 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -7.2e+77], t$95$3, If[LessEqual[y1, -6.4e-25], t$95$1, If[LessEqual[y1, -5.2e-184], N[(N[(y * a), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.3e-94], t$95$1, If[LessEqual[y1, 4.4e-44], t$95$2, If[LessEqual[y1, 3.7e+112], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -6.2000000000000004e255 or 3.3000000000000001e-94 < y1 < 4.40000000000000024e-44

   1. Initial program 25.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 33.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.5%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 33.5%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 33.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 63.4%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]

   if -6.2000000000000004e255 < y1 < -9.4999999999999997e193

   1. Initial program 12.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 62.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 62.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 62.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 56.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in k around inf 63.2%

      \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y2\right)\right)} \cdot y1 \]
   9. Step-by-step derivation

      1. associate-*r* 63.3%

         \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y2\right)} \cdot y1 \]

      2. *-commutative 63.3%

         \[\leadsto \left(\color{blue}{\left(y4 \cdot k\right)} \cdot y2\right) \cdot y1 \]

   10. Simplified 63.3%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot k\right) \cdot y2\right)} \cdot y1 \]

   if -9.4999999999999997e193 < y1 < -7.1999999999999996e77 or 3.70000000000000004e112 < y1

   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 28.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 53.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 53.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 53.4%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 54.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in x around inf 42.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 42.4%

         \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]

      2. *-commutative 42.4%

         \[\leadsto -y1 \cdot \left(a \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

      3. *-commutative 42.4%

         \[\leadsto -y1 \cdot \color{blue}{\left(\left(y2 \cdot x\right) \cdot a\right)} \]

      4. associate-*r* 43.8%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(y2 \cdot x\right)\right) \cdot a} \]

      5. distribute-rgt-neg-in 43.8%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(y2 \cdot x\right)\right) \cdot \left(-a\right)} \]

      6. *-commutative 43.8%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot x\right) \cdot y1\right)} \cdot \left(-a\right) \]

      7. *-commutative 43.8%

         \[\leadsto \left(\color{blue}{\left(x \cdot y2\right)} \cdot y1\right) \cdot \left(-a\right) \]

      8. associate-*l* 49.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y2 \cdot y1\right)\right)} \cdot \left(-a\right) \]

   10. Simplified 49.3%

       \[\leadsto \color{blue}{\left(x \cdot \left(y2 \cdot y1\right)\right) \cdot \left(-a\right)} \]

   if -7.1999999999999996e77 < y1 < -6.4000000000000002e-25 or -5.19999999999999957e-184 < y1 < 3.3000000000000001e-94 or 4.40000000000000024e-44 < y1 < 3.70000000000000004e112

   1. Initial program 29.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 41.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 41.6%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 41.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if -6.4000000000000002e-25 < y1 < -5.19999999999999957e-184

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 51.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 51.9%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 51.9%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 49.0%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in a around inf 42.5%

      \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(b \cdot x\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -6.2 \cdot 10^{+255}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq -9.5 \cdot 10^{+193}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;y1 \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -6.4 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq -5.2 \cdot 10^{-184}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y1 \leq 3.3 \cdot 10^{-94}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]

Alternative 20: 30.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{if}\;y0 \leq -1.75 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{+184}:\\ \;\;\;\;\left(c \cdot y2 - b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;y0 \leq -9 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{-117}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.04 \cdot 10^{-129}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y0 \leq 6.6 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.1 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y3) (- (* j y5) (* z c)))))
   (if (<= y0 -1.75e+241)
     t_1
     (if (<= y0 -4e+184)
       (* (- (* c y2) (* b j)) (* x y0))
       (if (<= y0 -9e+48)
         t_1
         (if (<= y0 -1.2e-117)
           (* y1 (* a (- (* z y3) (* x y2))))
           (if (<= y0 1.04e-129)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= y0 4.4e-51)
               (* (- (* y a) (* j y0)) (* x b))
               (if (<= y0 6.6e+21)
                 (* a (* y2 (- (* t y5) (* x y1))))
                 (if (<= y0 5.1e+151)
                   (* x (* y1 (- (* i j) (* a y2))))
                   (* y0 (* y5 (- (* j y3) (* k y2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (y0 <= -1.75e+241) {
		tmp = t_1;
	} else if (y0 <= -4e+184) {
		tmp = ((c * y2) - (b * j)) * (x * y0);
	} else if (y0 <= -9e+48) {
		tmp = t_1;
	} else if (y0 <= -1.2e-117) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 1.04e-129) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y0 <= 4.4e-51) {
		tmp = ((y * a) - (j * y0)) * (x * b);
	} else if (y0 <= 6.6e+21) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 5.1e+151) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y0 * y3) * ((j * y5) - (z * c))
    if (y0 <= (-1.75d+241)) then
        tmp = t_1
    else if (y0 <= (-4d+184)) then
        tmp = ((c * y2) - (b * j)) * (x * y0)
    else if (y0 <= (-9d+48)) then
        tmp = t_1
    else if (y0 <= (-1.2d-117)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y0 <= 1.04d-129) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y0 <= 4.4d-51) then
        tmp = ((y * a) - (j * y0)) * (x * b)
    else if (y0 <= 6.6d+21) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (y0 <= 5.1d+151) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (y0 <= -1.75e+241) {
		tmp = t_1;
	} else if (y0 <= -4e+184) {
		tmp = ((c * y2) - (b * j)) * (x * y0);
	} else if (y0 <= -9e+48) {
		tmp = t_1;
	} else if (y0 <= -1.2e-117) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 1.04e-129) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y0 <= 4.4e-51) {
		tmp = ((y * a) - (j * y0)) * (x * b);
	} else if (y0 <= 6.6e+21) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 5.1e+151) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y3) * ((j * y5) - (z * c))
	tmp = 0
	if y0 <= -1.75e+241:
		tmp = t_1
	elif y0 <= -4e+184:
		tmp = ((c * y2) - (b * j)) * (x * y0)
	elif y0 <= -9e+48:
		tmp = t_1
	elif y0 <= -1.2e-117:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y0 <= 1.04e-129:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y0 <= 4.4e-51:
		tmp = ((y * a) - (j * y0)) * (x * b)
	elif y0 <= 6.6e+21:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif y0 <= 5.1e+151:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)))
	tmp = 0.0
	if (y0 <= -1.75e+241)
		tmp = t_1;
	elseif (y0 <= -4e+184)
		tmp = Float64(Float64(Float64(c * y2) - Float64(b * j)) * Float64(x * y0));
	elseif (y0 <= -9e+48)
		tmp = t_1;
	elseif (y0 <= -1.2e-117)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y0 <= 1.04e-129)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y0 <= 4.4e-51)
		tmp = Float64(Float64(Float64(y * a) - Float64(j * y0)) * Float64(x * b));
	elseif (y0 <= 6.6e+21)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y0 <= 5.1e+151)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y3) * ((j * y5) - (z * c));
	tmp = 0.0;
	if (y0 <= -1.75e+241)
		tmp = t_1;
	elseif (y0 <= -4e+184)
		tmp = ((c * y2) - (b * j)) * (x * y0);
	elseif (y0 <= -9e+48)
		tmp = t_1;
	elseif (y0 <= -1.2e-117)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y0 <= 1.04e-129)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y0 <= 4.4e-51)
		tmp = ((y * a) - (j * y0)) * (x * b);
	elseif (y0 <= 6.6e+21)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (y0 <= 5.1e+151)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	else
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.75e+241], t$95$1, If[LessEqual[y0, -4e+184], N[(N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision] * N[(x * y0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -9e+48], t$95$1, If[LessEqual[y0, -1.2e-117], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.04e-129], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.4e-51], N[(N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.6e+21], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.1e+151], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -1.75e241 or -4.00000000000000007e184 < y0 < -8.99999999999999991e48

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.3%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y3 around inf 65.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot \left(y0 \cdot y3\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 65.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \cdot \left(y0 \cdot y3\right) \]

      2. associate-*r* 65.3%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\right)} \]

      3. mul-1-neg 65.3%

         \[\leadsto \color{blue}{-\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)} \]

      4. *-commutative 65.3%

         \[\leadsto -\color{blue}{\left(y0 \cdot y3\right) \cdot \left(c \cdot z - j \cdot y5\right)} \]

      5. *-commutative 65.3%

         \[\leadsto -\color{blue}{\left(y3 \cdot y0\right)} \cdot \left(c \cdot z - j \cdot y5\right) \]

      6. *-commutative 65.3%

         \[\leadsto -\left(y3 \cdot y0\right) \cdot \left(\color{blue}{z \cdot c} - j \cdot y5\right) \]

   9. Simplified 65.3%

      \[\leadsto \color{blue}{-\left(y3 \cdot y0\right) \cdot \left(z \cdot c - j \cdot y5\right)} \]

   if -1.75e241 < y0 < -4.00000000000000007e184

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.5%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in x around inf 60.8%

      \[\leadsto \color{blue}{\left(c \cdot y2 - b \cdot j\right) \cdot \left(y0 \cdot x\right)} \]

   if -8.99999999999999991e48 < y0 < -1.20000000000000007e-117

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in a around inf 53.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. *-commutative 50.7%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z - x \cdot y2\right) \]

      3. associate-*r* 53.2%

         \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      4. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot z - \color{blue}{y2 \cdot x}\right)\right) \]

   9. Simplified 53.2%

      \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - y2 \cdot x\right)\right)} \]

   if -1.20000000000000007e-117 < y0 < 1.04e-129

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 41.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.8%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 41.8%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 41.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 1.04e-129 < y0 < 4.4e-51

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 54.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 31.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 31.5%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 31.5%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 31.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 47.3%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   if 4.4e-51 < y0 < 6.6e21

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 56.3%

      \[\leadsto \color{blue}{\left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \cdot a \]

   if 6.6e21 < y0 < 5.09999999999999996e151

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 45.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 45.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 45.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 45.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 60.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 60.6%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 60.6%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 60.6%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   if 5.09999999999999996e151 < y0

   1. Initial program 9.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 9.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 64.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.75 \cdot 10^{+241}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -4 \cdot 10^{+184}:\\ \;\;\;\;\left(c \cdot y2 - b \cdot j\right) \cdot \left(x \cdot y0\right)\\ \mathbf{elif}\;y0 \leq -9 \cdot 10^{+48}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -1.2 \cdot 10^{-117}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.04 \cdot 10^{-129}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y0 \leq 6.6 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.1 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]

Alternative 21: 30.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{if}\;y0 \leq -7.5 \cdot 10^{+240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -6.6 \cdot 10^{+183}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.8 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -1.56 \cdot 10^{-108}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-130}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-53}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y0 \leq 4.6 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* (* y0 y3) (- (* j y5) (* z c)))))
   (if (<= y0 -7.5e+240)
     t_1
     (if (<= y0 -6.6e+183)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= y0 -1.8e+50)
         t_1
         (if (<= y0 -1.56e-108)
           (* y1 (* a (- (* z y3) (* x y2))))
           (if (<= y0 2e-130)
             (* c (* y4 (- (* y y3) (* t y2))))
             (if (<= y0 1.5e-53)
               (* (- (* y a) (* j y0)) (* x b))
               (if (<= y0 4.6e+23)
                 (* a (* y2 (- (* t y5) (* x y1))))
                 (if (<= y0 5.4e+151)
                   (* x (* y1 (- (* i j) (* a y2))))
                   (* y0 (* y5 (- (* j y3) (* k y2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (y0 <= -7.5e+240) {
		tmp = t_1;
	} else if (y0 <= -6.6e+183) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y0 <= -1.8e+50) {
		tmp = t_1;
	} else if (y0 <= -1.56e-108) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 2e-130) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y0 <= 1.5e-53) {
		tmp = ((y * a) - (j * y0)) * (x * b);
	} else if (y0 <= 4.6e+23) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 5.4e+151) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y0 * y3) * ((j * y5) - (z * c))
    if (y0 <= (-7.5d+240)) then
        tmp = t_1
    else if (y0 <= (-6.6d+183)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (y0 <= (-1.8d+50)) then
        tmp = t_1
    else if (y0 <= (-1.56d-108)) then
        tmp = y1 * (a * ((z * y3) - (x * y2)))
    else if (y0 <= 2d-130) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else if (y0 <= 1.5d-53) then
        tmp = ((y * a) - (j * y0)) * (x * b)
    else if (y0 <= 4.6d+23) then
        tmp = a * (y2 * ((t * y5) - (x * y1)))
    else if (y0 <= 5.4d+151) then
        tmp = x * (y1 * ((i * j) - (a * y2)))
    else
        tmp = y0 * (y5 * ((j * y3) - (k * y2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y0 * y3) * ((j * y5) - (z * c));
	double tmp;
	if (y0 <= -7.5e+240) {
		tmp = t_1;
	} else if (y0 <= -6.6e+183) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (y0 <= -1.8e+50) {
		tmp = t_1;
	} else if (y0 <= -1.56e-108) {
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	} else if (y0 <= 2e-130) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else if (y0 <= 1.5e-53) {
		tmp = ((y * a) - (j * y0)) * (x * b);
	} else if (y0 <= 4.6e+23) {
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	} else if (y0 <= 5.4e+151) {
		tmp = x * (y1 * ((i * j) - (a * y2)));
	} else {
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y0 * y3) * ((j * y5) - (z * c))
	tmp = 0
	if y0 <= -7.5e+240:
		tmp = t_1
	elif y0 <= -6.6e+183:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif y0 <= -1.8e+50:
		tmp = t_1
	elif y0 <= -1.56e-108:
		tmp = y1 * (a * ((z * y3) - (x * y2)))
	elif y0 <= 2e-130:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	elif y0 <= 1.5e-53:
		tmp = ((y * a) - (j * y0)) * (x * b)
	elif y0 <= 4.6e+23:
		tmp = a * (y2 * ((t * y5) - (x * y1)))
	elif y0 <= 5.4e+151:
		tmp = x * (y1 * ((i * j) - (a * y2)))
	else:
		tmp = y0 * (y5 * ((j * y3) - (k * y2)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y0 * y3) * Float64(Float64(j * y5) - Float64(z * c)))
	tmp = 0.0
	if (y0 <= -7.5e+240)
		tmp = t_1;
	elseif (y0 <= -6.6e+183)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (y0 <= -1.8e+50)
		tmp = t_1;
	elseif (y0 <= -1.56e-108)
		tmp = Float64(y1 * Float64(a * Float64(Float64(z * y3) - Float64(x * y2))));
	elseif (y0 <= 2e-130)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (y0 <= 1.5e-53)
		tmp = Float64(Float64(Float64(y * a) - Float64(j * y0)) * Float64(x * b));
	elseif (y0 <= 4.6e+23)
		tmp = Float64(a * Float64(y2 * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y0 <= 5.4e+151)
		tmp = Float64(x * Float64(y1 * Float64(Float64(i * j) - Float64(a * y2))));
	else
		tmp = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y0 * y3) * ((j * y5) - (z * c));
	tmp = 0.0;
	if (y0 <= -7.5e+240)
		tmp = t_1;
	elseif (y0 <= -6.6e+183)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (y0 <= -1.8e+50)
		tmp = t_1;
	elseif (y0 <= -1.56e-108)
		tmp = y1 * (a * ((z * y3) - (x * y2)));
	elseif (y0 <= 2e-130)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	elseif (y0 <= 1.5e-53)
		tmp = ((y * a) - (j * y0)) * (x * b);
	elseif (y0 <= 4.6e+23)
		tmp = a * (y2 * ((t * y5) - (x * y1)));
	elseif (y0 <= 5.4e+151)
		tmp = x * (y1 * ((i * j) - (a * y2)));
	else
		tmp = y0 * (y5 * ((j * y3) - (k * y2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y0 * y3), $MachinePrecision] * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -7.5e+240], t$95$1, If[LessEqual[y0, -6.6e+183], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.8e+50], t$95$1, If[LessEqual[y0, -1.56e-108], N[(y1 * N[(a * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2e-130], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.5e-53], N[(N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.6e+23], N[(a * N[(y2 * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.4e+151], N[(x * N[(y1 * N[(N[(i * j), $MachinePrecision] - N[(a * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -7.50000000000000038e240 or -6.60000000000000019e183 < y0 < -1.79999999999999993e50

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 62.3%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 62.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y3 around inf 65.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right) - -1 \cdot \left(j \cdot y5\right)\right) \cdot \left(y0 \cdot y3\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-out-- 65.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z - j \cdot y5\right)\right)} \cdot \left(y0 \cdot y3\right) \]

      2. associate-*r* 65.3%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)\right)} \]

      3. mul-1-neg 65.3%

         \[\leadsto \color{blue}{-\left(c \cdot z - j \cdot y5\right) \cdot \left(y0 \cdot y3\right)} \]

      4. *-commutative 65.3%

         \[\leadsto -\color{blue}{\left(y0 \cdot y3\right) \cdot \left(c \cdot z - j \cdot y5\right)} \]

      5. *-commutative 65.3%

         \[\leadsto -\color{blue}{\left(y3 \cdot y0\right)} \cdot \left(c \cdot z - j \cdot y5\right) \]

      6. *-commutative 65.3%

         \[\leadsto -\left(y3 \cdot y0\right) \cdot \left(\color{blue}{z \cdot c} - j \cdot y5\right) \]

   9. Simplified 65.3%

      \[\leadsto \color{blue}{-\left(y3 \cdot y0\right) \cdot \left(z \cdot c - j \cdot y5\right)} \]

   if -7.50000000000000038e240 < y0 < -6.60000000000000019e183

   1. Initial program 13.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.5%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in x around -inf 60.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right)} \]

      2. neg-mul-1 60.8%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(\left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right) \cdot x\right) \]

      3. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(x \cdot \left(-1 \cdot \left(c \cdot y2\right) - -1 \cdot \left(b \cdot j\right)\right)\right)} \]

      4. distribute-lft-out-- 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \left(c \cdot y2 - b \cdot j\right)\right)}\right) \]

      5. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(c \cdot y2 - \color{blue}{j \cdot b}\right)\right)\right) \]

      6. *-commutative 60.8%

         \[\leadsto \left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(\color{blue}{y2 \cdot c} - j \cdot b\right)\right)\right) \]

   9. Simplified 60.8%

      \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(x \cdot \left(-1 \cdot \left(y2 \cdot c - j \cdot b\right)\right)\right)} \]

   if -1.79999999999999993e50 < y0 < -1.56000000000000009e-108

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in a around inf 53.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto \color{blue}{\left(a \cdot y1\right) \cdot \left(y3 \cdot z - x \cdot y2\right)} \]

      2. *-commutative 50.7%

         \[\leadsto \color{blue}{\left(y1 \cdot a\right)} \cdot \left(y3 \cdot z - x \cdot y2\right) \]

      3. associate-*r* 53.2%

         \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - x \cdot y2\right)\right)} \]

      4. *-commutative 53.2%

         \[\leadsto y1 \cdot \left(a \cdot \left(y3 \cdot z - \color{blue}{y2 \cdot x}\right)\right) \]

   9. Simplified 53.2%

      \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z - y2 \cdot x\right)\right)} \]

   if -1.56000000000000009e-108 < y0 < 2.0000000000000002e-130

   1. Initial program 29.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 45.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 41.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 41.8%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 41.8%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 41.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 2.0000000000000002e-130 < y0 < 1.5000000000000001e-53

   1. Initial program 38.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 54.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 31.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 31.5%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 31.5%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 31.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 47.3%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   if 1.5000000000000001e-53 < y0 < 4.6000000000000001e23

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in a around inf 50.6%

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y \cdot x - t \cdot z\right) + -1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right) \cdot a} \]
   5. Step-by-step derivation

      1. associate--l+ 50.6%

         \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(-1 \cdot \left(y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right)} \cdot a \]

      2. mul-1-neg 50.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\color{blue}{\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right)} - -1 \cdot \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a \]

      3. mul-1-neg 50.6%

         \[\leadsto \left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \color{blue}{\left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)}\right)\right) \cdot a \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{\left(b \cdot \left(y \cdot x - t \cdot z\right) + \left(\left(-y1 \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(-\left(t \cdot y2 - y \cdot y3\right) \cdot y5\right)\right)\right) \cdot a} \]

   7. Taylor expanded in y2 around inf 56.3%

      \[\leadsto \color{blue}{\left(\left(t \cdot y5 - y1 \cdot x\right) \cdot y2\right)} \cdot a \]

   if 4.6000000000000001e23 < y0 < 5.4000000000000003e151

   1. Initial program 20.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 45.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 45.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 45.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 45.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 60.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 60.6%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 60.6%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 60.6%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   if 5.4000000000000003e151 < y0

   1. Initial program 9.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 9.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 64.3%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -7.5 \cdot 10^{+240}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -6.6 \cdot 10^{+183}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -1.8 \cdot 10^{+50}:\\ \;\;\;\;\left(y0 \cdot y3\right) \cdot \left(j \cdot y5 - z \cdot c\right)\\ \mathbf{elif}\;y0 \leq -1.56 \cdot 10^{-108}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(z \cdot y3 - x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 2 \cdot 10^{-130}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq 1.5 \cdot 10^{-53}:\\ \;\;\;\;\left(y \cdot a - j \cdot y0\right) \cdot \left(x \cdot b\right)\\ \mathbf{elif}\;y0 \leq 4.6 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(y2 \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.4 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \end{array} \]

Alternative 22: 27.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+215}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-78}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2)))))
        (t_2 (* k (* y4 (- (* y1 y2) (* y b))))))
   (if (<= x -1.9e+215)
     (* i (* j (* x y1)))
     (if (<= x -1.4e+27)
       (* y1 (* a (* x (- y2))))
       (if (<= x 8.2e-281)
         t_2
         (if (<= x 5e-193)
           t_1
           (if (<= x 1.35e-134)
             t_2
             (if (<= x 1.5e-78)
               (* y4 (* y3 (* y c)))
               (if (<= x 3e+162) t_1 (* b (* j (- (* t y4) (* x y0)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = k * (y4 * ((y1 * y2) - (y * b)));
	double tmp;
	if (x <= -1.9e+215) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.4e+27) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= 8.2e-281) {
		tmp = t_2;
	} else if (x <= 5e-193) {
		tmp = t_1;
	} else if (x <= 1.35e-134) {
		tmp = t_2;
	} else if (x <= 1.5e-78) {
		tmp = y4 * (y3 * (y * c));
	} else if (x <= 3e+162) {
		tmp = t_1;
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (y4 * ((y * y3) - (t * y2)))
    t_2 = k * (y4 * ((y1 * y2) - (y * b)))
    if (x <= (-1.9d+215)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-1.4d+27)) then
        tmp = y1 * (a * (x * -y2))
    else if (x <= 8.2d-281) then
        tmp = t_2
    else if (x <= 5d-193) then
        tmp = t_1
    else if (x <= 1.35d-134) then
        tmp = t_2
    else if (x <= 1.5d-78) then
        tmp = y4 * (y3 * (y * c))
    else if (x <= 3d+162) then
        tmp = t_1
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * (y4 * ((y * y3) - (t * y2)));
	double t_2 = k * (y4 * ((y1 * y2) - (y * b)));
	double tmp;
	if (x <= -1.9e+215) {
		tmp = i * (j * (x * y1));
	} else if (x <= -1.4e+27) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= 8.2e-281) {
		tmp = t_2;
	} else if (x <= 5e-193) {
		tmp = t_1;
	} else if (x <= 1.35e-134) {
		tmp = t_2;
	} else if (x <= 1.5e-78) {
		tmp = y4 * (y3 * (y * c));
	} else if (x <= 3e+162) {
		tmp = t_1;
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * (y4 * ((y * y3) - (t * y2)))
	t_2 = k * (y4 * ((y1 * y2) - (y * b)))
	tmp = 0
	if x <= -1.9e+215:
		tmp = i * (j * (x * y1))
	elif x <= -1.4e+27:
		tmp = y1 * (a * (x * -y2))
	elif x <= 8.2e-281:
		tmp = t_2
	elif x <= 5e-193:
		tmp = t_1
	elif x <= 1.35e-134:
		tmp = t_2
	elif x <= 1.5e-78:
		tmp = y4 * (y3 * (y * c))
	elif x <= 3e+162:
		tmp = t_1
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(k * Float64(y4 * Float64(Float64(y1 * y2) - Float64(y * b))))
	tmp = 0.0
	if (x <= -1.9e+215)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -1.4e+27)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (x <= 8.2e-281)
		tmp = t_2;
	elseif (x <= 5e-193)
		tmp = t_1;
	elseif (x <= 1.35e-134)
		tmp = t_2;
	elseif (x <= 1.5e-78)
		tmp = Float64(y4 * Float64(y3 * Float64(y * c)));
	elseif (x <= 3e+162)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * (y4 * ((y * y3) - (t * y2)));
	t_2 = k * (y4 * ((y1 * y2) - (y * b)));
	tmp = 0.0;
	if (x <= -1.9e+215)
		tmp = i * (j * (x * y1));
	elseif (x <= -1.4e+27)
		tmp = y1 * (a * (x * -y2));
	elseif (x <= 8.2e-281)
		tmp = t_2;
	elseif (x <= 5e-193)
		tmp = t_1;
	elseif (x <= 1.35e-134)
		tmp = t_2;
	elseif (x <= 1.5e-78)
		tmp = y4 * (y3 * (y * c));
	elseif (x <= 3e+162)
		tmp = t_1;
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y4 * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+215], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e+27], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-281], t$95$2, If[LessEqual[x, 5e-193], t$95$1, If[LessEqual[x, 1.35e-134], t$95$2, If[LessEqual[x, 1.5e-78], N[(y4 * N[(y3 * N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+162], t$95$1, N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.89999999999999984e215

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 55.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 55.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 55.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 67.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 67.4%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 67.4%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 67.4%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 56.3%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 56.3%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 56.2%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 56.2%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 61.6%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 61.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 61.6%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 67.0%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 67.0%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.89999999999999984e215 < x < -1.4e27

   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 30.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 53.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 53.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 53.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 53.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 56.0%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in x around inf 54.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)\right)} \cdot y1 \]
   9. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto \color{blue}{\left(-a \cdot \left(y2 \cdot x\right)\right)} \cdot y1 \]

      2. *-commutative 54.4%

         \[\leadsto \left(-\color{blue}{\left(y2 \cdot x\right) \cdot a}\right) \cdot y1 \]

      3. distribute-rgt-neg-in 54.4%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot x\right) \cdot \left(-a\right)\right)} \cdot y1 \]

      4. *-commutative 54.4%

         \[\leadsto \left(\color{blue}{\left(x \cdot y2\right)} \cdot \left(-a\right)\right) \cdot y1 \]

   10. Simplified 54.4%

       \[\leadsto \color{blue}{\left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)} \cdot y1 \]

   if -1.4e27 < x < 8.1999999999999998e-281 or 5.0000000000000005e-193 < x < 1.3499999999999999e-134

   1. Initial program 30.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in k around inf 40.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(-1 \cdot \left(y \cdot b\right) + y1 \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 40.0%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 + -1 \cdot \left(y \cdot b\right)\right)}\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto k \cdot \left(y4 \cdot \left(y1 \cdot y2 + \color{blue}{\left(-y \cdot b\right)}\right)\right) \]

      3. unsub-neg 40.0%

         \[\leadsto k \cdot \left(y4 \cdot \color{blue}{\left(y1 \cdot y2 - y \cdot b\right)}\right) \]

   7. Simplified 40.0%

      \[\leadsto \color{blue}{k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)} \]

   if 8.1999999999999998e-281 < x < 5.0000000000000005e-193 or 1.49999999999999994e-78 < x < 2.9999999999999998e162

   1. Initial program 26.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 47.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.3%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 47.3%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 47.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 1.3499999999999999e-134 < x < 1.49999999999999994e-78

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 58.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 67.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 67.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 67.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 59.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 59.0%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

      2. associate-*l* 59.0%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

      3. *-commutative 59.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot c\right) \]

      4. associate-*l* 59.0%

         \[\leadsto y4 \cdot \color{blue}{\left(y3 \cdot \left(y \cdot c\right)\right)} \]

      5. *-commutative 59.0%

         \[\leadsto y4 \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y\right)}\right) \]

   10. Simplified 59.0%

       \[\leadsto \color{blue}{y4 \cdot \left(y3 \cdot \left(c \cdot y\right)\right)} \]

   if 2.9999999999999998e162 < x

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 38.7%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+215}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-281}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-193}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-134}:\\ \;\;\;\;k \cdot \left(y4 \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-78}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+162}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 23: 28.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ t_2 := t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+215}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* y5 (- (* j y3) (* k y2)))))
        (t_2 (* t (* a (- (* y2 y5) (* z b))))))
   (if (<= x -1.9e+215)
     (* i (* j (* x y1)))
     (if (<= x -2.9e+27)
       (* y1 (* a (* x (- y2))))
       (if (<= x -7.6e-133)
         t_2
         (if (<= x -1.15e-203)
           t_1
           (if (<= x -2.3e-300)
             t_2
             (if (<= x 9e-226)
               t_1
               (if (<= x 3.3e+168)
                 (* c (* y4 (- (* y y3) (* t y2))))
                 (* b (* j (- (* t y4) (* x y0)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (x <= -1.9e+215) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.9e+27) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -7.6e-133) {
		tmp = t_2;
	} else if (x <= -1.15e-203) {
		tmp = t_1;
	} else if (x <= -2.3e-300) {
		tmp = t_2;
	} else if (x <= 9e-226) {
		tmp = t_1;
	} else if (x <= 3.3e+168) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
    t_2 = t * (a * ((y2 * y5) - (z * b)))
    if (x <= (-1.9d+215)) then
        tmp = i * (j * (x * y1))
    else if (x <= (-2.9d+27)) then
        tmp = y1 * (a * (x * -y2))
    else if (x <= (-7.6d-133)) then
        tmp = t_2
    else if (x <= (-1.15d-203)) then
        tmp = t_1
    else if (x <= (-2.3d-300)) then
        tmp = t_2
    else if (x <= 9d-226) then
        tmp = t_1
    else if (x <= 3.3d+168) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	double t_2 = t * (a * ((y2 * y5) - (z * b)));
	double tmp;
	if (x <= -1.9e+215) {
		tmp = i * (j * (x * y1));
	} else if (x <= -2.9e+27) {
		tmp = y1 * (a * (x * -y2));
	} else if (x <= -7.6e-133) {
		tmp = t_2;
	} else if (x <= -1.15e-203) {
		tmp = t_1;
	} else if (x <= -2.3e-300) {
		tmp = t_2;
	} else if (x <= 9e-226) {
		tmp = t_1;
	} else if (x <= 3.3e+168) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)))
	t_2 = t * (a * ((y2 * y5) - (z * b)))
	tmp = 0
	if x <= -1.9e+215:
		tmp = i * (j * (x * y1))
	elif x <= -2.9e+27:
		tmp = y1 * (a * (x * -y2))
	elif x <= -7.6e-133:
		tmp = t_2
	elif x <= -1.15e-203:
		tmp = t_1
	elif x <= -2.3e-300:
		tmp = t_2
	elif x <= 9e-226:
		tmp = t_1
	elif x <= 3.3e+168:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(y5 * Float64(Float64(j * y3) - Float64(k * y2))))
	t_2 = Float64(t * Float64(a * Float64(Float64(y2 * y5) - Float64(z * b))))
	tmp = 0.0
	if (x <= -1.9e+215)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (x <= -2.9e+27)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (x <= -7.6e-133)
		tmp = t_2;
	elseif (x <= -1.15e-203)
		tmp = t_1;
	elseif (x <= -2.3e-300)
		tmp = t_2;
	elseif (x <= 9e-226)
		tmp = t_1;
	elseif (x <= 3.3e+168)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (y5 * ((j * y3) - (k * y2)));
	t_2 = t * (a * ((y2 * y5) - (z * b)));
	tmp = 0.0;
	if (x <= -1.9e+215)
		tmp = i * (j * (x * y1));
	elseif (x <= -2.9e+27)
		tmp = y1 * (a * (x * -y2));
	elseif (x <= -7.6e-133)
		tmp = t_2;
	elseif (x <= -1.15e-203)
		tmp = t_1;
	elseif (x <= -2.3e-300)
		tmp = t_2;
	elseif (x <= 9e-226)
		tmp = t_1;
	elseif (x <= 3.3e+168)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(y5 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+215], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e+27], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.6e-133], t$95$2, If[LessEqual[x, -1.15e-203], t$95$1, If[LessEqual[x, -2.3e-300], t$95$2, If[LessEqual[x, 9e-226], t$95$1, If[LessEqual[x, 3.3e+168], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.89999999999999984e215

   1. Initial program 11.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 55.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 55.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 55.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 67.4%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 67.4%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 67.4%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 67.4%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 56.3%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 56.3%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 56.2%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 56.2%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 61.6%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 61.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 61.6%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 67.0%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 67.0%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.89999999999999984e215 < x < -2.9000000000000001e27

   1. Initial program 16.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 55.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 55.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 55.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 55.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 55.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 57.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in x around inf 55.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)\right)} \cdot y1 \]
   9. Step-by-step derivation

      1. mul-1-neg 55.7%

         \[\leadsto \color{blue}{\left(-a \cdot \left(y2 \cdot x\right)\right)} \cdot y1 \]

      2. *-commutative 55.7%

         \[\leadsto \left(-\color{blue}{\left(y2 \cdot x\right) \cdot a}\right) \cdot y1 \]

      3. distribute-rgt-neg-in 55.7%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot x\right) \cdot \left(-a\right)\right)} \cdot y1 \]

      4. *-commutative 55.7%

         \[\leadsto \left(\color{blue}{\left(x \cdot y2\right)} \cdot \left(-a\right)\right) \cdot y1 \]

   10. Simplified 55.7%

       \[\leadsto \color{blue}{\left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)} \cdot y1 \]

   if -2.9000000000000001e27 < x < -7.6000000000000006e-133 or -1.14999999999999996e-203 < x < -2.30000000000000001e-300

   1. Initial program 32.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in t around inf 47.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 47.0%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

      2. mul-1-neg 47.0%

         \[\leadsto t \cdot \left(\color{blue}{\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right)} + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right) \]

   6. Simplified 47.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(j \cdot \left(y4 \cdot b - i \cdot y5\right) - \left(c \cdot y4 - a \cdot y5\right) \cdot y2\right)\right)} \]

   7. Taylor expanded in a around -inf 45.8%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.8%

         \[\leadsto \color{blue}{\left(t \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right) \cdot a} \]

      2. associate-*l* 43.7%

         \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right) \cdot a\right)} \]

      3. *-commutative 43.7%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-1 \cdot \left(b \cdot z\right) + y5 \cdot y2\right)\right)} \]

      4. +-commutative 43.7%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 + -1 \cdot \left(b \cdot z\right)\right)}\right) \]

      5. mul-1-neg 43.7%

         \[\leadsto t \cdot \left(a \cdot \left(y5 \cdot y2 + \color{blue}{\left(-b \cdot z\right)}\right)\right) \]

      6. unsub-neg 43.7%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(y5 \cdot y2 - b \cdot z\right)}\right) \]

   9. Simplified 43.7%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(y5 \cdot y2 - b \cdot z\right)\right)} \]

   if -7.6000000000000006e-133 < x < -1.14999999999999996e-203 or -2.30000000000000001e-300 < x < 9.00000000000000023e-226

   1. Initial program 31.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y0 around inf 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.2%

         \[\leadsto y0 \cdot \left(\left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right) \]

   6. Simplified 76.2%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + c \cdot \left(y2 \cdot x - y3 \cdot z\right)\right) - \left(j \cdot x - k \cdot z\right) \cdot b\right)} \]

   7. Taylor expanded in y5 around inf 69.6%

      \[\leadsto \color{blue}{y0 \cdot \left(\left(y3 \cdot j - k \cdot y2\right) \cdot y5\right)} \]

   if 9.00000000000000023e-226 < x < 3.2999999999999999e168

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.0%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 43.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto c \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot y} - t \cdot y2\right)\right) \]

      2. *-commutative 43.7%

         \[\leadsto c \cdot \left(y4 \cdot \left(y3 \cdot y - \color{blue}{y2 \cdot t}\right)\right) \]

   7. Simplified 43.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y3 \cdot y - y2 \cdot t\right)\right)} \]

   if 3.2999999999999999e168 < x

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.7%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 38.7%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 46.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+215}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+27}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-203}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-300}:\\ \;\;\;\;t \cdot \left(a \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-226}:\\ \;\;\;\;y0 \cdot \left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+168}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

Alternative 24: 19.4% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq -2.7 \cdot 10^{+141}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 6.1 \cdot 10^{-260}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{-99}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y0 \cdot \left(-j\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+210}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= k -2.7e+141)
   (* y1 (* y2 (* k y4)))
   (if (<= k -4e+30)
     (* a (* y3 (* z y1)))
     (if (<= k 6.1e-260)
       (* (- a) (* x (* y1 y2)))
       (if (<= k 1.22e-99)
         (* (* x b) (* y0 (- j)))
         (if (<= k 1.05e+137)
           (* i (* j (* x y1)))
           (if (<= k 4e+210)
             (* (* y a) (* x b))
             (* y4 (* c (* t (- y2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -2.7e+141) {
		tmp = y1 * (y2 * (k * y4));
	} else if (k <= -4e+30) {
		tmp = a * (y3 * (z * y1));
	} else if (k <= 6.1e-260) {
		tmp = -a * (x * (y1 * y2));
	} else if (k <= 1.22e-99) {
		tmp = (x * b) * (y0 * -j);
	} else if (k <= 1.05e+137) {
		tmp = i * (j * (x * y1));
	} else if (k <= 4e+210) {
		tmp = (y * a) * (x * b);
	} else {
		tmp = y4 * (c * (t * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (k <= (-2.7d+141)) then
        tmp = y1 * (y2 * (k * y4))
    else if (k <= (-4d+30)) then
        tmp = a * (y3 * (z * y1))
    else if (k <= 6.1d-260) then
        tmp = -a * (x * (y1 * y2))
    else if (k <= 1.22d-99) then
        tmp = (x * b) * (y0 * -j)
    else if (k <= 1.05d+137) then
        tmp = i * (j * (x * y1))
    else if (k <= 4d+210) then
        tmp = (y * a) * (x * b)
    else
        tmp = y4 * (c * (t * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (k <= -2.7e+141) {
		tmp = y1 * (y2 * (k * y4));
	} else if (k <= -4e+30) {
		tmp = a * (y3 * (z * y1));
	} else if (k <= 6.1e-260) {
		tmp = -a * (x * (y1 * y2));
	} else if (k <= 1.22e-99) {
		tmp = (x * b) * (y0 * -j);
	} else if (k <= 1.05e+137) {
		tmp = i * (j * (x * y1));
	} else if (k <= 4e+210) {
		tmp = (y * a) * (x * b);
	} else {
		tmp = y4 * (c * (t * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if k <= -2.7e+141:
		tmp = y1 * (y2 * (k * y4))
	elif k <= -4e+30:
		tmp = a * (y3 * (z * y1))
	elif k <= 6.1e-260:
		tmp = -a * (x * (y1 * y2))
	elif k <= 1.22e-99:
		tmp = (x * b) * (y0 * -j)
	elif k <= 1.05e+137:
		tmp = i * (j * (x * y1))
	elif k <= 4e+210:
		tmp = (y * a) * (x * b)
	else:
		tmp = y4 * (c * (t * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (k <= -2.7e+141)
		tmp = Float64(y1 * Float64(y2 * Float64(k * y4)));
	elseif (k <= -4e+30)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (k <= 6.1e-260)
		tmp = Float64(Float64(-a) * Float64(x * Float64(y1 * y2)));
	elseif (k <= 1.22e-99)
		tmp = Float64(Float64(x * b) * Float64(y0 * Float64(-j)));
	elseif (k <= 1.05e+137)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (k <= 4e+210)
		tmp = Float64(Float64(y * a) * Float64(x * b));
	else
		tmp = Float64(y4 * Float64(c * Float64(t * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (k <= -2.7e+141)
		tmp = y1 * (y2 * (k * y4));
	elseif (k <= -4e+30)
		tmp = a * (y3 * (z * y1));
	elseif (k <= 6.1e-260)
		tmp = -a * (x * (y1 * y2));
	elseif (k <= 1.22e-99)
		tmp = (x * b) * (y0 * -j);
	elseif (k <= 1.05e+137)
		tmp = i * (j * (x * y1));
	elseif (k <= 4e+210)
		tmp = (y * a) * (x * b);
	else
		tmp = y4 * (c * (t * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[k, -2.7e+141], N[(y1 * N[(y2 * N[(k * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4e+30], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.1e-260], N[((-a) * N[(x * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.22e-99], N[(N[(x * b), $MachinePrecision] * N[(y0 * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.05e+137], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4e+210], N[(N[(y * a), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if k < -2.7000000000000001e141

   1. Initial program 30.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.3%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.3%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 37.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in k around inf 41.0%

      \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y2\right)\right)} \cdot y1 \]
   9. Step-by-step derivation

      1. associate-*r* 43.0%

         \[\leadsto \color{blue}{\left(\left(k \cdot y4\right) \cdot y2\right)} \cdot y1 \]

      2. *-commutative 43.0%

         \[\leadsto \left(\color{blue}{\left(y4 \cdot k\right)} \cdot y2\right) \cdot y1 \]

   10. Simplified 43.0%

       \[\leadsto \color{blue}{\left(\left(y4 \cdot k\right) \cdot y2\right)} \cdot y1 \]

   if -2.7000000000000001e141 < k < -4.0000000000000001e30

   1. Initial program 27.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 27.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 27.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 27.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 27.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 27.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 31.7%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 32.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 28.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 32.3%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 32.3%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if -4.0000000000000001e30 < k < 6.1000000000000003e-260

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 49.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 49.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 49.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 49.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 46.2%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in x around inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.9%

         \[\leadsto \color{blue}{-y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]

      2. *-commutative 32.9%

         \[\leadsto -y1 \cdot \left(a \cdot \color{blue}{\left(y2 \cdot x\right)}\right) \]

      3. *-commutative 32.9%

         \[\leadsto -y1 \cdot \color{blue}{\left(\left(y2 \cdot x\right) \cdot a\right)} \]

      4. associate-*r* 32.9%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(y2 \cdot x\right)\right) \cdot a} \]

      5. distribute-rgt-neg-in 32.9%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(y2 \cdot x\right)\right) \cdot \left(-a\right)} \]

      6. *-commutative 32.9%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot x\right) \cdot y1\right)} \cdot \left(-a\right) \]

      7. *-commutative 32.9%

         \[\leadsto \left(\color{blue}{\left(x \cdot y2\right)} \cdot y1\right) \cdot \left(-a\right) \]

      8. associate-*l* 37.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y2 \cdot y1\right)\right)} \cdot \left(-a\right) \]

   10. Simplified 37.0%

       \[\leadsto \color{blue}{\left(x \cdot \left(y2 \cdot y1\right)\right) \cdot \left(-a\right)} \]

   if 6.1000000000000003e-260 < k < 1.22e-99

   1. Initial program 16.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 40.4%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 40.4%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 40.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 40.8%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in a around 0 31.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

      2. neg-mul-1 31.6%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(j \cdot \left(b \cdot x\right)\right) \]

      3. associate-*r* 37.9%

         \[\leadsto \color{blue}{\left(\left(-y0\right) \cdot j\right) \cdot \left(b \cdot x\right)} \]

      4. *-commutative 37.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(-y0\right)\right)} \cdot \left(b \cdot x\right) \]

   10. Simplified 37.9%

       \[\leadsto \color{blue}{\left(j \cdot \left(-y0\right)\right) \cdot \left(b \cdot x\right)} \]

   if 1.22e-99 < k < 1.05e137

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 44.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 44.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 44.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 44.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 46.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.5%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 44.5%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 44.5%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 44.5%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 29.8%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 29.8%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 31.8%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 31.8%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 29.8%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 29.8%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 29.8%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 33.8%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 33.8%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if 1.05e137 < k < 3.99999999999999971e210

   1. Initial program 6.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 6.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 50.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.6%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 50.6%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 50.8%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in a around inf 44.9%

      \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(b \cdot x\right) \]

   if 3.99999999999999971e210 < k

   1. Initial program 16.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 28.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 48.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 48.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around 0 44.6%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 44.6%

         \[\leadsto y4 \cdot \color{blue}{\left(-c \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 44.6%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 44.6%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-c\right)\right)} \]

      4. *-commutative 44.6%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y2 \cdot t\right)} \cdot \left(-c\right)\right) \]

   10. Simplified 44.6%

       \[\leadsto y4 \cdot \color{blue}{\left(\left(y2 \cdot t\right) \cdot \left(-c\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.7 \cdot 10^{+141}:\\ \;\;\;\;y1 \cdot \left(y2 \cdot \left(k \cdot y4\right)\right)\\ \mathbf{elif}\;k \leq -4 \cdot 10^{+30}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 6.1 \cdot 10^{-260}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;k \leq 1.22 \cdot 10^{-99}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y0 \cdot \left(-j\right)\right)\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+137}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+210}:\\ \;\;\;\;\left(y \cdot a\right) \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \end{array} \]

Alternative 25: 22.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{if}\;y2 \leq -2.4 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -1.1 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{-111}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.15 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{+125}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (* t (- y2))))))
   (if (<= y2 -2.4e+159)
     t_1
     (if (<= y2 -1.1e-70)
       (* i (* j (* x y1)))
       (if (<= y2 2.3e-111)
         (* c (* y4 (* y y3)))
         (if (<= y2 2.15e+18)
           (* a (* y3 (* z y1)))
           (if (<= y2 6.5e+125) (* b (* j (* x (- y0)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * (t * -y2));
	double tmp;
	if (y2 <= -2.4e+159) {
		tmp = t_1;
	} else if (y2 <= -1.1e-70) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2.3e-111) {
		tmp = c * (y4 * (y * y3));
	} else if (y2 <= 2.15e+18) {
		tmp = a * (y3 * (z * y1));
	} else if (y2 <= 6.5e+125) {
		tmp = b * (j * (x * -y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (c * (t * -y2))
    if (y2 <= (-2.4d+159)) then
        tmp = t_1
    else if (y2 <= (-1.1d-70)) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 2.3d-111) then
        tmp = c * (y4 * (y * y3))
    else if (y2 <= 2.15d+18) then
        tmp = a * (y3 * (z * y1))
    else if (y2 <= 6.5d+125) then
        tmp = b * (j * (x * -y0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (c * (t * -y2));
	double tmp;
	if (y2 <= -2.4e+159) {
		tmp = t_1;
	} else if (y2 <= -1.1e-70) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 2.3e-111) {
		tmp = c * (y4 * (y * y3));
	} else if (y2 <= 2.15e+18) {
		tmp = a * (y3 * (z * y1));
	} else if (y2 <= 6.5e+125) {
		tmp = b * (j * (x * -y0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (c * (t * -y2))
	tmp = 0
	if y2 <= -2.4e+159:
		tmp = t_1
	elif y2 <= -1.1e-70:
		tmp = i * (j * (x * y1))
	elif y2 <= 2.3e-111:
		tmp = c * (y4 * (y * y3))
	elif y2 <= 2.15e+18:
		tmp = a * (y3 * (z * y1))
	elif y2 <= 6.5e+125:
		tmp = b * (j * (x * -y0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(c * Float64(t * Float64(-y2))))
	tmp = 0.0
	if (y2 <= -2.4e+159)
		tmp = t_1;
	elseif (y2 <= -1.1e-70)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 2.3e-111)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y2 <= 2.15e+18)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y2 <= 6.5e+125)
		tmp = Float64(b * Float64(j * Float64(x * Float64(-y0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (c * (t * -y2));
	tmp = 0.0;
	if (y2 <= -2.4e+159)
		tmp = t_1;
	elseif (y2 <= -1.1e-70)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 2.3e-111)
		tmp = c * (y4 * (y * y3));
	elseif (y2 <= 2.15e+18)
		tmp = a * (y3 * (z * y1));
	elseif (y2 <= 6.5e+125)
		tmp = b * (j * (x * -y0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(c * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -2.4e+159], t$95$1, If[LessEqual[y2, -1.1e-70], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.3e-111], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.15e+18], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 6.5e+125], N[(b * N[(j * N[(x * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -2.4e159 or 6.4999999999999999e125 < y2

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 48.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.9%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 48.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around 0 46.1%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto y4 \cdot \color{blue}{\left(-c \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 46.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 46.1%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-c\right)\right)} \]

      4. *-commutative 46.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y2 \cdot t\right)} \cdot \left(-c\right)\right) \]

   10. Simplified 46.1%

       \[\leadsto y4 \cdot \color{blue}{\left(\left(y2 \cdot t\right) \cdot \left(-c\right)\right)} \]

   if -2.4e159 < y2 < -1.0999999999999999e-70

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 33.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 33.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 33.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 40.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.7%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 36.7%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 36.7%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 36.7%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 26.0%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 26.0%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 26.1%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 26.1%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 30.2%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 28.1%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 28.1%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 30.2%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 30.2%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.0999999999999999e-70 < y2 < 2.3e-111

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 37.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 37.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 37.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 28.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 2.3e-111 < y2 < 2.15e18

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 45.6%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 39.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 39.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 39.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 42.7%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 42.7%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if 2.15e18 < y2 < 6.4999999999999999e125

   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 38.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 33.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.8%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 39.9%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]

   8. Taylor expanded in y4 around 0 40.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(j \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(j \cdot x\right)\right)} \]

      2. neg-mul-1 40.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(j \cdot x\right)\right) \]

      3. *-commutative 40.0%

         \[\leadsto b \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(x \cdot j\right)}\right) \]

      4. associate-*r* 40.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(\left(-y0\right) \cdot x\right) \cdot j\right)} \]

      5. *-commutative 40.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(x \cdot \left(-y0\right)\right)} \cdot j\right) \]

      6. distribute-rgt-neg-in 40.0%

         \[\leadsto b \cdot \left(\color{blue}{\left(-x \cdot y0\right)} \cdot j\right) \]

   10. Simplified 40.0%

       \[\leadsto b \cdot \color{blue}{\left(\left(-x \cdot y0\right) \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -2.4 \cdot 10^{+159}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.1 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 2.3 \cdot 10^{-111}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 2.15 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 6.5 \cdot 10^{+125}:\\ \;\;\;\;b \cdot \left(j \cdot \left(x \cdot \left(-y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \end{array} \]

Alternative 26: 22.4% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{if}\;y2 \leq -4.5 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 9 \cdot 10^{-112}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+126}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y0 \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (* t (- y2))))))
   (if (<= y2 -4.5e+159)
     t_1
     (if (<= y2 -1.85e-70)
       (* i (* j (* x y1)))
       (if (<= y2 9e-112)
         (* c (* y4 (* y y3)))
         (if (<= y2 1.9e+18)
           (* a (* y3 (* z y1)))
           (if (<= y2 4.8e+126) (* (* x b) (* y0 (- 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 = y4 * (c * (t * -y2));
	double tmp;
	if (y2 <= -4.5e+159) {
		tmp = t_1;
	} else if (y2 <= -1.85e-70) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 9e-112) {
		tmp = c * (y4 * (y * y3));
	} else if (y2 <= 1.9e+18) {
		tmp = a * (y3 * (z * y1));
	} else if (y2 <= 4.8e+126) {
		tmp = (x * b) * (y0 * -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 = y4 * (c * (t * -y2))
    if (y2 <= (-4.5d+159)) then
        tmp = t_1
    else if (y2 <= (-1.85d-70)) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 9d-112) then
        tmp = c * (y4 * (y * y3))
    else if (y2 <= 1.9d+18) then
        tmp = a * (y3 * (z * y1))
    else if (y2 <= 4.8d+126) then
        tmp = (x * b) * (y0 * -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 = y4 * (c * (t * -y2));
	double tmp;
	if (y2 <= -4.5e+159) {
		tmp = t_1;
	} else if (y2 <= -1.85e-70) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 9e-112) {
		tmp = c * (y4 * (y * y3));
	} else if (y2 <= 1.9e+18) {
		tmp = a * (y3 * (z * y1));
	} else if (y2 <= 4.8e+126) {
		tmp = (x * b) * (y0 * -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 = y4 * (c * (t * -y2))
	tmp = 0
	if y2 <= -4.5e+159:
		tmp = t_1
	elif y2 <= -1.85e-70:
		tmp = i * (j * (x * y1))
	elif y2 <= 9e-112:
		tmp = c * (y4 * (y * y3))
	elif y2 <= 1.9e+18:
		tmp = a * (y3 * (z * y1))
	elif y2 <= 4.8e+126:
		tmp = (x * b) * (y0 * -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(y4 * Float64(c * Float64(t * Float64(-y2))))
	tmp = 0.0
	if (y2 <= -4.5e+159)
		tmp = t_1;
	elseif (y2 <= -1.85e-70)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 9e-112)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y2 <= 1.9e+18)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y2 <= 4.8e+126)
		tmp = Float64(Float64(x * b) * Float64(y0 * Float64(-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 = y4 * (c * (t * -y2));
	tmp = 0.0;
	if (y2 <= -4.5e+159)
		tmp = t_1;
	elseif (y2 <= -1.85e-70)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 9e-112)
		tmp = c * (y4 * (y * y3));
	elseif (y2 <= 1.9e+18)
		tmp = a * (y3 * (z * y1));
	elseif (y2 <= 4.8e+126)
		tmp = (x * b) * (y0 * -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[(y4 * N[(c * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -4.5e+159], t$95$1, If[LessEqual[y2, -1.85e-70], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9e-112], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.9e+18], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.8e+126], N[(N[(x * b), $MachinePrecision] * N[(y0 * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -4.50000000000000026e159 or 4.80000000000000024e126 < y2

   1. Initial program 13.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 48.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.9%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 48.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around 0 46.1%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 46.1%

         \[\leadsto y4 \cdot \color{blue}{\left(-c \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 46.1%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 46.1%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-c\right)\right)} \]

      4. *-commutative 46.1%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y2 \cdot t\right)} \cdot \left(-c\right)\right) \]

   10. Simplified 46.1%

       \[\leadsto y4 \cdot \color{blue}{\left(\left(y2 \cdot t\right) \cdot \left(-c\right)\right)} \]

   if -4.50000000000000026e159 < y2 < -1.85e-70

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 33.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 33.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 33.9%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 33.9%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 40.8%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.7%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 36.7%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 36.7%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 36.7%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 26.0%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 26.0%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 26.1%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 26.1%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 30.2%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 28.1%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 28.1%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 30.2%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 30.2%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -1.85e-70 < y2 < 9.00000000000000024e-112

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 37.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 37.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 37.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 28.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 9.00000000000000024e-112 < y2 < 1.9e18

   1. Initial program 26.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 45.6%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 39.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 39.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 39.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 42.7%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 42.7%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if 1.9e18 < y2 < 4.80000000000000024e126

   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 38.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 33.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.8%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 67.0%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in a around 0 34.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 34.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

      2. neg-mul-1 34.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(j \cdot \left(b \cdot x\right)\right) \]

      3. associate-*r* 45.3%

         \[\leadsto \color{blue}{\left(\left(-y0\right) \cdot j\right) \cdot \left(b \cdot x\right)} \]

      4. *-commutative 45.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(-y0\right)\right)} \cdot \left(b \cdot x\right) \]

   10. Simplified 45.3%

       \[\leadsto \color{blue}{\left(j \cdot \left(-y0\right)\right) \cdot \left(b \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -4.5 \cdot 10^{+159}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq -1.85 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 9 \cdot 10^{-112}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.9 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 4.8 \cdot 10^{+126}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y0 \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \end{array} \]

Alternative 27: 21.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c\right)\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-255}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-225}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-46}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+205}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y -3.4e-50)
   (* y4 (* y3 (* y c)))
   (if (<= y -1.2e-255)
     (* y4 (* k (* y1 y2)))
     (if (<= y 1.8e-225)
       (* i (* j (* x y1)))
       (if (<= y 9.2e-46)
         (* y4 (* t (* b j)))
         (if (<= y 3.4e+205) (* y1 (* i (* x j))) (* c (* y4 (* y y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -3.4e-50) {
		tmp = y4 * (y3 * (y * c));
	} else if (y <= -1.2e-255) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y <= 1.8e-225) {
		tmp = i * (j * (x * y1));
	} else if (y <= 9.2e-46) {
		tmp = y4 * (t * (b * j));
	} else if (y <= 3.4e+205) {
		tmp = y1 * (i * (x * j));
	} else {
		tmp = c * (y4 * (y * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y <= (-3.4d-50)) then
        tmp = y4 * (y3 * (y * c))
    else if (y <= (-1.2d-255)) then
        tmp = y4 * (k * (y1 * y2))
    else if (y <= 1.8d-225) then
        tmp = i * (j * (x * y1))
    else if (y <= 9.2d-46) then
        tmp = y4 * (t * (b * j))
    else if (y <= 3.4d+205) then
        tmp = y1 * (i * (x * j))
    else
        tmp = c * (y4 * (y * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y <= -3.4e-50) {
		tmp = y4 * (y3 * (y * c));
	} else if (y <= -1.2e-255) {
		tmp = y4 * (k * (y1 * y2));
	} else if (y <= 1.8e-225) {
		tmp = i * (j * (x * y1));
	} else if (y <= 9.2e-46) {
		tmp = y4 * (t * (b * j));
	} else if (y <= 3.4e+205) {
		tmp = y1 * (i * (x * j));
	} else {
		tmp = c * (y4 * (y * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y <= -3.4e-50:
		tmp = y4 * (y3 * (y * c))
	elif y <= -1.2e-255:
		tmp = y4 * (k * (y1 * y2))
	elif y <= 1.8e-225:
		tmp = i * (j * (x * y1))
	elif y <= 9.2e-46:
		tmp = y4 * (t * (b * j))
	elif y <= 3.4e+205:
		tmp = y1 * (i * (x * j))
	else:
		tmp = c * (y4 * (y * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y <= -3.4e-50)
		tmp = Float64(y4 * Float64(y3 * Float64(y * c)));
	elseif (y <= -1.2e-255)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	elseif (y <= 1.8e-225)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y <= 9.2e-46)
		tmp = Float64(y4 * Float64(t * Float64(b * j)));
	elseif (y <= 3.4e+205)
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	else
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y <= -3.4e-50)
		tmp = y4 * (y3 * (y * c));
	elseif (y <= -1.2e-255)
		tmp = y4 * (k * (y1 * y2));
	elseif (y <= 1.8e-225)
		tmp = i * (j * (x * y1));
	elseif (y <= 9.2e-46)
		tmp = y4 * (t * (b * j));
	elseif (y <= 3.4e+205)
		tmp = y1 * (i * (x * j));
	else
		tmp = c * (y4 * (y * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y, -3.4e-50], N[(y4 * N[(y3 * N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-255], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-225], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-46], N[(y4 * N[(t * N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+205], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.40000000000000014e-50

   1. Initial program 22.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 42.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 42.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 42.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 30.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 30.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

      2. associate-*l* 32.0%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

      3. *-commutative 32.0%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y3 \cdot y\right)} \cdot c\right) \]

      4. associate-*l* 34.5%

         \[\leadsto y4 \cdot \color{blue}{\left(y3 \cdot \left(y \cdot c\right)\right)} \]

      5. *-commutative 34.5%

         \[\leadsto y4 \cdot \left(y3 \cdot \color{blue}{\left(c \cdot y\right)}\right) \]

   10. Simplified 34.5%

       \[\leadsto \color{blue}{y4 \cdot \left(y3 \cdot \left(c \cdot y\right)\right)} \]

   if -3.40000000000000014e-50 < y < -1.1999999999999999e-255

   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 23.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 37.7%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 38.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.2%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around inf 27.2%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 27.2%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 27.2%

       \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1\right)\right)} \]

   if -1.1999999999999999e-255 < y < 1.80000000000000005e-225

   1. Initial program 36.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 48.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 49.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 49.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 49.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 49.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 34.9%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 37.6%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 37.6%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 37.6%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 37.6%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 23.1%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 23.1%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 26.2%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 26.2%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 28.9%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 28.8%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 28.8%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 34.6%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 34.6%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if 1.80000000000000005e-225 < y < 9.1999999999999997e-46

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 44.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 44.1%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 44.1%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 39.8%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]

   8. Taylor expanded in y4 around inf 34.8%

      \[\leadsto \color{blue}{y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)} \]

   if 9.1999999999999997e-46 < y < 3.4e205

   1. Initial program 22.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 40.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 40.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 40.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 40.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 38.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 36.8%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 36.8%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 36.8%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 36.8%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around -inf 29.6%

       \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]

   if 3.4e205 < y

   1. Initial program 16.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 16.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 44.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 50.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 50.3%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 50.3%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 50.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;y4 \cdot \left(y3 \cdot \left(y \cdot c\right)\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-255}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-225}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-46}:\\ \;\;\;\;y4 \cdot \left(t \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+205}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \end{array} \]

Alternative 28: 21.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-68}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 270000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* k (* y1 y2)))))
   (if (<= z -8.8e+102)
     (* a (* y3 (* z y1)))
     (if (<= z -1.55e-68)
       (* y4 (* y2 (* t (- c))))
       (if (<= z -4.9e-203)
         t_1
         (if (<= z 2.55e-228)
           (* y1 (* i (* x j)))
           (if (<= z 270000000000.0) t_1 (* (* z y3) (* a y1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (k * (y1 * y2));
	double tmp;
	if (z <= -8.8e+102) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= -1.55e-68) {
		tmp = y4 * (y2 * (t * -c));
	} else if (z <= -4.9e-203) {
		tmp = t_1;
	} else if (z <= 2.55e-228) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 270000000000.0) {
		tmp = t_1;
	} else {
		tmp = (z * y3) * (a * y1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y4 * (k * (y1 * y2))
    if (z <= (-8.8d+102)) then
        tmp = a * (y3 * (z * y1))
    else if (z <= (-1.55d-68)) then
        tmp = y4 * (y2 * (t * -c))
    else if (z <= (-4.9d-203)) then
        tmp = t_1
    else if (z <= 2.55d-228) then
        tmp = y1 * (i * (x * j))
    else if (z <= 270000000000.0d0) then
        tmp = t_1
    else
        tmp = (z * y3) * (a * y1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y4 * (k * (y1 * y2));
	double tmp;
	if (z <= -8.8e+102) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= -1.55e-68) {
		tmp = y4 * (y2 * (t * -c));
	} else if (z <= -4.9e-203) {
		tmp = t_1;
	} else if (z <= 2.55e-228) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 270000000000.0) {
		tmp = t_1;
	} else {
		tmp = (z * y3) * (a * y1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y4 * (k * (y1 * y2))
	tmp = 0
	if z <= -8.8e+102:
		tmp = a * (y3 * (z * y1))
	elif z <= -1.55e-68:
		tmp = y4 * (y2 * (t * -c))
	elif z <= -4.9e-203:
		tmp = t_1
	elif z <= 2.55e-228:
		tmp = y1 * (i * (x * j))
	elif z <= 270000000000.0:
		tmp = t_1
	else:
		tmp = (z * y3) * (a * y1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y4 * Float64(k * Float64(y1 * y2)))
	tmp = 0.0
	if (z <= -8.8e+102)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (z <= -1.55e-68)
		tmp = Float64(y4 * Float64(y2 * Float64(t * Float64(-c))));
	elseif (z <= -4.9e-203)
		tmp = t_1;
	elseif (z <= 2.55e-228)
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	elseif (z <= 270000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * y3) * Float64(a * y1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y4 * (k * (y1 * y2));
	tmp = 0.0;
	if (z <= -8.8e+102)
		tmp = a * (y3 * (z * y1));
	elseif (z <= -1.55e-68)
		tmp = y4 * (y2 * (t * -c));
	elseif (z <= -4.9e-203)
		tmp = t_1;
	elseif (z <= 2.55e-228)
		tmp = y1 * (i * (x * j));
	elseif (z <= 270000000000.0)
		tmp = t_1;
	else
		tmp = (z * y3) * (a * y1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+102], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-68], N[(y4 * N[(y2 * N[(t * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-203], t$95$1, If[LessEqual[z, 2.55e-228], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 270000000000.0], t$95$1, N[(N[(z * y3), $MachinePrecision] * N[(a * y1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.8000000000000003e102

   1. Initial program 19.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 19.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 35.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 35.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 35.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 35.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 44.1%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 42.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 38.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 40.0%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 40.0%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if -8.8000000000000003e102 < z < -1.55e-68

   1. Initial program 13.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 13.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 31.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 42.1%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.1%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around 0 35.5%

      \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot t\right)\right)}\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 35.5%

         \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(-c \cdot t\right)}\right) \]

      2. distribute-rgt-neg-in 35.5%

         \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(c \cdot \left(-t\right)\right)}\right) \]

      3. *-commutative 35.5%

         \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(\left(-t\right) \cdot c\right)}\right) \]

   10. Simplified 35.5%

       \[\leadsto y4 \cdot \left(y2 \cdot \color{blue}{\left(\left(-t\right) \cdot c\right)}\right) \]

   if -1.55e-68 < z < -4.9e-203 or 2.5500000000000001e-228 < z < 2.7e11

   1. Initial program 36.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 48.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 39.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.6%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 39.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around inf 34.1%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.1%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 34.1%

       \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1\right)\right)} \]

   if -4.9e-203 < z < 2.5500000000000001e-228

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 51.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 51.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 51.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 51.4%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 52.3%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.1%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 44.1%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 44.1%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 44.1%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around -inf 32.6%

       \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]

   if 2.7e11 < z

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 33.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.7%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 33.7%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 33.7%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 33.7%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 30.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 34.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 31.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 34.3%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 34.3%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   11. Taylor expanded in a around 0 32.9%

       \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative 32.9%

          \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right) \cdot y1} \]

       2. *-commutative 32.9%

          \[\leadsto \color{blue}{\left(\left(y3 \cdot z\right) \cdot a\right)} \cdot y1 \]

       3. associate-*l* 35.7%

          \[\leadsto \color{blue}{\left(y3 \cdot z\right) \cdot \left(a \cdot y1\right)} \]

       4. *-commutative 35.7%

          \[\leadsto \color{blue}{\left(z \cdot y3\right)} \cdot \left(a \cdot y1\right) \]

   13. Simplified 35.7%

       \[\leadsto \color{blue}{\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-68}:\\ \;\;\;\;y4 \cdot \left(y2 \cdot \left(t \cdot \left(-c\right)\right)\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-203}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 270000000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \end{array} \]

Alternative 29: 25.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y2 \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.16 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+128}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y0 \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y2 -7.2e-22)
   (* y1 (* a (* x (- y2))))
   (if (<= y2 4.7e-79)
     (* b (* j (- (* t y4) (* x y0))))
     (if (<= y2 2.16e+18)
       (* a (* y3 (* z y1)))
       (if (<= y2 9.5e+128)
         (* (* x b) (* y0 (- j)))
         (* y4 (* c (* t (- y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -7.2e-22) {
		tmp = y1 * (a * (x * -y2));
	} else if (y2 <= 4.7e-79) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 2.16e+18) {
		tmp = a * (y3 * (z * y1));
	} else if (y2 <= 9.5e+128) {
		tmp = (x * b) * (y0 * -j);
	} else {
		tmp = y4 * (c * (t * -y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y2 <= (-7.2d-22)) then
        tmp = y1 * (a * (x * -y2))
    else if (y2 <= 4.7d-79) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y2 <= 2.16d+18) then
        tmp = a * (y3 * (z * y1))
    else if (y2 <= 9.5d+128) then
        tmp = (x * b) * (y0 * -j)
    else
        tmp = y4 * (c * (t * -y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y2 <= -7.2e-22) {
		tmp = y1 * (a * (x * -y2));
	} else if (y2 <= 4.7e-79) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y2 <= 2.16e+18) {
		tmp = a * (y3 * (z * y1));
	} else if (y2 <= 9.5e+128) {
		tmp = (x * b) * (y0 * -j);
	} else {
		tmp = y4 * (c * (t * -y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -7.2e-22:
		tmp = y1 * (a * (x * -y2))
	elif y2 <= 4.7e-79:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y2 <= 2.16e+18:
		tmp = a * (y3 * (z * y1))
	elif y2 <= 9.5e+128:
		tmp = (x * b) * (y0 * -j)
	else:
		tmp = y4 * (c * (t * -y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y2 <= -7.2e-22)
		tmp = Float64(y1 * Float64(a * Float64(x * Float64(-y2))));
	elseif (y2 <= 4.7e-79)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y2 <= 2.16e+18)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (y2 <= 9.5e+128)
		tmp = Float64(Float64(x * b) * Float64(y0 * Float64(-j)));
	else
		tmp = Float64(y4 * Float64(c * Float64(t * Float64(-y2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y2 <= -7.2e-22)
		tmp = y1 * (a * (x * -y2));
	elseif (y2 <= 4.7e-79)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y2 <= 2.16e+18)
		tmp = a * (y3 * (z * y1));
	elseif (y2 <= 9.5e+128)
		tmp = (x * b) * (y0 * -j);
	else
		tmp = y4 * (c * (t * -y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y2, -7.2e-22], N[(y1 * N[(a * N[(x * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 4.7e-79], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 2.16e+18], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.5e+128], N[(N[(x * b), $MachinePrecision] * N[(y0 * (-j)), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y2 < -7.1999999999999996e-22

   1. Initial program 26.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 42.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 42.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 42.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 42.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 46.7%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in x around inf 39.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(y2 \cdot x\right)\right)\right)} \cdot y1 \]
   9. Step-by-step derivation

      1. mul-1-neg 39.7%

         \[\leadsto \color{blue}{\left(-a \cdot \left(y2 \cdot x\right)\right)} \cdot y1 \]

      2. *-commutative 39.7%

         \[\leadsto \left(-\color{blue}{\left(y2 \cdot x\right) \cdot a}\right) \cdot y1 \]

      3. distribute-rgt-neg-in 39.7%

         \[\leadsto \color{blue}{\left(\left(y2 \cdot x\right) \cdot \left(-a\right)\right)} \cdot y1 \]

      4. *-commutative 39.7%

         \[\leadsto \left(\color{blue}{\left(x \cdot y2\right)} \cdot \left(-a\right)\right) \cdot y1 \]

   10. Simplified 39.7%

       \[\leadsto \color{blue}{\left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)} \cdot y1 \]

   if -7.1999999999999996e-22 < y2 < 4.7000000000000002e-79

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 31.6%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 31.6%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 31.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 34.1%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]

   if 4.7000000000000002e-79 < y2 < 2.16e18

   1. Initial program 29.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 38.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 38.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 38.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 38.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 50.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 42.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 42.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 46.5%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 46.5%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if 2.16e18 < y2 < 9.50000000000000014e128

   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 38.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 33.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 33.8%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 67.0%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in a around 0 34.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 34.7%

         \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

      2. neg-mul-1 34.7%

         \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(j \cdot \left(b \cdot x\right)\right) \]

      3. associate-*r* 45.3%

         \[\leadsto \color{blue}{\left(\left(-y0\right) \cdot j\right) \cdot \left(b \cdot x\right)} \]

      4. *-commutative 45.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(-y0\right)\right)} \cdot \left(b \cdot x\right) \]

   10. Simplified 45.3%

       \[\leadsto \color{blue}{\left(j \cdot \left(-y0\right)\right) \cdot \left(b \cdot x\right)} \]

   if 9.50000000000000014e128 < y2

   1. Initial program 11.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 11.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 46.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.6%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 46.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around 0 48.6%

      \[\leadsto y4 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 48.6%

         \[\leadsto y4 \cdot \color{blue}{\left(-c \cdot \left(t \cdot y2\right)\right)} \]

      2. *-commutative 48.6%

         \[\leadsto y4 \cdot \left(-\color{blue}{\left(t \cdot y2\right) \cdot c}\right) \]

      3. distribute-rgt-neg-in 48.6%

         \[\leadsto y4 \cdot \color{blue}{\left(\left(t \cdot y2\right) \cdot \left(-c\right)\right)} \]

      4. *-commutative 48.6%

         \[\leadsto y4 \cdot \left(\color{blue}{\left(y2 \cdot t\right)} \cdot \left(-c\right)\right) \]

   10. Simplified 48.6%

       \[\leadsto y4 \cdot \color{blue}{\left(\left(y2 \cdot t\right) \cdot \left(-c\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -7.2 \cdot 10^{-22}:\\ \;\;\;\;y1 \cdot \left(a \cdot \left(x \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;y2 \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y2 \leq 2.16 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+128}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \left(y0 \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \end{array} \]

Alternative 30: 21.9% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ t_2 := a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{if}\;y4 \leq -2 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y4 \leq 42:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 6.8 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* j (* t y4)))) (t_2 (* a (* y3 (* z y1)))))
   (if (<= y4 -2e+72)
     t_1
     (if (<= y4 -4.5e-187)
       t_2
       (if (<= y4 42.0) (* a (* y (* x b))) (if (<= y4 6.8e+104) 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 = b * (j * (t * y4));
	double t_2 = a * (y3 * (z * y1));
	double tmp;
	if (y4 <= -2e+72) {
		tmp = t_1;
	} else if (y4 <= -4.5e-187) {
		tmp = t_2;
	} else if (y4 <= 42.0) {
		tmp = a * (y * (x * b));
	} else if (y4 <= 6.8e+104) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (j * (t * y4))
    t_2 = a * (y3 * (z * y1))
    if (y4 <= (-2d+72)) then
        tmp = t_1
    else if (y4 <= (-4.5d-187)) then
        tmp = t_2
    else if (y4 <= 42.0d0) then
        tmp = a * (y * (x * b))
    else if (y4 <= 6.8d+104) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (j * (t * y4));
	double t_2 = a * (y3 * (z * y1));
	double tmp;
	if (y4 <= -2e+72) {
		tmp = t_1;
	} else if (y4 <= -4.5e-187) {
		tmp = t_2;
	} else if (y4 <= 42.0) {
		tmp = a * (y * (x * b));
	} else if (y4 <= 6.8e+104) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = b * (j * (t * y4))
	t_2 = a * (y3 * (z * y1))
	tmp = 0
	if y4 <= -2e+72:
		tmp = t_1
	elif y4 <= -4.5e-187:
		tmp = t_2
	elif y4 <= 42.0:
		tmp = a * (y * (x * b))
	elif y4 <= 6.8e+104:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(j * Float64(t * y4)))
	t_2 = Float64(a * Float64(y3 * Float64(z * y1)))
	tmp = 0.0
	if (y4 <= -2e+72)
		tmp = t_1;
	elseif (y4 <= -4.5e-187)
		tmp = t_2;
	elseif (y4 <= 42.0)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y4 <= 6.8e+104)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = b * (j * (t * y4));
	t_2 = a * (y3 * (z * y1));
	tmp = 0.0;
	if (y4 <= -2e+72)
		tmp = t_1;
	elseif (y4 <= -4.5e-187)
		tmp = t_2;
	elseif (y4 <= 42.0)
		tmp = a * (y * (x * b));
	elseif (y4 <= 6.8e+104)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -2e+72], t$95$1, If[LessEqual[y4, -4.5e-187], t$95$2, If[LessEqual[y4, 42.0], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.8e+104], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -1.99999999999999989e72 or 6.7999999999999994e104 < y4

   1. Initial program 21.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 30.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 30.4%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 30.4%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 30.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in j around inf 40.7%

      \[\leadsto \color{blue}{b \cdot \left(j \cdot \left(y4 \cdot t - y0 \cdot x\right)\right)} \]

   8. Taylor expanded in y4 around inf 36.3%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(y4 \cdot t\right)}\right) \]

   if -1.99999999999999989e72 < y4 < -4.4999999999999998e-187 or 42 < y4 < 6.7999999999999994e104

   1. Initial program 21.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 37.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.5%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 37.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 37.5%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 37.5%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 39.2%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 25.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 24.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 24.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 27.0%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 27.0%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if -4.4999999999999998e-187 < y4 < 42

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 39.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 39.3%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 39.3%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 39.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 33.4%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in y around inf 25.2%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y4 \leq -2 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \mathbf{elif}\;y4 \leq -4.5 \cdot 10^{-187}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;y4 \leq 42:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y4 \leq 6.8 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4\right)\right)\\ \end{array} \]

Alternative 31: 22.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -1.2 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-71}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{-111}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.66 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* k (* y1 y2)))))
   (if (<= y2 -1.2e+140)
     t_1
     (if (<= y2 -8.5e-71)
       (* i (* j (* x y1)))
       (if (<= y2 1.3e-111)
         (* c (* y4 (* y y3)))
         (if (<= y2 1.66e+50) (* a (* y3 (* z 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 = y4 * (k * (y1 * y2));
	double tmp;
	if (y2 <= -1.2e+140) {
		tmp = t_1;
	} else if (y2 <= -8.5e-71) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 1.3e-111) {
		tmp = c * (y4 * (y * y3));
	} else if (y2 <= 1.66e+50) {
		tmp = a * (y3 * (z * 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) :: tmp
    t_1 = y4 * (k * (y1 * y2))
    if (y2 <= (-1.2d+140)) then
        tmp = t_1
    else if (y2 <= (-8.5d-71)) then
        tmp = i * (j * (x * y1))
    else if (y2 <= 1.3d-111) then
        tmp = c * (y4 * (y * y3))
    else if (y2 <= 1.66d+50) then
        tmp = a * (y3 * (z * 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 = y4 * (k * (y1 * y2));
	double tmp;
	if (y2 <= -1.2e+140) {
		tmp = t_1;
	} else if (y2 <= -8.5e-71) {
		tmp = i * (j * (x * y1));
	} else if (y2 <= 1.3e-111) {
		tmp = c * (y4 * (y * y3));
	} else if (y2 <= 1.66e+50) {
		tmp = a * (y3 * (z * 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 = y4 * (k * (y1 * y2))
	tmp = 0
	if y2 <= -1.2e+140:
		tmp = t_1
	elif y2 <= -8.5e-71:
		tmp = i * (j * (x * y1))
	elif y2 <= 1.3e-111:
		tmp = c * (y4 * (y * y3))
	elif y2 <= 1.66e+50:
		tmp = a * (y3 * (z * 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(y4 * Float64(k * Float64(y1 * y2)))
	tmp = 0.0
	if (y2 <= -1.2e+140)
		tmp = t_1;
	elseif (y2 <= -8.5e-71)
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	elseif (y2 <= 1.3e-111)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y2 <= 1.66e+50)
		tmp = Float64(a * Float64(y3 * Float64(z * 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 = y4 * (k * (y1 * y2));
	tmp = 0.0;
	if (y2 <= -1.2e+140)
		tmp = t_1;
	elseif (y2 <= -8.5e-71)
		tmp = i * (j * (x * y1));
	elseif (y2 <= 1.3e-111)
		tmp = c * (y4 * (y * y3));
	elseif (y2 <= 1.66e+50)
		tmp = a * (y3 * (z * 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[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.2e+140], t$95$1, If[LessEqual[y2, -8.5e-71], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.3e-111], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.66e+50], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y2 < -1.2e140 or 1.66000000000000004e50 < y2

   1. Initial program 15.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 15.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 46.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.4%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 46.4%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around inf 34.2%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 34.2%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 34.2%

       \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1\right)\right)} \]

   if -1.2e140 < y2 < -8.49999999999999988e-71

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 36.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 36.3%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 36.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 36.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 36.3%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 43.7%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.2%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 39.2%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 39.2%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 39.2%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 27.8%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 27.8%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 27.8%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 27.8%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 32.3%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 30.0%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 30.0%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 32.2%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 32.2%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]

   if -8.49999999999999988e-71 < y2 < 1.29999999999999991e-111

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 41.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 37.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 37.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 37.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 28.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 1.29999999999999991e-111 < y2 < 1.66000000000000004e50

   1. Initial program 27.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 43.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 43.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 43.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 43.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 46.3%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 36.1%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 36.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 38.8%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 38.8%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.2 \cdot 10^{+140}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -8.5 \cdot 10^{-71}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y2 \leq 1.3 \cdot 10^{-111}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y2 \leq 1.66 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \end{array} \]

Alternative 32: 22.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 12000000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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)))))
   (if (<= z -2.4e+71)
     t_1
     (if (<= z -1.02e-234)
       (* y1 (* k (* y2 y4)))
       (if (<= z 2.55e-228)
         (* y1 (* i (* x j)))
         (if (<= z 12000000000.0) (* y4 (* k (* y1 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));
	double tmp;
	if (z <= -2.4e+71) {
		tmp = t_1;
	} else if (z <= -1.02e-234) {
		tmp = y1 * (k * (y2 * y4));
	} else if (z <= 2.55e-228) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 12000000000.0) {
		tmp = y4 * (k * (y1 * 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))
    if (z <= (-2.4d+71)) then
        tmp = t_1
    else if (z <= (-1.02d-234)) then
        tmp = y1 * (k * (y2 * y4))
    else if (z <= 2.55d-228) then
        tmp = y1 * (i * (x * j))
    else if (z <= 12000000000.0d0) then
        tmp = y4 * (k * (y1 * 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));
	double tmp;
	if (z <= -2.4e+71) {
		tmp = t_1;
	} else if (z <= -1.02e-234) {
		tmp = y1 * (k * (y2 * y4));
	} else if (z <= 2.55e-228) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 12000000000.0) {
		tmp = y4 * (k * (y1 * 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))
	tmp = 0
	if z <= -2.4e+71:
		tmp = t_1
	elif z <= -1.02e-234:
		tmp = y1 * (k * (y2 * y4))
	elif z <= 2.55e-228:
		tmp = y1 * (i * (x * j))
	elif z <= 12000000000.0:
		tmp = y4 * (k * (y1 * 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(z * y1)))
	tmp = 0.0
	if (z <= -2.4e+71)
		tmp = t_1;
	elseif (z <= -1.02e-234)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (z <= 2.55e-228)
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	elseif (z <= 12000000000.0)
		tmp = Float64(y4 * Float64(k * Float64(y1 * 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));
	tmp = 0.0;
	if (z <= -2.4e+71)
		tmp = t_1;
	elseif (z <= -1.02e-234)
		tmp = y1 * (k * (y2 * y4));
	elseif (z <= 2.55e-228)
		tmp = y1 * (i * (x * j));
	elseif (z <= 12000000000.0)
		tmp = y4 * (k * (y1 * 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[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+71], t$95$1, If[LessEqual[z, -1.02e-234], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-228], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12000000000.0], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.39999999999999981e71 or 1.2e10 < z

   1. Initial program 17.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 33.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 33.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 33.1%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 33.1%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 35.2%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 36.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 33.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 33.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 35.5%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 35.5%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if -2.39999999999999981e71 < z < -1.01999999999999999e-234

   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 28.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 48.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 48.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 48.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 48.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 41.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in k around inf 28.2%

      \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y2\right)\right)} \cdot y1 \]

   if -1.01999999999999999e-234 < z < 2.5500000000000001e-228

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 55.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 46.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 46.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 46.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 46.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 42.1%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 42.1%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 42.1%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around -inf 35.6%

       \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]

   if 2.5500000000000001e-228 < z < 1.2e10

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 34.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around inf 30.1%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 30.1%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 30.1%

       \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 12000000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \]

Alternative 33: 21.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 9000000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -2.3e+71)
   (* a (* y3 (* z y1)))
   (if (<= z -3.6e-234)
     (* y1 (* k (* y2 y4)))
     (if (<= z 2.15e-228)
       (* y1 (* i (* x j)))
       (if (<= z 9000000000.0)
         (* y4 (* k (* y1 y2)))
         (* (* z y3) (* a y1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.3e+71) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= -3.6e-234) {
		tmp = y1 * (k * (y2 * y4));
	} else if (z <= 2.15e-228) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 9000000000.0) {
		tmp = y4 * (k * (y1 * y2));
	} else {
		tmp = (z * y3) * (a * y1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-2.3d+71)) then
        tmp = a * (y3 * (z * y1))
    else if (z <= (-3.6d-234)) then
        tmp = y1 * (k * (y2 * y4))
    else if (z <= 2.15d-228) then
        tmp = y1 * (i * (x * j))
    else if (z <= 9000000000.0d0) then
        tmp = y4 * (k * (y1 * y2))
    else
        tmp = (z * y3) * (a * y1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -2.3e+71) {
		tmp = a * (y3 * (z * y1));
	} else if (z <= -3.6e-234) {
		tmp = y1 * (k * (y2 * y4));
	} else if (z <= 2.15e-228) {
		tmp = y1 * (i * (x * j));
	} else if (z <= 9000000000.0) {
		tmp = y4 * (k * (y1 * y2));
	} else {
		tmp = (z * y3) * (a * y1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -2.3e+71:
		tmp = a * (y3 * (z * y1))
	elif z <= -3.6e-234:
		tmp = y1 * (k * (y2 * y4))
	elif z <= 2.15e-228:
		tmp = y1 * (i * (x * j))
	elif z <= 9000000000.0:
		tmp = y4 * (k * (y1 * y2))
	else:
		tmp = (z * y3) * (a * y1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -2.3e+71)
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	elseif (z <= -3.6e-234)
		tmp = Float64(y1 * Float64(k * Float64(y2 * y4)));
	elseif (z <= 2.15e-228)
		tmp = Float64(y1 * Float64(i * Float64(x * j)));
	elseif (z <= 9000000000.0)
		tmp = Float64(y4 * Float64(k * Float64(y1 * y2)));
	else
		tmp = Float64(Float64(z * y3) * Float64(a * y1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -2.3e+71)
		tmp = a * (y3 * (z * y1));
	elseif (z <= -3.6e-234)
		tmp = y1 * (k * (y2 * y4));
	elseif (z <= 2.15e-228)
		tmp = y1 * (i * (x * j));
	elseif (z <= 9000000000.0)
		tmp = y4 * (k * (y1 * y2));
	else
		tmp = (z * y3) * (a * y1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -2.3e+71], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-234], N[(y1 * N[(k * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-228], N[(y1 * N[(i * N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9000000000.0], N[(y4 * N[(k * N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y3), $MachinePrecision] * N[(a * y1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.3000000000000002e71

   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%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 32.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 32.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 32.4%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 32.4%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 40.5%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 38.8%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 35.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 35.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 36.9%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 36.9%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if -2.3000000000000002e71 < z < -3.5999999999999998e-234

   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 28.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 48.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 48.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 48.2%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 48.2%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 41.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in k around inf 28.2%

      \[\leadsto \color{blue}{\left(k \cdot \left(y4 \cdot y2\right)\right)} \cdot y1 \]

   if -3.5999999999999998e-234 < z < 2.15e-228

   1. Initial program 38.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 55.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 46.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 46.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 46.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 46.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 42.1%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 42.1%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 42.1%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around -inf 35.6%

       \[\leadsto \color{blue}{y1 \cdot \left(i \cdot \left(j \cdot x\right)\right)} \]

   if 2.15e-228 < z < 9e9

   1. Initial program 37.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 43.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in y2 around inf 34.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(k \cdot y1 - c \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto y4 \cdot \left(y2 \cdot \left(\color{blue}{y1 \cdot k} - c \cdot t\right)\right) \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{y4 \cdot \left(y2 \cdot \left(y1 \cdot k - c \cdot t\right)\right)} \]

   8. Taylor expanded in y1 around inf 30.1%

      \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y1 \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 30.1%

         \[\leadsto y4 \cdot \left(k \cdot \color{blue}{\left(y2 \cdot y1\right)}\right) \]

   10. Simplified 30.1%

       \[\leadsto y4 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y1\right)\right)} \]

   if 9e9 < z

   1. Initial program 16.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 33.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.7%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 33.7%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 33.7%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 33.7%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 30.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 34.4%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 31.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 34.3%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 34.3%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   11. Taylor expanded in a around 0 32.9%

       \[\leadsto \color{blue}{y1 \cdot \left(a \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative 32.9%

          \[\leadsto \color{blue}{\left(a \cdot \left(y3 \cdot z\right)\right) \cdot y1} \]

       2. *-commutative 32.9%

          \[\leadsto \color{blue}{\left(\left(y3 \cdot z\right) \cdot a\right)} \cdot y1 \]

       3. associate-*l* 35.7%

          \[\leadsto \color{blue}{\left(y3 \cdot z\right) \cdot \left(a \cdot y1\right)} \]

       4. *-commutative 35.7%

          \[\leadsto \color{blue}{\left(z \cdot y3\right)} \cdot \left(a \cdot y1\right) \]

   13. Simplified 35.7%

       \[\leadsto \color{blue}{\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-234}:\\ \;\;\;\;y1 \cdot \left(k \cdot \left(y2 \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-228}:\\ \;\;\;\;y1 \cdot \left(i \cdot \left(x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 9000000000:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y3\right) \cdot \left(a \cdot y1\right)\\ \end{array} \]

Alternative 34: 22.5% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -15500000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.15 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -15500000.0)
   (* a (* z (* y1 y3)))
   (if (<= y1 -2.15e-184)
     (* a (* y (* x b)))
     (if (<= y1 4.5e+19) (* c (* y4 (* y y3))) (* a (* y3 (* z y1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -15500000.0) {
		tmp = a * (z * (y1 * y3));
	} else if (y1 <= -2.15e-184) {
		tmp = a * (y * (x * b));
	} else if (y1 <= 4.5e+19) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-15500000.0d0)) then
        tmp = a * (z * (y1 * y3))
    else if (y1 <= (-2.15d-184)) then
        tmp = a * (y * (x * b))
    else if (y1 <= 4.5d+19) then
        tmp = c * (y4 * (y * y3))
    else
        tmp = a * (y3 * (z * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -15500000.0) {
		tmp = a * (z * (y1 * y3));
	} else if (y1 <= -2.15e-184) {
		tmp = a * (y * (x * b));
	} else if (y1 <= 4.5e+19) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = a * (y3 * (z * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -15500000.0:
		tmp = a * (z * (y1 * y3))
	elif y1 <= -2.15e-184:
		tmp = a * (y * (x * b))
	elif y1 <= 4.5e+19:
		tmp = c * (y4 * (y * y3))
	else:
		tmp = a * (y3 * (z * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -15500000.0)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	elseif (y1 <= -2.15e-184)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y1 <= 4.5e+19)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	else
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -15500000.0)
		tmp = a * (z * (y1 * y3));
	elseif (y1 <= -2.15e-184)
		tmp = a * (y * (x * b));
	elseif (y1 <= 4.5e+19)
		tmp = c * (y4 * (y * y3));
	else
		tmp = a * (y3 * (z * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -15500000.0], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.15e-184], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 4.5e+19], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -1.55e7

   1. Initial program 18.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 49.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 49.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 49.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 49.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 46.0%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 31.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 33.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 33.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 33.1%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 33.1%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   11. Taylor expanded in y3 around 0 31.5%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 33.2%

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       2. *-commutative 33.2%

          \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y1 \cdot y3\right)\right)} \]

   13. Simplified 33.2%

       \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y1 \cdot y3\right)\right)} \]

   if -1.55e7 < y1 < -2.15000000000000003e-184

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 50.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.0%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 50.0%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 39.7%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in y around inf 34.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -2.15000000000000003e-184 < y1 < 4.5e19

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.9%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 38.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 38.9%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 38.9%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 24.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 4.5e19 < y1

   1. Initial program 27.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 50.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.3%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 50.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 50.3%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 55.0%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 27.2%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 28.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 30.1%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 30.1%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -15500000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.15 \cdot 10^{-184}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 4.5 \cdot 10^{+19}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \end{array} \]

Alternative 35: 23.0% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -14200000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{-183}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -14200000.0)
   (* a (* z (* y1 y3)))
   (if (<= y1 -2.2e-183)
     (* a (* y (* x b)))
     (if (<= y1 1.55e+16) (* c (* y4 (* y y3))) (* i (* j (* x y1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -14200000.0) {
		tmp = a * (z * (y1 * y3));
	} else if (y1 <= -2.2e-183) {
		tmp = a * (y * (x * b));
	} else if (y1 <= 1.55e+16) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y1 <= (-14200000.0d0)) then
        tmp = a * (z * (y1 * y3))
    else if (y1 <= (-2.2d-183)) then
        tmp = a * (y * (x * b))
    else if (y1 <= 1.55d+16) then
        tmp = c * (y4 * (y * y3))
    else
        tmp = i * (j * (x * y1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -14200000.0) {
		tmp = a * (z * (y1 * y3));
	} else if (y1 <= -2.2e-183) {
		tmp = a * (y * (x * b));
	} else if (y1 <= 1.55e+16) {
		tmp = c * (y4 * (y * y3));
	} else {
		tmp = i * (j * (x * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -14200000.0:
		tmp = a * (z * (y1 * y3))
	elif y1 <= -2.2e-183:
		tmp = a * (y * (x * b))
	elif y1 <= 1.55e+16:
		tmp = c * (y4 * (y * y3))
	else:
		tmp = i * (j * (x * y1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -14200000.0)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	elseif (y1 <= -2.2e-183)
		tmp = Float64(a * Float64(y * Float64(x * b)));
	elseif (y1 <= 1.55e+16)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	else
		tmp = Float64(i * Float64(j * Float64(x * y1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y1 <= -14200000.0)
		tmp = a * (z * (y1 * y3));
	elseif (y1 <= -2.2e-183)
		tmp = a * (y * (x * b));
	elseif (y1 <= 1.55e+16)
		tmp = c * (y4 * (y * y3));
	else
		tmp = i * (j * (x * y1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -14200000.0], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.2e-183], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.55e+16], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -1.42e7

   1. Initial program 18.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 22.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 49.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 49.6%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 49.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 49.6%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 49.6%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 46.0%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 31.5%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 33.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 33.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 33.1%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 33.1%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   11. Taylor expanded in y3 around 0 31.5%

       \[\leadsto a \cdot \color{blue}{\left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 33.2%

          \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

       2. *-commutative 33.2%

          \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y1 \cdot y3\right)\right)} \]

   13. Simplified 33.2%

       \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(y1 \cdot y3\right)\right)} \]

   if -1.42e7 < y1 < -2.2e-183

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 50.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 50.0%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 50.0%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 39.7%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in y around inf 34.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

   if -2.2e-183 < y1 < 1.55e16

   1. Initial program 29.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in b around 0 38.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(\color{blue}{y2 \cdot t} - y \cdot y3\right)\right) \]

      2. *-commutative 38.2%

         \[\leadsto y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - \color{blue}{y3 \cdot y}\right)\right) \]

   7. Simplified 38.2%

      \[\leadsto \color{blue}{y4 \cdot \left(y1 \cdot \left(k \cdot y2 - y3 \cdot j\right) - c \cdot \left(y2 \cdot t - y3 \cdot y\right)\right)} \]

   8. Taylor expanded in y around inf 24.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if 1.55e16 < y1

   1. Initial program 27.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 51.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 51.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 51.0%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 51.0%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in x around inf 45.5%

      \[\leadsto \color{blue}{y1 \cdot \left(\left(i \cdot j - a \cdot y2\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 48.5%

         \[\leadsto \color{blue}{\left(y1 \cdot \left(i \cdot j - a \cdot y2\right)\right) \cdot x} \]

      2. *-commutative 48.5%

         \[\leadsto \left(y1 \cdot \left(\color{blue}{j \cdot i} - a \cdot y2\right)\right) \cdot x \]

      3. *-commutative 48.5%

         \[\leadsto \left(y1 \cdot \left(j \cdot i - \color{blue}{y2 \cdot a}\right)\right) \cdot x \]

   9. Simplified 48.5%

      \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i - y2 \cdot a\right)\right) \cdot x} \]

   10. Taylor expanded in j around inf 29.7%

       \[\leadsto \color{blue}{\left(i \cdot \left(y1 \cdot j\right)\right)} \cdot x \]
   11. Step-by-step derivation

       1. *-commutative 29.7%

          \[\leadsto \color{blue}{\left(\left(y1 \cdot j\right) \cdot i\right)} \cdot x \]

       2. associate-*r* 29.7%

          \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   12. Simplified 29.7%

       \[\leadsto \color{blue}{\left(y1 \cdot \left(j \cdot i\right)\right)} \cdot x \]

   13. Taylor expanded in y1 around 0 35.3%

       \[\leadsto \color{blue}{i \cdot \left(y1 \cdot \left(j \cdot x\right)\right)} \]
   14. Step-by-step derivation

       1. associate-*r* 35.3%

          \[\leadsto i \cdot \color{blue}{\left(\left(y1 \cdot j\right) \cdot x\right)} \]

       2. *-commutative 35.3%

          \[\leadsto i \cdot \left(\color{blue}{\left(j \cdot y1\right)} \cdot x\right) \]

       3. associate-*l* 38.1%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(y1 \cdot x\right)\right)} \]

   15. Simplified 38.1%

       \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(y1 \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y1 \leq -14200000:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq -2.2 \cdot 10^{-183}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y1 \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(x \cdot y1\right)\right)\\ \end{array} \]

Alternative 36: 21.9% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+104} \lor \neg \left(z \leq 3100000000000\right):\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= z -8e+104) (not (<= z 3100000000000.0)))
   (* a (* y3 (* z y1)))
   (* 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) {
	double tmp;
	if ((z <= -8e+104) || !(z <= 3100000000000.0)) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((z <= (-8d+104)) .or. (.not. (z <= 3100000000000.0d0))) then
        tmp = a * (y3 * (z * y1))
    else
        tmp = a * (y * (x * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((z <= -8e+104) || !(z <= 3100000000000.0)) {
		tmp = a * (y3 * (z * y1));
	} else {
		tmp = a * (y * (x * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (z <= -8e+104) or not (z <= 3100000000000.0):
		tmp = a * (y3 * (z * y1))
	else:
		tmp = a * (y * (x * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((z <= -8e+104) || !(z <= 3100000000000.0))
		tmp = Float64(a * Float64(y3 * Float64(z * y1)));
	else
		tmp = Float64(a * Float64(y * Float64(x * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((z <= -8e+104) || ~((z <= 3100000000000.0)))
		tmp = a * (y3 * (z * y1));
	else
		tmp = a * (y * (x * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[z, -8e+104], N[Not[LessEqual[z, 3100000000000.0]], $MachinePrecision]], N[(a * N[(y3 * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e104 or 3.1e12 < z

   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 22.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y1 around inf 33.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1} \]
   5. Step-by-step derivation

      1. mul-1-neg 33.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right) \cdot y1 \]

      2. mul-1-neg 33.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right) \cdot y1 \]

      3. sub-neg 33.8%

         \[\leadsto \left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right) \cdot y1 \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{\left(\left(-a \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(i \cdot \left(j \cdot x - k \cdot z\right) + y4 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y1} \]

   7. Taylor expanded in i around 0 35.9%

      \[\leadsto \color{blue}{\left(y4 \cdot \left(k \cdot y2 - y3 \cdot j\right) - \left(x \cdot y2 - y3 \cdot z\right) \cdot a\right) \cdot y1} \]

   8. Taylor expanded in z around inf 38.0%

      \[\leadsto \color{blue}{a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 34.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 34.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(y3 \cdot y1\right)} \cdot z\right) \]

      3. associate-*l* 37.0%

         \[\leadsto a \cdot \color{blue}{\left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   10. Simplified 37.0%

       \[\leadsto \color{blue}{a \cdot \left(y3 \cdot \left(y1 \cdot z\right)\right)} \]

   if -8e104 < z < 3.1e12

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in b around inf 37.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 37.2%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

      2. mul-1-neg 37.2%

         \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

   6. Simplified 37.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 27.4%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

   8. Taylor expanded in y around inf 19.6%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+104} \lor \neg \left(z \leq 3100000000000\right):\\ \;\;\;\;a \cdot \left(y3 \cdot \left(z \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 37: 17.3% 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 25.6%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 28.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

4. Taylor expanded in b around inf 33.8%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
5. Step-by-step derivation

   1. associate--l+ 33.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   2. mul-1-neg 33.8%

      \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

6. Simplified 33.8%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

7. Taylor expanded in x around inf 27.6%

   \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

8. Taylor expanded in a around inf 17.4%

   \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
9. Step-by-step derivation

   1. *-commutative 17.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(b \cdot x\right)\right) \cdot y} \]

   2. associate-*r* 17.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot x\right) \cdot y\right)} \]

   3. associate-*l* 15.1%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot \left(x \cdot y\right)\right)} \]

10. Simplified 15.1%

    \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(x \cdot y\right)\right)} \]

11. Final simplification 15.1%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]

Alternative 38: 17.3% 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 25.6%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 28.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

4. Taylor expanded in b around inf 33.8%

   \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(y \cdot x - t \cdot z\right) + y4 \cdot \left(t \cdot j - k \cdot y\right)\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)} \]
5. Step-by-step derivation

   1. associate--l+ 33.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(-1 \cdot \left(k \cdot z\right) + j \cdot x\right)\right)\right)} \]

   2. mul-1-neg 33.8%

      \[\leadsto b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\color{blue}{\left(-k \cdot z\right)} + j \cdot x\right)\right)\right) \]

6. Simplified 33.8%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot \left(y \cdot x - t \cdot z\right) + \left(y4 \cdot \left(t \cdot j - k \cdot y\right) - y0 \cdot \left(\left(-k \cdot z\right) + j \cdot x\right)\right)\right)} \]

7. Taylor expanded in x around inf 27.6%

   \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]

8. Taylor expanded in y around inf 17.0%

   \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

9. Final simplification 17.0%

   \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]

Developer target: 28.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot c - y5 \cdot a\\ t_2 := x \cdot y2 - z \cdot y3\\ t_3 := y2 \cdot t - y3 \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := y4 \cdot b - y5 \cdot i\\ t_6 := \left(j \cdot t - k \cdot y\right) \cdot t_5\\ t_7 := b \cdot a - i \cdot c\\ t_8 := t_7 \cdot \left(y \cdot x - t \cdot z\right)\\ t_9 := j \cdot x - k \cdot z\\ t_10 := \left(b \cdot y0 - i \cdot y1\right) \cdot t_9\\ t_11 := t_9 \cdot \left(y0 \cdot b - i \cdot y1\right)\\ t_12 := y4 \cdot y1 - y5 \cdot y0\\ t_13 := t_4 \cdot t_12\\ t_14 := \left(y2 \cdot k - y3 \cdot j\right) \cdot t_12\\ t_15 := \left(\left(\left(\left(k \cdot y\right) \cdot \left(y5 \cdot i\right) - \left(y \cdot b\right) \cdot \left(y4 \cdot k\right)\right) - \left(y5 \cdot t\right) \cdot \left(i \cdot j\right)\right) - \left(t_3 \cdot t_1 - t_14\right)\right) + \left(t_8 - \left(t_11 - \left(y2 \cdot x - y3 \cdot z\right) \cdot \left(c \cdot y0 - y1 \cdot a\right)\right)\right)\\ t_16 := \left(\left(t_6 - \left(y3 \cdot y\right) \cdot \left(y5 \cdot a - y4 \cdot c\right)\right) + \left(\left(y5 \cdot a\right) \cdot \left(t \cdot y2\right) + t_13\right)\right) + \left(t_2 \cdot \left(c \cdot y0 - a \cdot y1\right) - \left(t_10 - \left(y \cdot x - z \cdot t\right) \cdot t_7\right)\right)\\ t_17 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;y4 < -7.206256231996481 \cdot 10^{+60}:\\ \;\;\;\;\left(t_8 - \left(t_11 - t_6\right)\right) - \left(\frac{t_3}{\frac{1}{t_1}} - t_14\right)\\ \mathbf{elif}\;y4 < -3.364603505246317 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(\left(\left(t \cdot c\right) \cdot \left(i \cdot z\right) - \left(a \cdot t\right) \cdot \left(b \cdot z\right)\right) - \left(y \cdot c\right) \cdot \left(i \cdot x\right)\right) - t_10\right) + \left(\left(y0 \cdot c - a \cdot y1\right) \cdot t_2 - \left(t_17 \cdot \left(y4 \cdot c - a \cdot y5\right) - \left(y1 \cdot y4 - y5 \cdot y0\right) \cdot t_4\right)\right)\\ \mathbf{elif}\;y4 < -1.2000065055686116 \cdot 10^{-105}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 6.718963124057495 \cdot 10^{-279}:\\ \;\;\;\;t_15\\ \mathbf{elif}\;y4 < 4.77962681403792 \cdot 10^{-222}:\\ \;\;\;\;t_16\\ \mathbf{elif}\;y4 < 2.2852241541266835 \cdot 10^{-175}:\\ \;\;\;\;t_15\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(k \cdot \left(i \cdot \left(z \cdot y1\right)\right) - \left(j \cdot \left(i \cdot \left(x \cdot y1\right)\right) + y0 \cdot \left(k \cdot \left(z \cdot b\right)\right)\right)\right)\right) + \left(z \cdot \left(y3 \cdot \left(a \cdot y1\right)\right) - \left(y2 \cdot \left(x \cdot \left(a \cdot y1\right)\right) + y0 \cdot \left(z \cdot \left(c \cdot y3\right)\right)\right)\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot t_5\right) - t_17 \cdot t_1\right) + t_13\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y4 c) (* y5 a)))
        (t_2 (- (* x y2) (* z y3)))
        (t_3 (- (* y2 t) (* y3 y)))
        (t_4 (- (* k y2) (* j y3)))
        (t_5 (- (* y4 b) (* y5 i)))
        (t_6 (* (- (* j t) (* k y)) t_5))
        (t_7 (- (* b a) (* i c)))
        (t_8 (* t_7 (- (* y x) (* t z))))
        (t_9 (- (* j x) (* k z)))
        (t_10 (* (- (* b y0) (* i y1)) t_9))
        (t_11 (* t_9 (- (* y0 b) (* i y1))))
        (t_12 (- (* y4 y1) (* y5 y0)))
        (t_13 (* t_4 t_12))
        (t_14 (* (- (* y2 k) (* y3 j)) t_12))
        (t_15
         (+
          (-
           (-
            (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k)))
            (* (* y5 t) (* i j)))
           (- (* t_3 t_1) t_14))
          (- t_8 (- t_11 (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))))
        (t_16
         (+
          (+
           (- t_6 (* (* y3 y) (- (* y5 a) (* y4 c))))
           (+ (* (* y5 a) (* t y2)) t_13))
          (-
           (* t_2 (- (* c y0) (* a y1)))
           (- t_10 (* (- (* y x) (* z t)) t_7)))))
        (t_17 (- (* t y2) (* y y3))))
   (if (< y4 -7.206256231996481e+60)
     (- (- t_8 (- t_11 t_6)) (- (/ t_3 (/ 1.0 t_1)) t_14))
     (if (< y4 -3.364603505246317e-66)
       (+
        (-
         (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x)))
         t_10)
        (-
         (* (- (* y0 c) (* a y1)) t_2)
         (- (* t_17 (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) t_4))))
       (if (< y4 -1.2000065055686116e-105)
         t_16
         (if (< y4 6.718963124057495e-279)
           t_15
           (if (< y4 4.77962681403792e-222)
             t_16
             (if (< y4 2.2852241541266835e-175)
               t_15
               (+
                (-
                 (+
                  (+
                   (-
                    (* (- (* x y) (* z t)) (- (* a b) (* c i)))
                    (-
                     (* k (* i (* z y1)))
                     (+ (* j (* i (* x y1))) (* y0 (* k (* z b))))))
                   (-
                    (* z (* y3 (* a y1)))
                    (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3))))))
                  (* (- (* t j) (* y k)) t_5))
                 (* t_17 t_1))
                t_13)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_10
    real(8) :: t_11
    real(8) :: t_12
    real(8) :: t_13
    real(8) :: t_14
    real(8) :: t_15
    real(8) :: t_16
    real(8) :: t_17
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: t_9
    real(8) :: tmp
    t_1 = (y4 * c) - (y5 * a)
    t_2 = (x * y2) - (z * y3)
    t_3 = (y2 * t) - (y3 * y)
    t_4 = (k * y2) - (j * y3)
    t_5 = (y4 * b) - (y5 * i)
    t_6 = ((j * t) - (k * y)) * t_5
    t_7 = (b * a) - (i * c)
    t_8 = t_7 * ((y * x) - (t * z))
    t_9 = (j * x) - (k * z)
    t_10 = ((b * y0) - (i * y1)) * t_9
    t_11 = t_9 * ((y0 * b) - (i * y1))
    t_12 = (y4 * y1) - (y5 * y0)
    t_13 = t_4 * t_12
    t_14 = ((y2 * k) - (y3 * j)) * t_12
    t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
    t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
    t_17 = (t * y2) - (y * y3)
    if (y4 < (-7.206256231996481d+60)) then
        tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0d0 / t_1)) - t_14)
    else if (y4 < (-3.364603505246317d-66)) then
        tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
    else if (y4 < (-1.2000065055686116d-105)) then
        tmp = t_16
    else if (y4 < 6.718963124057495d-279) then
        tmp = t_15
    else if (y4 < 4.77962681403792d-222) then
        tmp = t_16
    else if (y4 < 2.2852241541266835d-175) then
        tmp = t_15
    else
        tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * c) - (y5 * a);
	double t_2 = (x * y2) - (z * y3);
	double t_3 = (y2 * t) - (y3 * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = (y4 * b) - (y5 * i);
	double t_6 = ((j * t) - (k * y)) * t_5;
	double t_7 = (b * a) - (i * c);
	double t_8 = t_7 * ((y * x) - (t * z));
	double t_9 = (j * x) - (k * z);
	double t_10 = ((b * y0) - (i * y1)) * t_9;
	double t_11 = t_9 * ((y0 * b) - (i * y1));
	double t_12 = (y4 * y1) - (y5 * y0);
	double t_13 = t_4 * t_12;
	double t_14 = ((y2 * k) - (y3 * j)) * t_12;
	double t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	double t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	double t_17 = (t * y2) - (y * y3);
	double tmp;
	if (y4 < -7.206256231996481e+60) {
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	} else if (y4 < -3.364603505246317e-66) {
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	} else if (y4 < -1.2000065055686116e-105) {
		tmp = t_16;
	} else if (y4 < 6.718963124057495e-279) {
		tmp = t_15;
	} else if (y4 < 4.77962681403792e-222) {
		tmp = t_16;
	} else if (y4 < 2.2852241541266835e-175) {
		tmp = t_15;
	} else {
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y4 * c) - (y5 * a)
	t_2 = (x * y2) - (z * y3)
	t_3 = (y2 * t) - (y3 * y)
	t_4 = (k * y2) - (j * y3)
	t_5 = (y4 * b) - (y5 * i)
	t_6 = ((j * t) - (k * y)) * t_5
	t_7 = (b * a) - (i * c)
	t_8 = t_7 * ((y * x) - (t * z))
	t_9 = (j * x) - (k * z)
	t_10 = ((b * y0) - (i * y1)) * t_9
	t_11 = t_9 * ((y0 * b) - (i * y1))
	t_12 = (y4 * y1) - (y5 * y0)
	t_13 = t_4 * t_12
	t_14 = ((y2 * k) - (y3 * j)) * t_12
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))))
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)))
	t_17 = (t * y2) - (y * y3)
	tmp = 0
	if y4 < -7.206256231996481e+60:
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14)
	elif y4 < -3.364603505246317e-66:
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)))
	elif y4 < -1.2000065055686116e-105:
		tmp = t_16
	elif y4 < 6.718963124057495e-279:
		tmp = t_15
	elif y4 < 4.77962681403792e-222:
		tmp = t_16
	elif y4 < 2.2852241541266835e-175:
		tmp = t_15
	else:
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y4 * c) - Float64(y5 * a))
	t_2 = Float64(Float64(x * y2) - Float64(z * y3))
	t_3 = Float64(Float64(y2 * t) - Float64(y3 * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(Float64(y4 * b) - Float64(y5 * i))
	t_6 = Float64(Float64(Float64(j * t) - Float64(k * y)) * t_5)
	t_7 = Float64(Float64(b * a) - Float64(i * c))
	t_8 = Float64(t_7 * Float64(Float64(y * x) - Float64(t * z)))
	t_9 = Float64(Float64(j * x) - Float64(k * z))
	t_10 = Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_9)
	t_11 = Float64(t_9 * Float64(Float64(y0 * b) - Float64(i * y1)))
	t_12 = Float64(Float64(y4 * y1) - Float64(y5 * y0))
	t_13 = Float64(t_4 * t_12)
	t_14 = Float64(Float64(Float64(y2 * k) - Float64(y3 * j)) * t_12)
	t_15 = Float64(Float64(Float64(Float64(Float64(Float64(k * y) * Float64(y5 * i)) - Float64(Float64(y * b) * Float64(y4 * k))) - Float64(Float64(y5 * t) * Float64(i * j))) - Float64(Float64(t_3 * t_1) - t_14)) + Float64(t_8 - Float64(t_11 - Float64(Float64(Float64(y2 * x) - Float64(y3 * z)) * Float64(Float64(c * y0) - Float64(y1 * a))))))
	t_16 = Float64(Float64(Float64(t_6 - Float64(Float64(y3 * y) * Float64(Float64(y5 * a) - Float64(y4 * c)))) + Float64(Float64(Float64(y5 * a) * Float64(t * y2)) + t_13)) + Float64(Float64(t_2 * Float64(Float64(c * y0) - Float64(a * y1))) - Float64(t_10 - Float64(Float64(Float64(y * x) - Float64(z * t)) * t_7))))
	t_17 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (y4 < -7.206256231996481e+60)
		tmp = Float64(Float64(t_8 - Float64(t_11 - t_6)) - Float64(Float64(t_3 / Float64(1.0 / t_1)) - t_14));
	elseif (y4 < -3.364603505246317e-66)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * c) * Float64(i * z)) - Float64(Float64(a * t) * Float64(b * z))) - Float64(Float64(y * c) * Float64(i * x))) - t_10) + Float64(Float64(Float64(Float64(y0 * c) - Float64(a * y1)) * t_2) - Float64(Float64(t_17 * Float64(Float64(y4 * c) - Float64(a * y5))) - Float64(Float64(Float64(y1 * y4) - Float64(y5 * y0)) * t_4))));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(k * Float64(i * Float64(z * y1))) - Float64(Float64(j * Float64(i * Float64(x * y1))) + Float64(y0 * Float64(k * Float64(z * b)))))) + Float64(Float64(z * Float64(y3 * Float64(a * y1))) - Float64(Float64(y2 * Float64(x * Float64(a * y1))) + Float64(y0 * Float64(z * Float64(c * y3)))))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * t_5)) - Float64(t_17 * t_1)) + t_13);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y4 * c) - (y5 * a);
	t_2 = (x * y2) - (z * y3);
	t_3 = (y2 * t) - (y3 * y);
	t_4 = (k * y2) - (j * y3);
	t_5 = (y4 * b) - (y5 * i);
	t_6 = ((j * t) - (k * y)) * t_5;
	t_7 = (b * a) - (i * c);
	t_8 = t_7 * ((y * x) - (t * z));
	t_9 = (j * x) - (k * z);
	t_10 = ((b * y0) - (i * y1)) * t_9;
	t_11 = t_9 * ((y0 * b) - (i * y1));
	t_12 = (y4 * y1) - (y5 * y0);
	t_13 = t_4 * t_12;
	t_14 = ((y2 * k) - (y3 * j)) * t_12;
	t_15 = (((((k * y) * (y5 * i)) - ((y * b) * (y4 * k))) - ((y5 * t) * (i * j))) - ((t_3 * t_1) - t_14)) + (t_8 - (t_11 - (((y2 * x) - (y3 * z)) * ((c * y0) - (y1 * a)))));
	t_16 = ((t_6 - ((y3 * y) * ((y5 * a) - (y4 * c)))) + (((y5 * a) * (t * y2)) + t_13)) + ((t_2 * ((c * y0) - (a * y1))) - (t_10 - (((y * x) - (z * t)) * t_7)));
	t_17 = (t * y2) - (y * y3);
	tmp = 0.0;
	if (y4 < -7.206256231996481e+60)
		tmp = (t_8 - (t_11 - t_6)) - ((t_3 / (1.0 / t_1)) - t_14);
	elseif (y4 < -3.364603505246317e-66)
		tmp = (((((t * c) * (i * z)) - ((a * t) * (b * z))) - ((y * c) * (i * x))) - t_10) + ((((y0 * c) - (a * y1)) * t_2) - ((t_17 * ((y4 * c) - (a * y5))) - (((y1 * y4) - (y5 * y0)) * t_4)));
	elseif (y4 < -1.2000065055686116e-105)
		tmp = t_16;
	elseif (y4 < 6.718963124057495e-279)
		tmp = t_15;
	elseif (y4 < 4.77962681403792e-222)
		tmp = t_16;
	elseif (y4 < 2.2852241541266835e-175)
		tmp = t_15;
	else
		tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - ((k * (i * (z * y1))) - ((j * (i * (x * y1))) + (y0 * (k * (z * b)))))) + ((z * (y3 * (a * y1))) - ((y2 * (x * (a * y1))) + (y0 * (z * (c * y3)))))) + (((t * j) - (y * k)) * t_5)) - (t_17 * t_1)) + t_13;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y2 * t), $MachinePrecision] - N[(y3 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(N[(b * a), $MachinePrecision] - N[(i * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(t$95$7 * N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$9), $MachinePrecision]}, Block[{t$95$11 = N[(t$95$9 * N[(N[(y0 * b), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$12 = N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$13 = N[(t$95$4 * t$95$12), $MachinePrecision]}, Block[{t$95$14 = N[(N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] * t$95$12), $MachinePrecision]}, Block[{t$95$15 = N[(N[(N[(N[(N[(N[(k * y), $MachinePrecision] * N[(y5 * i), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * N[(y4 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y5 * t), $MachinePrecision] * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 * t$95$1), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 - N[(t$95$11 - N[(N[(N[(y2 * x), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$16 = N[(N[(N[(t$95$6 - N[(N[(y3 * y), $MachinePrecision] * N[(N[(y5 * a), $MachinePrecision] - N[(y4 * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y5 * a), $MachinePrecision] * N[(t * y2), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$10 - N[(N[(N[(y * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$7), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$17 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[Less[y4, -7.206256231996481e+60], N[(N[(t$95$8 - N[(t$95$11 - t$95$6), $MachinePrecision]), $MachinePrecision] - N[(N[(t$95$3 / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$14), $MachinePrecision]), $MachinePrecision], If[Less[y4, -3.364603505246317e-66], N[(N[(N[(N[(N[(N[(t * c), $MachinePrecision] * N[(i * z), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * c), $MachinePrecision] * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$10), $MachinePrecision] + N[(N[(N[(N[(y0 * c), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] - N[(N[(t$95$17 * N[(N[(y4 * c), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y4, -1.2000065055686116e-105], t$95$16, If[Less[y4, 6.718963124057495e-279], t$95$15, If[Less[y4, 4.77962681403792e-222], t$95$16, If[Less[y4, 2.2852241541266835e-175], t$95$15, N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * N[(i * N[(z * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(k * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y3 * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y2 * N[(x * N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(z * N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t$95$17 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$13), $MachinePrecision]]]]]]]]]]]]]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y4 -7.206256231996481e+60) (- (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))))) (- (/ (- (* y2 t) (* y3 y)) (/ 1.0 (- (* y4 c) (* y5 a)))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (if (< y4 -3.364603505246317e-66) (+ (- (- (- (* (* t c) (* i z)) (* (* a t) (* b z))) (* (* y c) (* i x))) (* (- (* b y0) (* i y1)) (- (* j x) (* k z)))) (- (* (- (* y0 c) (* a y1)) (- (* x y2) (* z y3))) (- (* (- (* t y2) (* y y3)) (- (* y4 c) (* a y5))) (* (- (* y1 y4) (* y5 y0)) (- (* k y2) (* j y3)))))) (if (< y4 -1.2000065055686116e-105) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 6.718963124057495e-279) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (if (< y4 4.77962681403792e-222) (+ (+ (- (* (- (* j t) (* k y)) (- (* y4 b) (* y5 i))) (* (* y3 y) (- (* y5 a) (* y4 c)))) (+ (* (* y5 a) (* t y2)) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))) (- (* (- (* b y0) (* i y1)) (- (* j x) (* k z))) (* (- (* y x) (* z t)) (- (* b a) (* i c)))))) (if (< y4 2.2852241541266835e-175) (+ (- (- (- (* (* k y) (* y5 i)) (* (* y b) (* y4 k))) (* (* y5 t) (* i j))) (- (* (- (* y2 t) (* y3 y)) (- (* y4 c) (* y5 a))) (* (- (* y2 k) (* y3 j)) (- (* y4 y1) (* y5 y0))))) (- (* (- (* b a) (* i c)) (- (* y x) (* t z))) (- (* (- (* j x) (* k z)) (- (* y0 b) (* i y1))) (* (- (* y2 x) (* y3 z)) (- (* c y0) (* y1 a)))))) (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (- (* k (* i (* z y1))) (+ (* j (* i (* x y1))) (* y0 (* k (* z b)))))) (- (* z (* y3 (* a y1))) (+ (* y2 (* x (* a y1))) (* y0 (* z (* c y3)))))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))))))))

  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))