Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.8% → 36.7%

Time: 1.6min

Alternatives: 38

Speedup: 5.5×

• 89.0% 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: 30.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 36.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ t_2 := a \cdot b - c \cdot i\\ t_3 := i \cdot y1 - b \cdot y0\\ t_4 := x \cdot \left(\left(y \cdot t_2 + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_3\right)\\ t_5 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \left(x \cdot t_2\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+88}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot t_5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+27}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t_5\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+179}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+216}:\\ \;\;\;\;j \cdot \left(x \cdot t_3\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+251}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          z
          (+
           (* y3 (- (* a y1) (* c y0)))
           (+ (* k (- (* b y0) (* i y1))) (* t (- (* c i) (* a b)))))))
        (t_2 (- (* a b) (* c i)))
        (t_3 (- (* i y1) (* b y0)))
        (t_4 (* x (+ (+ (* y t_2) (* y2 (- (* c y0) (* a y1)))) (* j t_3))))
        (t_5 (* c (- (* y y3) (* t y2)))))
   (if (<= x -2.1e+213)
     (* y (* x t_2))
     (if (<= x -1.3e+88)
       t_4
       (if (<= x -3.9e-38)
         (*
          i
          (-
           (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))
           (* c (- (* x y) (* z t)))))
         (if (<= x -1.5e-132)
           (* j (* t (- (* b y4) (* i y5))))
           (if (<= x -4.5e-212)
             t_1
             (if (<= x 7e-202)
               (* y4 t_5)
               (if (<= x 1.25e-157)
                 t_1
                 (if (<= x 1.95e+27)
                   (*
                    y4
                    (+
                     (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
                     t_5))
                   (if (<= x 1.16e+179)
                     (* y2 (* a (- (* t y5) (* x y1))))
                     (if (<= x 3.4e+216)
                       (* j (* x t_3))
                       (if (<= x 4.6e+251)
                         t_4
                         (* y0 (* x (- (* c y2) (* b j)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	double t_2 = (a * b) - (c * i);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * t_2) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	double t_5 = c * ((y * y3) - (t * y2));
	double tmp;
	if (x <= -2.1e+213) {
		tmp = y * (x * t_2);
	} else if (x <= -1.3e+88) {
		tmp = t_4;
	} else if (x <= -3.9e-38) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * ((x * y) - (z * t))));
	} else if (x <= -1.5e-132) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (x <= -4.5e-212) {
		tmp = t_1;
	} else if (x <= 7e-202) {
		tmp = y4 * t_5;
	} else if (x <= 1.25e-157) {
		tmp = t_1;
	} else if (x <= 1.95e+27) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_5);
	} else if (x <= 1.16e+179) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (x <= 3.4e+216) {
		tmp = j * (x * t_3);
	} else if (x <= 4.6e+251) {
		tmp = t_4;
	} else {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	}
	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 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
    t_2 = (a * b) - (c * i)
    t_3 = (i * y1) - (b * y0)
    t_4 = x * (((y * t_2) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
    t_5 = c * ((y * y3) - (t * y2))
    if (x <= (-2.1d+213)) then
        tmp = y * (x * t_2)
    else if (x <= (-1.3d+88)) then
        tmp = t_4
    else if (x <= (-3.9d-38)) then
        tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * ((x * y) - (z * t))))
    else if (x <= (-1.5d-132)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (x <= (-4.5d-212)) then
        tmp = t_1
    else if (x <= 7d-202) then
        tmp = y4 * t_5
    else if (x <= 1.25d-157) then
        tmp = t_1
    else if (x <= 1.95d+27) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_5)
    else if (x <= 1.16d+179) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (x <= 3.4d+216) then
        tmp = j * (x * t_3)
    else if (x <= 4.6d+251) then
        tmp = t_4
    else
        tmp = y0 * (x * ((c * y2) - (b * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	double t_2 = (a * b) - (c * i);
	double t_3 = (i * y1) - (b * y0);
	double t_4 = x * (((y * t_2) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	double t_5 = c * ((y * y3) - (t * y2));
	double tmp;
	if (x <= -2.1e+213) {
		tmp = y * (x * t_2);
	} else if (x <= -1.3e+88) {
		tmp = t_4;
	} else if (x <= -3.9e-38) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * ((x * y) - (z * t))));
	} else if (x <= -1.5e-132) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (x <= -4.5e-212) {
		tmp = t_1;
	} else if (x <= 7e-202) {
		tmp = y4 * t_5;
	} else if (x <= 1.25e-157) {
		tmp = t_1;
	} else if (x <= 1.95e+27) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_5);
	} else if (x <= 1.16e+179) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (x <= 3.4e+216) {
		tmp = j * (x * t_3);
	} else if (x <= 4.6e+251) {
		tmp = t_4;
	} else {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
	t_2 = (a * b) - (c * i)
	t_3 = (i * y1) - (b * y0)
	t_4 = x * (((y * t_2) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3))
	t_5 = c * ((y * y3) - (t * y2))
	tmp = 0
	if x <= -2.1e+213:
		tmp = y * (x * t_2)
	elif x <= -1.3e+88:
		tmp = t_4
	elif x <= -3.9e-38:
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * ((x * y) - (z * t))))
	elif x <= -1.5e-132:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif x <= -4.5e-212:
		tmp = t_1
	elif x <= 7e-202:
		tmp = y4 * t_5
	elif x <= 1.25e-157:
		tmp = t_1
	elif x <= 1.95e+27:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_5)
	elif x <= 1.16e+179:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif x <= 3.4e+216:
		tmp = j * (x * t_3)
	elif x <= 4.6e+251:
		tmp = t_4
	else:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))))
	t_2 = Float64(Float64(a * b) - Float64(c * i))
	t_3 = Float64(Float64(i * y1) - Float64(b * y0))
	t_4 = Float64(x * Float64(Float64(Float64(y * t_2) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_3)))
	t_5 = Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))
	tmp = 0.0
	if (x <= -2.1e+213)
		tmp = Float64(y * Float64(x * t_2));
	elseif (x <= -1.3e+88)
		tmp = t_4;
	elseif (x <= -3.9e-38)
		tmp = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))) - Float64(c * Float64(Float64(x * y) - Float64(z * t)))));
	elseif (x <= -1.5e-132)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (x <= -4.5e-212)
		tmp = t_1;
	elseif (x <= 7e-202)
		tmp = Float64(y4 * t_5);
	elseif (x <= 1.25e-157)
		tmp = t_1;
	elseif (x <= 1.95e+27)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_5));
	elseif (x <= 1.16e+179)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (x <= 3.4e+216)
		tmp = Float64(j * Float64(x * t_3));
	elseif (x <= 4.6e+251)
		tmp = t_4;
	else
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	t_2 = (a * b) - (c * i);
	t_3 = (i * y1) - (b * y0);
	t_4 = x * (((y * t_2) + (y2 * ((c * y0) - (a * y1)))) + (j * t_3));
	t_5 = c * ((y * y3) - (t * y2));
	tmp = 0.0;
	if (x <= -2.1e+213)
		tmp = y * (x * t_2);
	elseif (x <= -1.3e+88)
		tmp = t_4;
	elseif (x <= -3.9e-38)
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * ((x * y) - (z * t))));
	elseif (x <= -1.5e-132)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (x <= -4.5e-212)
		tmp = t_1;
	elseif (x <= 7e-202)
		tmp = y4 * t_5;
	elseif (x <= 1.25e-157)
		tmp = t_1;
	elseif (x <= 1.95e+27)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_5);
	elseif (x <= 1.16e+179)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (x <= 3.4e+216)
		tmp = j * (x * t_3);
	elseif (x <= 4.6e+251)
		tmp = t_4;
	else
		tmp = y0 * (x * ((c * y2) - (b * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(N[(y * t$95$2), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+213], N[(y * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e+88], t$95$4, If[LessEqual[x, -3.9e-38], N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e-132], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-212], t$95$1, If[LessEqual[x, 7e-202], N[(y4 * t$95$5), $MachinePrecision], If[LessEqual[x, 1.25e-157], t$95$1, If[LessEqual[x, 1.95e+27], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.16e+179], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+216], N[(j * N[(x * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+251], t$95$4, N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if x < -2.1000000000000001e213

   1. Initial program 8.5%

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

   3. Simplified 8.5%

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

   4. Taylor expanded in x around inf 44.0%

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

   5. Taylor expanded in y around inf 60.2%

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

   if -2.1000000000000001e213 < x < -1.3e88 or 3.40000000000000026e216 < x < 4.59999999999999976e251

   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 31.3%

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

   4. Taylor expanded in x around inf 69.1%

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

   if -1.3e88 < x < -3.8999999999999999e-38

   1. Initial program 44.0%

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

   3. Simplified 44.0%

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

   4. Taylor expanded in i around -inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. associate--l+ 52.7%

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

   6. Simplified 52.7%

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

   if -3.8999999999999999e-38 < x < -1.5e-132

   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 40.4%

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

   4. Taylor expanded in j around inf 64.5%

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

   5. Taylor expanded in t around inf 56.7%

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

   if -1.5e-132 < x < -4.4999999999999999e-212 or 6.9999999999999998e-202 < x < 1.25000000000000005e-157

   1. Initial program 20.7%

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

   3. Simplified 20.7%

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

   4. Taylor expanded in z around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate--l+ 66.7%

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

   6. Simplified 66.7%

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

   if -4.4999999999999999e-212 < x < 6.9999999999999998e-202

   1. Initial program 34.2%

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

   3. Simplified 34.2%

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

   4. Taylor expanded in y4 around inf 45.9%

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

   5. Taylor expanded in c around inf 60.3%

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

      1. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   if 1.25000000000000005e-157 < x < 1.9499999999999999e27

   1. Initial program 28.7%

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

   3. Simplified 28.7%

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

   4. Taylor expanded in y4 around inf 54.9%

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

   if 1.9499999999999999e27 < x < 1.16e179

   1. Initial program 25.9%

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

   3. Simplified 25.9%

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

   4. Taylor expanded in y2 around inf 52.2%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*l* 78.2%

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

      4. cancel-sign-sub-inv 78.2%

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

      5. metadata-eval 78.2%

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

      6. *-lft-identity 78.2%

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

      7. +-commutative 78.2%

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

      8. mul-1-neg 78.2%

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

      9. unsub-neg 78.2%

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

      10. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   if 1.16e179 < x < 3.40000000000000026e216

   1. Initial program 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in j around inf 77.8%

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

   5. Taylor expanded in x around inf 88.9%

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

   if 4.59999999999999976e251 < x

   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 11.1%

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

   4. Taylor expanded in x around inf 33.3%

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

   5. Taylor expanded in y0 around inf 100.0%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+88}:\\ \;\;\;\;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 -3.9 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-132}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-212}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-157}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+27}:\\ \;\;\;\;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 1.16 \cdot 10^{+179}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+216}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+251}:\\ \;\;\;\;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{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \end{array} \]

Alternative 2: 54.0% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y5) (* c y4)))
        (t_2 (- (* b y4) (* i y5)))
        (t_3
         (+
          (+
           (+
            (+
             (+
              (* (- (* a b) (* c i)) (- (* x y) (* z t)))
              (* (- (* b y0) (* i y1)) (- (* z k) (* x j))))
             (* (- (* x y2) (* z y3)) (- (* c y0) (* a y1))))
            (* t_2 (- (* t j) (* y k))))
           (* (- (* t y2) (* y y3)) t_1))
          (* (- (* y1 y4) (* y0 y5)) (- (* k y2) (* j y3))))))
   (if (<= t_3 INFINITY)
     t_3
     (* t (+ (* z (- (* c i) (* a b))) (+ (* y2 t_1) (* j 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 = (a * y5) - (c * y4);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_1) + (j * 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 = (a * y5) - (c * y4);
	double t_2 = (b * y4) - (i * y5);
	double t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_1) + (j * 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 = (a * y5) - (c * y4)
	t_2 = (b * y4) - (i * y5)
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_1) + (j * 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(a * y5) - Float64(c * y4))
	t_2 = Float64(Float64(b * y4) - Float64(i * y5))
	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(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(t_2 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(Float64(Float64(t * y2) - Float64(y * y3)) * t_1)) + Float64(Float64(Float64(y1 * y4) - Float64(y0 * y5)) * Float64(Float64(k * y2) - Float64(j * y3))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(y2 * t_1) + Float64(j * 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 = (a * y5) - (c * y4);
	t_2 = (b * y4) - (i * y5);
	t_3 = (((((((a * b) - (c * i)) * ((x * y) - (z * t))) + (((b * y0) - (i * y1)) * ((z * k) - (x * j)))) + (((x * y2) - (z * y3)) * ((c * y0) - (a * y1)))) + (t_2 * ((t * j) - (y * k)))) + (((t * y2) - (y * y3)) * t_1)) + (((y1 * y4) - (y0 * y5)) * ((k * y2) - (j * y3)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_1) + (j * 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[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $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[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y2 * t$95$1), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

   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 8.0%

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

   4. Taylor expanded in t around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. mul-1-neg 39.6%

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

      3. sub-neg 39.6%

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

   6. Simplified 39.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(-z \cdot \left(a \cdot b - c \cdot i\right)\right) + \left(\left(a \cdot y5 - c \cdot y4\right) \cdot y2 + j \cdot \left(y4 \cdot b - i \cdot y5\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

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

Alternative 3: 39.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b - c \cdot i\\ t_2 := a \cdot y5 - c \cdot y4\\ t_3 := y \cdot y3 - t \cdot y2\\ t_4 := y4 \cdot t_3\\ t_5 := t \cdot j - y \cdot k\\ t_6 := z \cdot k - x \cdot j\\ t_7 := x \cdot y2 - z \cdot y3\\ t_8 := x \cdot y - z \cdot t\\ t_9 := c \cdot y0 - a \cdot y1\\ t_10 := b \cdot y4 - i \cdot y5\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{+110}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot t_7 + t_4\right)\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+61}:\\ \;\;\;\;y3 \cdot \left(\left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot t_8\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_8 + y4 \cdot t_5\right) + y0 \cdot t_6\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \left(\left(y \cdot t_1 + y2 \cdot t_9\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(y2 \cdot t_2 + j \cdot t_10\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-95}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_9 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot t_2\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+111}:\\ \;\;\;\;\left(\left(t_1 \cdot t_8 + \left(b \cdot y0 - i \cdot y1\right) \cdot t_6\right) + \left(t_10 \cdot t_5 + t_7 \cdot t_9\right)\right) + c \cdot t_4\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a b) (* c i)))
        (t_2 (- (* a y5) (* c y4)))
        (t_3 (- (* y y3) (* t y2)))
        (t_4 (* y4 t_3))
        (t_5 (- (* t j) (* y k)))
        (t_6 (- (* z k) (* x j)))
        (t_7 (- (* x y2) (* z y3)))
        (t_8 (- (* x y) (* z t)))
        (t_9 (- (* c y0) (* a y1)))
        (t_10 (- (* b y4) (* i y5))))
   (if (<= c -4.4e+110)
     (* c (+ (* i (- (* z t) (* x y))) (+ (* y0 t_7) t_4)))
     (if (<= c -1.45e+61)
       (*
        y3
        (+
         (+ (* z (- (* a y1) (* c y0))) (* j (- (* y0 y5) (* y1 y4))))
         (* y (- (* c y4) (* a y5)))))
       (if (<= c -4.8e+27)
         (*
          i
          (-
           (+ (* y1 (- (* x j) (* z k))) (* y5 (- (* y k) (* t j))))
           (* c t_8)))
         (if (<= c -7.2e-9)
           (* b (+ (+ (* a t_8) (* y4 t_5)) (* y0 t_6)))
           (if (<= c -7.5e-216)
             (* x (+ (+ (* y t_1) (* y2 t_9)) (* j (- (* i y1) (* b y0)))))
             (if (<= c 1.85e-230)
               (* t (+ (* z (- (* c i) (* a b))) (+ (* y2 t_2) (* j t_10))))
               (if (<= c 5.5e-95)
                 (*
                  y2
                  (+ (+ (* x t_9) (* k (- (* y1 y4) (* y0 y5)))) (* t t_2)))
                 (if (<= c 1.35e+111)
                   (+
                    (+
                     (+ (* t_1 t_8) (* (- (* b y0) (* i y1)) t_6))
                     (+ (* t_10 t_5) (* t_7 t_9)))
                    (* c t_4))
                   (* y4 (* c t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * t_3;
	double t_5 = (t * j) - (y * k);
	double t_6 = (z * k) - (x * j);
	double t_7 = (x * y2) - (z * y3);
	double t_8 = (x * y) - (z * t);
	double t_9 = (c * y0) - (a * y1);
	double t_10 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -4.4e+110) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + t_4));
	} else if (c <= -1.45e+61) {
		tmp = y3 * (((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))) + (y * ((c * y4) - (a * y5))));
	} else if (c <= -4.8e+27) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_8));
	} else if (c <= -7.2e-9) {
		tmp = b * (((a * t_8) + (y4 * t_5)) + (y0 * t_6));
	} else if (c <= -7.5e-216) {
		tmp = x * (((y * t_1) + (y2 * t_9)) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 1.85e-230) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_2) + (j * t_10)));
	} else if (c <= 5.5e-95) {
		tmp = y2 * (((x * t_9) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	} else if (c <= 1.35e+111) {
		tmp = (((t_1 * t_8) + (((b * y0) - (i * y1)) * t_6)) + ((t_10 * t_5) + (t_7 * t_9))) + (c * t_4);
	} else {
		tmp = y4 * (c * 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_10
    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 = (a * b) - (c * i)
    t_2 = (a * y5) - (c * y4)
    t_3 = (y * y3) - (t * y2)
    t_4 = y4 * t_3
    t_5 = (t * j) - (y * k)
    t_6 = (z * k) - (x * j)
    t_7 = (x * y2) - (z * y3)
    t_8 = (x * y) - (z * t)
    t_9 = (c * y0) - (a * y1)
    t_10 = (b * y4) - (i * y5)
    if (c <= (-4.4d+110)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + t_4))
    else if (c <= (-1.45d+61)) then
        tmp = y3 * (((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))) + (y * ((c * y4) - (a * y5))))
    else if (c <= (-4.8d+27)) then
        tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_8))
    else if (c <= (-7.2d-9)) then
        tmp = b * (((a * t_8) + (y4 * t_5)) + (y0 * t_6))
    else if (c <= (-7.5d-216)) then
        tmp = x * (((y * t_1) + (y2 * t_9)) + (j * ((i * y1) - (b * y0))))
    else if (c <= 1.85d-230) then
        tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_2) + (j * t_10)))
    else if (c <= 5.5d-95) then
        tmp = y2 * (((x * t_9) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
    else if (c <= 1.35d+111) then
        tmp = (((t_1 * t_8) + (((b * y0) - (i * y1)) * t_6)) + ((t_10 * t_5) + (t_7 * t_9))) + (c * t_4)
    else
        tmp = y4 * (c * t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * b) - (c * i);
	double t_2 = (a * y5) - (c * y4);
	double t_3 = (y * y3) - (t * y2);
	double t_4 = y4 * t_3;
	double t_5 = (t * j) - (y * k);
	double t_6 = (z * k) - (x * j);
	double t_7 = (x * y2) - (z * y3);
	double t_8 = (x * y) - (z * t);
	double t_9 = (c * y0) - (a * y1);
	double t_10 = (b * y4) - (i * y5);
	double tmp;
	if (c <= -4.4e+110) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + t_4));
	} else if (c <= -1.45e+61) {
		tmp = y3 * (((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))) + (y * ((c * y4) - (a * y5))));
	} else if (c <= -4.8e+27) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_8));
	} else if (c <= -7.2e-9) {
		tmp = b * (((a * t_8) + (y4 * t_5)) + (y0 * t_6));
	} else if (c <= -7.5e-216) {
		tmp = x * (((y * t_1) + (y2 * t_9)) + (j * ((i * y1) - (b * y0))));
	} else if (c <= 1.85e-230) {
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_2) + (j * t_10)));
	} else if (c <= 5.5e-95) {
		tmp = y2 * (((x * t_9) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	} else if (c <= 1.35e+111) {
		tmp = (((t_1 * t_8) + (((b * y0) - (i * y1)) * t_6)) + ((t_10 * t_5) + (t_7 * t_9))) + (c * t_4);
	} else {
		tmp = y4 * (c * t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * b) - (c * i)
	t_2 = (a * y5) - (c * y4)
	t_3 = (y * y3) - (t * y2)
	t_4 = y4 * t_3
	t_5 = (t * j) - (y * k)
	t_6 = (z * k) - (x * j)
	t_7 = (x * y2) - (z * y3)
	t_8 = (x * y) - (z * t)
	t_9 = (c * y0) - (a * y1)
	t_10 = (b * y4) - (i * y5)
	tmp = 0
	if c <= -4.4e+110:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + t_4))
	elif c <= -1.45e+61:
		tmp = y3 * (((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))) + (y * ((c * y4) - (a * y5))))
	elif c <= -4.8e+27:
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_8))
	elif c <= -7.2e-9:
		tmp = b * (((a * t_8) + (y4 * t_5)) + (y0 * t_6))
	elif c <= -7.5e-216:
		tmp = x * (((y * t_1) + (y2 * t_9)) + (j * ((i * y1) - (b * y0))))
	elif c <= 1.85e-230:
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_2) + (j * t_10)))
	elif c <= 5.5e-95:
		tmp = y2 * (((x * t_9) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2))
	elif c <= 1.35e+111:
		tmp = (((t_1 * t_8) + (((b * y0) - (i * y1)) * t_6)) + ((t_10 * t_5) + (t_7 * t_9))) + (c * t_4)
	else:
		tmp = y4 * (c * t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * b) - Float64(c * i))
	t_2 = Float64(Float64(a * y5) - Float64(c * y4))
	t_3 = Float64(Float64(y * y3) - Float64(t * y2))
	t_4 = Float64(y4 * t_3)
	t_5 = Float64(Float64(t * j) - Float64(y * k))
	t_6 = Float64(Float64(z * k) - Float64(x * j))
	t_7 = Float64(Float64(x * y2) - Float64(z * y3))
	t_8 = Float64(Float64(x * y) - Float64(z * t))
	t_9 = Float64(Float64(c * y0) - Float64(a * y1))
	t_10 = Float64(Float64(b * y4) - Float64(i * y5))
	tmp = 0.0
	if (c <= -4.4e+110)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * t_7) + t_4)));
	elseif (c <= -1.45e+61)
		tmp = Float64(y3 * Float64(Float64(Float64(z * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (c <= -4.8e+27)
		tmp = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * Float64(Float64(y * k) - Float64(t * j)))) - Float64(c * t_8)));
	elseif (c <= -7.2e-9)
		tmp = Float64(b * Float64(Float64(Float64(a * t_8) + Float64(y4 * t_5)) + Float64(y0 * t_6)));
	elseif (c <= -7.5e-216)
		tmp = Float64(x * Float64(Float64(Float64(y * t_1) + Float64(y2 * t_9)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (c <= 1.85e-230)
		tmp = Float64(t * Float64(Float64(z * Float64(Float64(c * i) - Float64(a * b))) + Float64(Float64(y2 * t_2) + Float64(j * t_10))));
	elseif (c <= 5.5e-95)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_9) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * t_2)));
	elseif (c <= 1.35e+111)
		tmp = Float64(Float64(Float64(Float64(t_1 * t_8) + Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_6)) + Float64(Float64(t_10 * t_5) + Float64(t_7 * t_9))) + Float64(c * t_4));
	else
		tmp = Float64(y4 * Float64(c * t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * b) - (c * i);
	t_2 = (a * y5) - (c * y4);
	t_3 = (y * y3) - (t * y2);
	t_4 = y4 * t_3;
	t_5 = (t * j) - (y * k);
	t_6 = (z * k) - (x * j);
	t_7 = (x * y2) - (z * y3);
	t_8 = (x * y) - (z * t);
	t_9 = (c * y0) - (a * y1);
	t_10 = (b * y4) - (i * y5);
	tmp = 0.0;
	if (c <= -4.4e+110)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * t_7) + t_4));
	elseif (c <= -1.45e+61)
		tmp = y3 * (((z * ((a * y1) - (c * y0))) + (j * ((y0 * y5) - (y1 * y4)))) + (y * ((c * y4) - (a * y5))));
	elseif (c <= -4.8e+27)
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * ((y * k) - (t * j)))) - (c * t_8));
	elseif (c <= -7.2e-9)
		tmp = b * (((a * t_8) + (y4 * t_5)) + (y0 * t_6));
	elseif (c <= -7.5e-216)
		tmp = x * (((y * t_1) + (y2 * t_9)) + (j * ((i * y1) - (b * y0))));
	elseif (c <= 1.85e-230)
		tmp = t * ((z * ((c * i) - (a * b))) + ((y2 * t_2) + (j * t_10)));
	elseif (c <= 5.5e-95)
		tmp = y2 * (((x * t_9) + (k * ((y1 * y4) - (y0 * y5)))) + (t * t_2));
	elseif (c <= 1.35e+111)
		tmp = (((t_1 * t_8) + (((b * y0) - (i * y1)) * t_6)) + ((t_10 * t_5) + (t_7 * t_9))) + (c * t_4);
	else
		tmp = y4 * (c * t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$10 = N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.4e+110], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * t$95$7), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.45e+61], N[(y3 * N[(N[(N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.8e+27], N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$8), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.2e-9], N[(b * N[(N[(N[(a * t$95$8), $MachinePrecision] + N[(y4 * t$95$5), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.5e-216], N[(x * N[(N[(N[(y * t$95$1), $MachinePrecision] + N[(y2 * t$95$9), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e-230], N[(t * N[(N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y2 * t$95$2), $MachinePrecision] + N[(j * t$95$10), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e-95], N[(y2 * N[(N[(N[(x * t$95$9), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e+111], N[(N[(N[(N[(t$95$1 * t$95$8), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$10 * t$95$5), $MachinePrecision] + N[(t$95$7 * t$95$9), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * t$95$4), $MachinePrecision]), $MachinePrecision], N[(y4 * N[(c * t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -4.39999999999999984e110

   1. Initial program 26.7%

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

   3. Simplified 26.7%

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

   4. Taylor expanded in c around inf 63.1%

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

      1. associate--l+ 63.1%

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

      2. mul-1-neg 63.1%

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

   6. Simplified 63.1%

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

   if -4.39999999999999984e110 < c < -1.45e61

   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 y3 around -inf 70.5%

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

   if -1.45e61 < c < -4.79999999999999995e27

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in i around -inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. associate--l+ 75.0%

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

   6. Simplified 75.0%

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

   if -4.79999999999999995e27 < c < -7.2e-9

   1. Initial program 25.4%

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

   3. Simplified 25.4%

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

   4. Taylor expanded in b around inf 75.3%

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

   if -7.2e-9 < c < -7.50000000000000064e-216

   1. Initial program 33.6%

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

   3. Simplified 33.6%

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

   4. Taylor expanded in x around inf 54.4%

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

   if -7.50000000000000064e-216 < c < 1.84999999999999991e-230

   1. Initial program 22.8%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in t around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. mul-1-neg 65.4%

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

      3. sub-neg 65.4%

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

   6. Simplified 65.4%

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

   if 1.84999999999999991e-230 < c < 5.50000000000000003e-95

   1. Initial program 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in y2 around inf 59.1%

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

   if 5.50000000000000003e-95 < c < 1.3499999999999999e111

   1. Initial program 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in c around inf 58.4%

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

   if 1.3499999999999999e111 < c

   1. Initial program 15.2%

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

   3. Simplified 15.2%

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

   4. Taylor expanded in y4 around inf 41.4%

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

   5. Taylor expanded in c around inf 59.0%

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

      1. *-commutative 59.0%

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

   7. Simplified 59.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.4 \cdot 10^{+110}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+61}:\\ \;\;\;\;y3 \cdot \left(\left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-216}:\\ \;\;\;\;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}\;c \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-95}:\\ \;\;\;\;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 1.35 \cdot 10^{+111}:\\ \;\;\;\;\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(\left(b \cdot y4 - i \cdot y5\right) \cdot \left(t \cdot j - y \cdot k\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right) + c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 4: 35.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot j - y \cdot k\\ t_2 := y \cdot y3 - t \cdot y2\\ t_3 := c \cdot t_2\\ t_4 := z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ t_5 := i \cdot y1 - b \cdot y0\\ \mathbf{if}\;x \leq -8 \cdot 10^{+177}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-8}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_2\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_1\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot t_3\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+30}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_1 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t_3\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+179}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+216}:\\ \;\;\;\;j \cdot \left(x \cdot t_5\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+252}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_5\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* t j) (* y k)))
        (t_2 (- (* y y3) (* t y2)))
        (t_3 (* c t_2))
        (t_4
         (*
          z
          (+
           (* y3 (- (* a y1) (* c y0)))
           (+ (* k (- (* b y0) (* i y1))) (* t (- (* c i) (* a b)))))))
        (t_5 (- (* i y1) (* b y0))))
   (if (<= x -8e+177)
     (* j (* y0 (- (* y3 y5) (* x b))))
     (if (<= x -4.8e-8)
       (*
        c
        (+
         (* i (- (* z t) (* x y)))
         (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_2))))
       (if (<= x -4e-108)
         (*
          b
          (+
           (+ (* a (- (* x y) (* z t))) (* y4 t_1))
           (* y0 (- (* z k) (* x j)))))
         (if (<= x -3.5e-185)
           (* j (* y5 (- (* y0 y3) (* t i))))
           (if (<= x -3.6e-212)
             t_4
             (if (<= x 1.02e-202)
               (* y4 t_3)
               (if (<= x 3.9e-148)
                 t_4
                 (if (<= x 3.3e+30)
                   (* y4 (+ (+ (* b t_1) (* y1 (- (* k y2) (* j y3)))) t_3))
                   (if (<= x 3.4e+179)
                     (* y2 (* a (- (* t y5) (* x y1))))
                     (if (<= x 2.3e+216)
                       (* j (* x t_5))
                       (if (<= x 2.8e+252)
                         (*
                          x
                          (+
                           (+
                            (* y (- (* a b) (* c i)))
                            (* y2 (- (* c y0) (* a y1))))
                           (* j t_5)))
                         (* y0 (* x (- (* c y2) (* b j)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = c * t_2;
	double t_4 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	double t_5 = (i * y1) - (b * y0);
	double tmp;
	if (x <= -8e+177) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (x <= -4.8e-8) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)));
	} else if (x <= -4e-108) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (x <= -3.5e-185) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (x <= -3.6e-212) {
		tmp = t_4;
	} else if (x <= 1.02e-202) {
		tmp = y4 * t_3;
	} else if (x <= 3.9e-148) {
		tmp = t_4;
	} else if (x <= 3.3e+30) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + t_3);
	} else if (x <= 3.4e+179) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (x <= 2.3e+216) {
		tmp = j * (x * t_5);
	} else if (x <= 2.8e+252) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	} else {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (t * j) - (y * k)
    t_2 = (y * y3) - (t * y2)
    t_3 = c * t_2
    t_4 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
    t_5 = (i * y1) - (b * y0)
    if (x <= (-8d+177)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (x <= (-4.8d-8)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)))
    else if (x <= (-4d-108)) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
    else if (x <= (-3.5d-185)) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (x <= (-3.6d-212)) then
        tmp = t_4
    else if (x <= 1.02d-202) then
        tmp = y4 * t_3
    else if (x <= 3.9d-148) then
        tmp = t_4
    else if (x <= 3.3d+30) then
        tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + t_3)
    else if (x <= 3.4d+179) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (x <= 2.3d+216) then
        tmp = j * (x * t_5)
    else if (x <= 2.8d+252) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5))
    else
        tmp = y0 * (x * ((c * y2) - (b * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (t * j) - (y * k);
	double t_2 = (y * y3) - (t * y2);
	double t_3 = c * t_2;
	double t_4 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	double t_5 = (i * y1) - (b * y0);
	double tmp;
	if (x <= -8e+177) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (x <= -4.8e-8) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)));
	} else if (x <= -4e-108) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	} else if (x <= -3.5e-185) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (x <= -3.6e-212) {
		tmp = t_4;
	} else if (x <= 1.02e-202) {
		tmp = y4 * t_3;
	} else if (x <= 3.9e-148) {
		tmp = t_4;
	} else if (x <= 3.3e+30) {
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + t_3);
	} else if (x <= 3.4e+179) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (x <= 2.3e+216) {
		tmp = j * (x * t_5);
	} else if (x <= 2.8e+252) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	} else {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (t * j) - (y * k)
	t_2 = (y * y3) - (t * y2)
	t_3 = c * t_2
	t_4 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))))
	t_5 = (i * y1) - (b * y0)
	tmp = 0
	if x <= -8e+177:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif x <= -4.8e-8:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)))
	elif x <= -4e-108:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))))
	elif x <= -3.5e-185:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif x <= -3.6e-212:
		tmp = t_4
	elif x <= 1.02e-202:
		tmp = y4 * t_3
	elif x <= 3.9e-148:
		tmp = t_4
	elif x <= 3.3e+30:
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + t_3)
	elif x <= 3.4e+179:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif x <= 2.3e+216:
		tmp = j * (x * t_5)
	elif x <= 2.8e+252:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5))
	else:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(t * j) - Float64(y * k))
	t_2 = Float64(Float64(y * y3) - Float64(t * y2))
	t_3 = Float64(c * t_2)
	t_4 = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * Float64(Float64(c * i) - Float64(a * b))))))
	t_5 = Float64(Float64(i * y1) - Float64(b * y0))
	tmp = 0.0
	if (x <= -8e+177)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (x <= -4.8e-8)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_2))));
	elseif (x <= -4e-108)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_1)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (x <= -3.5e-185)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (x <= -3.6e-212)
		tmp = t_4;
	elseif (x <= 1.02e-202)
		tmp = Float64(y4 * t_3);
	elseif (x <= 3.9e-148)
		tmp = t_4;
	elseif (x <= 3.3e+30)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_1) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_3));
	elseif (x <= 3.4e+179)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (x <= 2.3e+216)
		tmp = Float64(j * Float64(x * t_5));
	elseif (x <= 2.8e+252)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_5)));
	else
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (t * j) - (y * k);
	t_2 = (y * y3) - (t * y2);
	t_3 = c * t_2;
	t_4 = z * ((y3 * ((a * y1) - (c * y0))) + ((k * ((b * y0) - (i * y1))) + (t * ((c * i) - (a * b)))));
	t_5 = (i * y1) - (b * y0);
	tmp = 0.0;
	if (x <= -8e+177)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (x <= -4.8e-8)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_2)));
	elseif (x <= -4e-108)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_1)) + (y0 * ((z * k) - (x * j))));
	elseif (x <= -3.5e-185)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (x <= -3.6e-212)
		tmp = t_4;
	elseif (x <= 1.02e-202)
		tmp = y4 * t_3;
	elseif (x <= 3.9e-148)
		tmp = t_4;
	elseif (x <= 3.3e+30)
		tmp = y4 * (((b * t_1) + (y1 * ((k * y2) - (j * y3)))) + t_3);
	elseif (x <= 3.4e+179)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (x <= 2.3e+216)
		tmp = j * (x * t_5);
	elseif (x <= 2.8e+252)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_5));
	else
		tmp = y0 * (x * ((c * y2) - (b * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+177], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-8], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-108], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-185], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e-212], t$95$4, If[LessEqual[x, 1.02e-202], N[(y4 * t$95$3), $MachinePrecision], If[LessEqual[x, 3.9e-148], t$95$4, If[LessEqual[x, 3.3e+30], N[(y4 * N[(N[(N[(b * t$95$1), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+179], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+216], N[(j * N[(x * t$95$5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+252], 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 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if x < -8.0000000000000001e177

   1. Initial program 18.5%

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

   3. Simplified 21.6%

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

   4. Taylor expanded in j around inf 34.0%

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

   5. Taylor expanded in y0 around inf 58.5%

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

   if -8.0000000000000001e177 < x < -4.79999999999999997e-8

   1. Initial program 38.2%

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

   3. Simplified 38.2%

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

   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. associate--l+ 56.7%

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

      2. mul-1-neg 56.7%

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

   6. Simplified 56.7%

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

   if -4.79999999999999997e-8 < x < -4.00000000000000016e-108

   1. Initial program 26.5%

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

   3. Simplified 26.5%

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

   4. Taylor expanded in b around inf 53.7%

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

   if -4.00000000000000016e-108 < x < -3.4999999999999998e-185

   1. Initial program 30.6%

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

   3. Simplified 43.6%

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

   4. Taylor expanded in j around inf 39.9%

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

   5. Taylor expanded in y5 around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   7. Simplified 56.8%

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

   if -3.4999999999999998e-185 < x < -3.6000000000000001e-212 or 1.01999999999999997e-202 < x < 3.89999999999999994e-148

   1. Initial program 26.3%

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

   3. Simplified 26.3%

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

   4. Taylor expanded in z around -inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. associate--l+ 77.0%

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

   6. Simplified 77.0%

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

   if -3.6000000000000001e-212 < x < 1.01999999999999997e-202

   1. Initial program 34.2%

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

   3. Simplified 34.2%

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

   4. Taylor expanded in y4 around inf 45.9%

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

   5. Taylor expanded in c around inf 60.3%

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

      1. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   if 3.89999999999999994e-148 < x < 3.30000000000000026e30

   1. Initial program 28.7%

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

   3. Simplified 28.7%

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

   4. Taylor expanded in y4 around inf 54.9%

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

   if 3.30000000000000026e30 < x < 3.39999999999999996e179

   1. Initial program 25.9%

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

   3. Simplified 25.9%

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

   4. Taylor expanded in y2 around inf 52.2%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*l* 78.2%

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

      4. cancel-sign-sub-inv 78.2%

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

      5. metadata-eval 78.2%

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

      6. *-lft-identity 78.2%

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

      7. +-commutative 78.2%

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

      8. mul-1-neg 78.2%

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

      9. unsub-neg 78.2%

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

      10. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   if 3.39999999999999996e179 < x < 2.29999999999999996e216

   1. Initial program 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in j around inf 77.8%

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

   5. Taylor expanded in x around inf 88.9%

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

   if 2.29999999999999996e216 < x < 2.80000000000000003e252

   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 x around inf 88.7%

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

   if 2.80000000000000003e252 < x

   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 11.1%

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

   4. Taylor expanded in x around inf 33.3%

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

   5. Taylor expanded in y0 around inf 100.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+177}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-8}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-185}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-212}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-202}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+30}:\\ \;\;\;\;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 3.4 \cdot 10^{+179}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+216}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+252}:\\ \;\;\;\;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{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \end{array} \]

Alternative 5: 35.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot y3 - t \cdot y2\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := z \cdot \left(c \cdot i - a \cdot b\right)\\ t_4 := c \cdot t_1\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+179}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot t_1\right)\right)\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-214}:\\ \;\;\;\;t \cdot \left(t_3 + \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-201}:\\ \;\;\;\;y4 \cdot t_4\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-162}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-148}:\\ \;\;\;\;t \cdot t_3\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t_4\right)\\ \mathbf{elif}\;x \leq 10^{+179}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+216}:\\ \;\;\;\;j \cdot \left(x \cdot t_2\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+249}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \end{array} \end{array} \]

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 (- (* i y1) (* b y0)))
        (t_3 (* z (- (* c i) (* a b))))
        (t_4 (* c t_1)))
   (if (<= x -1.6e+179)
     (* j (* y0 (- (* y3 y5) (* x b))))
     (if (<= x -9.2e+35)
       (*
        c
        (+
         (* i (- (* z t) (* x y)))
         (+ (* y0 (- (* x y2) (* z y3))) (* y4 t_1))))
       (if (<= x -1.02e-214)
         (*
          t
          (+ t_3 (+ (* y2 (- (* a y5) (* c y4))) (* j (- (* b y4) (* i y5))))))
         (if (<= x 9.4e-201)
           (* y4 t_4)
           (if (<= x 8e-162)
             (* (* z y0) (- (* b k) (* c y3)))
             (if (<= x 1.55e-148)
               (* t t_3)
               (if (<= x 3.6e+26)
                 (*
                  y4
                  (+
                   (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
                   t_4))
                 (if (<= x 1e+179)
                   (* y2 (* a (- (* t y5) (* x y1))))
                   (if (<= x 9.5e+216)
                     (* j (* x t_2))
                     (if (<= x 2.2e+249)
                       (*
                        x
                        (+
                         (+
                          (* y (- (* a b) (* c i)))
                          (* y2 (- (* c y0) (* a y1))))
                         (* j t_2)))
                       (* y0 (* x (- (* c y2) (* b j))))))))))))))))

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 = (i * y1) - (b * y0);
	double t_3 = z * ((c * i) - (a * b));
	double t_4 = c * t_1;
	double tmp;
	if (x <= -1.6e+179) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (x <= -9.2e+35) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)));
	} else if (x <= -1.02e-214) {
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	} else if (x <= 9.4e-201) {
		tmp = y4 * t_4;
	} else if (x <= 8e-162) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (x <= 1.55e-148) {
		tmp = t * t_3;
	} else if (x <= 3.6e+26) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_4);
	} else if (x <= 1e+179) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (x <= 9.5e+216) {
		tmp = j * (x * t_2);
	} else if (x <= 2.2e+249) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	} else {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * y3) - (t * y2)
    t_2 = (i * y1) - (b * y0)
    t_3 = z * ((c * i) - (a * b))
    t_4 = c * t_1
    if (x <= (-1.6d+179)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (x <= (-9.2d+35)) then
        tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)))
    else if (x <= (-1.02d-214)) then
        tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))))
    else if (x <= 9.4d-201) then
        tmp = y4 * t_4
    else if (x <= 8d-162) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (x <= 1.55d-148) then
        tmp = t * t_3
    else if (x <= 3.6d+26) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_4)
    else if (x <= 1d+179) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (x <= 9.5d+216) then
        tmp = j * (x * t_2)
    else if (x <= 2.2d+249) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
    else
        tmp = y0 * (x * ((c * y2) - (b * j)))
    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 = (i * y1) - (b * y0);
	double t_3 = z * ((c * i) - (a * b));
	double t_4 = c * t_1;
	double tmp;
	if (x <= -1.6e+179) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (x <= -9.2e+35) {
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)));
	} else if (x <= -1.02e-214) {
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	} else if (x <= 9.4e-201) {
		tmp = y4 * t_4;
	} else if (x <= 8e-162) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (x <= 1.55e-148) {
		tmp = t * t_3;
	} else if (x <= 3.6e+26) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_4);
	} else if (x <= 1e+179) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (x <= 9.5e+216) {
		tmp = j * (x * t_2);
	} else if (x <= 2.2e+249) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	} else {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	}
	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 = (i * y1) - (b * y0)
	t_3 = z * ((c * i) - (a * b))
	t_4 = c * t_1
	tmp = 0
	if x <= -1.6e+179:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif x <= -9.2e+35:
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)))
	elif x <= -1.02e-214:
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))))
	elif x <= 9.4e-201:
		tmp = y4 * t_4
	elif x <= 8e-162:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif x <= 1.55e-148:
		tmp = t * t_3
	elif x <= 3.6e+26:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_4)
	elif x <= 1e+179:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif x <= 9.5e+216:
		tmp = j * (x * t_2)
	elif x <= 2.2e+249:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2))
	else:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	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(i * y1) - Float64(b * y0))
	t_3 = Float64(z * Float64(Float64(c * i) - Float64(a * b)))
	t_4 = Float64(c * t_1)
	tmp = 0.0
	if (x <= -1.6e+179)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (x <= -9.2e+35)
		tmp = Float64(c * Float64(Float64(i * Float64(Float64(z * t) - Float64(x * y))) + Float64(Float64(y0 * Float64(Float64(x * y2) - Float64(z * y3))) + Float64(y4 * t_1))));
	elseif (x <= -1.02e-214)
		tmp = Float64(t * Float64(t_3 + Float64(Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5))))));
	elseif (x <= 9.4e-201)
		tmp = Float64(y4 * t_4);
	elseif (x <= 8e-162)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (x <= 1.55e-148)
		tmp = Float64(t * t_3);
	elseif (x <= 3.6e+26)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_4));
	elseif (x <= 1e+179)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (x <= 9.5e+216)
		tmp = Float64(j * Float64(x * t_2));
	elseif (x <= 2.2e+249)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_2)));
	else
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	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 = (i * y1) - (b * y0);
	t_3 = z * ((c * i) - (a * b));
	t_4 = c * t_1;
	tmp = 0.0;
	if (x <= -1.6e+179)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (x <= -9.2e+35)
		tmp = c * ((i * ((z * t) - (x * y))) + ((y0 * ((x * y2) - (z * y3))) + (y4 * t_1)));
	elseif (x <= -1.02e-214)
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	elseif (x <= 9.4e-201)
		tmp = y4 * t_4;
	elseif (x <= 8e-162)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (x <= 1.55e-148)
		tmp = t * t_3;
	elseif (x <= 3.6e+26)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_4);
	elseif (x <= 1e+179)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (x <= 9.5e+216)
		tmp = j * (x * t_2);
	elseif (x <= 2.2e+249)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_2));
	else
		tmp = y0 * (x * ((c * y2) - (b * j)));
	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[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * t$95$1), $MachinePrecision]}, If[LessEqual[x, -1.6e+179], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e+35], N[(c * N[(N[(i * N[(N[(z * t), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.02e-214], N[(t * N[(t$95$3 + N[(N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.4e-201], N[(y4 * t$95$4), $MachinePrecision], If[LessEqual[x, 8e-162], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-148], N[(t * t$95$3), $MachinePrecision], If[LessEqual[x, 3.6e+26], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+179], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+216], N[(j * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+249], 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 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 11 regimes

2. if x < -1.6000000000000001e179

   1. Initial program 18.5%

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

   3. Simplified 21.6%

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

   4. Taylor expanded in j around inf 34.0%

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

   5. Taylor expanded in y0 around inf 58.5%

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

   if -1.6000000000000001e179 < x < -9.1999999999999993e35

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in c around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. mul-1-neg 62.5%

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

   6. Simplified 62.5%

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

   if -9.1999999999999993e35 < x < -1.0200000000000001e-214

   1. Initial program 34.1%

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

   3. Simplified 44.3%

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

   4. Taylor expanded in t around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. mul-1-neg 51.3%

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

      3. sub-neg 51.3%

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

   6. Simplified 51.3%

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

   if -1.0200000000000001e-214 < x < 9.39999999999999989e-201

   1. Initial program 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in y4 around inf 44.4%

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

   5. Taylor expanded in c around inf 62.1%

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

      1. *-commutative 62.1%

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

   7. Simplified 62.1%

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

   if 9.39999999999999989e-201 < x < 7.99999999999999963e-162

   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 z around -inf 66.3%

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

      1. mul-1-neg 66.3%

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

      2. associate--l+ 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in y0 around inf 61.6%

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

      1. associate-*r* 70.7%

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

      2. *-commutative 70.7%

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

   9. Simplified 70.7%

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

   if 7.99999999999999963e-162 < x < 1.5500000000000001e-148

   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 z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate--l+ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if 1.5500000000000001e-148 < x < 3.60000000000000024e26

   1. Initial program 28.7%

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

   3. Simplified 28.7%

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

   4. Taylor expanded in y4 around inf 54.9%

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

   if 3.60000000000000024e26 < x < 9.9999999999999998e178

   1. Initial program 25.9%

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

   3. Simplified 25.9%

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

   4. Taylor expanded in y2 around inf 52.2%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*l* 78.2%

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

      4. cancel-sign-sub-inv 78.2%

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

      5. metadata-eval 78.2%

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

      6. *-lft-identity 78.2%

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

      7. +-commutative 78.2%

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

      8. mul-1-neg 78.2%

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

      9. unsub-neg 78.2%

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

      10. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   if 9.9999999999999998e178 < x < 9.50000000000000005e216

   1. Initial program 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in j around inf 77.8%

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

   5. Taylor expanded in x around inf 88.9%

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

   if 9.50000000000000005e216 < x < 2.1999999999999998e249

   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 x around inf 88.7%

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

   if 2.1999999999999998e249 < x

   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 11.1%

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

   4. Taylor expanded in x around inf 33.3%

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

   5. Taylor expanded in y0 around inf 100.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+179}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(i \cdot \left(z \cdot t - x \cdot y\right) + \left(y0 \cdot \left(x \cdot y2 - z \cdot y3\right) + y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-214}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-201}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-162}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 10^{+179}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+216}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+249}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \end{array} \]

Alternative 6: 32.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y \cdot y3 - t \cdot y2\right)\\ t_2 := i \cdot y1 - b \cdot y0\\ t_3 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y0 \leq -1.9 \cdot 10^{+60}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -2 \cdot 10^{-42}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -7.6 \cdot 10^{-118}:\\ \;\;\;\;y4 \cdot t_1\\ \mathbf{elif}\;y0 \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{-233}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + t_1\right)\\ \mathbf{elif}\;y0 \leq -3.3 \cdot 10^{-286}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.3 \cdot 10^{-262}:\\ \;\;\;\;y2 \cdot \left(x \cdot t_3\right)\\ \mathbf{elif}\;y0 \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_3\right) + j \cdot t_2\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(x \cdot t_2\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{+180}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+273}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{\left(y0 \cdot y2\right) \cdot \left(y0 \cdot y2\right) - \left(y \cdot i\right) \cdot \left(y \cdot i\right)}{y0 \cdot y2 + y \cdot i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (- (* y y3) (* t y2))))
        (t_2 (- (* i y1) (* b y0)))
        (t_3 (- (* c y0) (* a y1))))
   (if (<= y0 -1.9e+60)
     (* j (* y0 (- (* y3 y5) (* x b))))
     (if (<= y0 -2e-42)
       (* y3 (+ (* y (- (* c y4) (* a y5))) (* z (- (* a y1) (* c y0)))))
       (if (<= y0 -7.6e-118)
         (* y4 t_1)
         (if (<= y0 -5.2e-199)
           (* y2 (* a (- (* t y5) (* x y1))))
           (if (<= y0 -1.45e-233)
             (*
              y4
              (+
               (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
               t_1))
             (if (<= y0 -3.3e-286)
               (* j (* i (- (* x y1) (* t y5))))
               (if (<= y0 1.3e-262)
                 (* y2 (* x t_3))
                 (if (<= y0 5.6e-18)
                   (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_3)) (* j t_2)))
                   (if (<= y0 9e+120)
                     (* j (* x t_2))
                     (if (<= y0 2.2e+180)
                       (* (* z y0) (- (* b k) (* c y3)))
                       (if (<= y0 3.9e+273)
                         (* y0 (* y2 (- (* x c) (* k y5))))
                         (*
                          x
                          (*
                           c
                           (/
                            (- (* (* y0 y2) (* y0 y2)) (* (* y i) (* y i)))
                            (+ (* y0 y2) (* y i))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((y * y3) - (t * y2));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y0 <= -1.9e+60) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y0 <= -2e-42) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (y0 <= -7.6e-118) {
		tmp = y4 * t_1;
	} else if (y0 <= -5.2e-199) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y0 <= -1.45e-233) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	} else if (y0 <= -3.3e-286) {
		tmp = j * (i * ((x * y1) - (t * y5)));
	} else if (y0 <= 1.3e-262) {
		tmp = y2 * (x * t_3);
	} else if (y0 <= 5.6e-18) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * t_2));
	} else if (y0 <= 9e+120) {
		tmp = j * (x * t_2);
	} else if (y0 <= 2.2e+180) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= 3.9e+273) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((y * y3) - (t * y2))
    t_2 = (i * y1) - (b * y0)
    t_3 = (c * y0) - (a * y1)
    if (y0 <= (-1.9d+60)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y0 <= (-2d-42)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
    else if (y0 <= (-7.6d-118)) then
        tmp = y4 * t_1
    else if (y0 <= (-5.2d-199)) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (y0 <= (-1.45d-233)) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
    else if (y0 <= (-3.3d-286)) then
        tmp = j * (i * ((x * y1) - (t * y5)))
    else if (y0 <= 1.3d-262) then
        tmp = y2 * (x * t_3)
    else if (y0 <= 5.6d-18) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * t_2))
    else if (y0 <= 9d+120) then
        tmp = j * (x * t_2)
    else if (y0 <= 2.2d+180) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (y0 <= 3.9d+273) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else
        tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = c * ((y * y3) - (t * y2));
	double t_2 = (i * y1) - (b * y0);
	double t_3 = (c * y0) - (a * y1);
	double tmp;
	if (y0 <= -1.9e+60) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y0 <= -2e-42) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (y0 <= -7.6e-118) {
		tmp = y4 * t_1;
	} else if (y0 <= -5.2e-199) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (y0 <= -1.45e-233) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	} else if (y0 <= -3.3e-286) {
		tmp = j * (i * ((x * y1) - (t * y5)));
	} else if (y0 <= 1.3e-262) {
		tmp = y2 * (x * t_3);
	} else if (y0 <= 5.6e-18) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * t_2));
	} else if (y0 <= 9e+120) {
		tmp = j * (x * t_2);
	} else if (y0 <= 2.2e+180) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= 3.9e+273) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = c * ((y * y3) - (t * y2))
	t_2 = (i * y1) - (b * y0)
	t_3 = (c * y0) - (a * y1)
	tmp = 0
	if y0 <= -1.9e+60:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y0 <= -2e-42:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
	elif y0 <= -7.6e-118:
		tmp = y4 * t_1
	elif y0 <= -5.2e-199:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif y0 <= -1.45e-233:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1)
	elif y0 <= -3.3e-286:
		tmp = j * (i * ((x * y1) - (t * y5)))
	elif y0 <= 1.3e-262:
		tmp = y2 * (x * t_3)
	elif y0 <= 5.6e-18:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * t_2))
	elif y0 <= 9e+120:
		tmp = j * (x * t_2)
	elif y0 <= 2.2e+180:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif y0 <= 3.9e+273:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	else:
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	t_3 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y0 <= -1.9e+60)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y0 <= -2e-42)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))));
	elseif (y0 <= -7.6e-118)
		tmp = Float64(y4 * t_1);
	elseif (y0 <= -5.2e-199)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (y0 <= -1.45e-233)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + t_1));
	elseif (y0 <= -3.3e-286)
		tmp = Float64(j * Float64(i * Float64(Float64(x * y1) - Float64(t * y5))));
	elseif (y0 <= 1.3e-262)
		tmp = Float64(y2 * Float64(x * t_3));
	elseif (y0 <= 5.6e-18)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_3)) + Float64(j * t_2)));
	elseif (y0 <= 9e+120)
		tmp = Float64(j * Float64(x * t_2));
	elseif (y0 <= 2.2e+180)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (y0 <= 3.9e+273)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(x * Float64(c * Float64(Float64(Float64(Float64(y0 * y2) * Float64(y0 * y2)) - Float64(Float64(y * i) * Float64(y * i))) / Float64(Float64(y0 * y2) + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = c * ((y * y3) - (t * y2));
	t_2 = (i * y1) - (b * y0);
	t_3 = (c * y0) - (a * y1);
	tmp = 0.0;
	if (y0 <= -1.9e+60)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y0 <= -2e-42)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	elseif (y0 <= -7.6e-118)
		tmp = y4 * t_1;
	elseif (y0 <= -5.2e-199)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (y0 <= -1.45e-233)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + t_1);
	elseif (y0 <= -3.3e-286)
		tmp = j * (i * ((x * y1) - (t * y5)));
	elseif (y0 <= 1.3e-262)
		tmp = y2 * (x * t_3);
	elseif (y0 <= 5.6e-18)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_3)) + (j * t_2));
	elseif (y0 <= 9e+120)
		tmp = j * (x * t_2);
	elseif (y0 <= 2.2e+180)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (y0 <= 3.9e+273)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	else
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.9e+60], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2e-42], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -7.6e-118], N[(y4 * t$95$1), $MachinePrecision], If[LessEqual[y0, -5.2e-199], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.45e-233], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.3e-286], N[(j * N[(i * N[(N[(x * y1), $MachinePrecision] - N[(t * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.3e-262], N[(y2 * N[(x * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.6e-18], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9e+120], N[(j * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.2e+180], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.9e+273], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(c * N[(N[(N[(N[(y0 * y2), $MachinePrecision] * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y0 * y2), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 12 regimes

2. if y0 < -1.90000000000000005e60

   1. Initial program 23.2%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 41.4%

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

   5. Taylor expanded in y0 around inf 57.9%

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

   if -1.90000000000000005e60 < y0 < -2.00000000000000008e-42

   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 y3 around -inf 52.8%

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

   5. Taylor expanded in j around 0 61.5%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot z - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot y3\right) \]
   6. Step-by-step derivation

      1. *-commutative 61.5%

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

      2. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   if -2.00000000000000008e-42 < y0 < -7.6000000000000002e-118

   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 y4 around inf 64.7%

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

   5. Taylor expanded in c around inf 70.8%

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

      1. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if -7.6000000000000002e-118 < y0 < -5.2000000000000001e-199

   1. Initial program 26.9%

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

   3. Simplified 26.9%

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

   4. Taylor expanded in y2 around inf 47.2%

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

   5. Taylor expanded in a around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. *-commutative 41.0%

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

      3. associate-*l* 60.4%

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

      4. cancel-sign-sub-inv 60.4%

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

      5. metadata-eval 60.4%

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

      6. *-lft-identity 60.4%

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

      7. +-commutative 60.4%

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

      8. mul-1-neg 60.4%

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

      9. unsub-neg 60.4%

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

      10. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   if -5.2000000000000001e-199 < y0 < -1.44999999999999991e-233

   1. Initial program 44.3%

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

   3. Simplified 44.3%

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

   4. Taylor expanded in y4 around inf 72.9%

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

   if -1.44999999999999991e-233 < y0 < -3.2999999999999999e-286

   1. Initial program 43.8%

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

   3. Simplified 43.8%

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

   4. Taylor expanded in j around inf 63.2%

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

   5. Taylor expanded in i around inf 69.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(-1 \cdot \left(t \cdot y5\right) - -1 \cdot \left(y1 \cdot x\right)\right)\right)} \cdot j \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 69.1%

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

   7. Simplified 69.1%

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

   if -3.2999999999999999e-286 < y0 < 1.2999999999999999e-262

   1. Initial program 25.4%

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

   3. Simplified 25.4%

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

   4. Taylor expanded in x around inf 50.6%

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

      1. add-cbrt-cube 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 44.3%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 44.3%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 44.3%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in y2 around inf 50.9%

      \[\leadsto \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 50.9%

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

       2. associate-*l* 51.0%

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

   11. Simplified 51.0%

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

   if 1.2999999999999999e-262 < y0 < 5.60000000000000025e-18

   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 x around inf 54.7%

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

   if 5.60000000000000025e-18 < y0 < 8.99999999999999953e120

   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%

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

   4. Taylor expanded in j around inf 41.1%

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

   5. Taylor expanded in x around inf 53.5%

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

   if 8.99999999999999953e120 < y0 < 2.1999999999999999e180

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in z around -inf 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate--l+ 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in y0 around inf 51.5%

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

      1. associate-*r* 71.8%

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

      2. *-commutative 71.8%

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

   9. Simplified 71.8%

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

   if 2.1999999999999999e180 < y0 < 3.9000000000000001e273

   1. Initial program 28.0%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in y2 around inf 52.5%

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

   5. Taylor expanded in y0 around -inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

      4. *-commutative 65.3%

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

      5. mul-1-neg 65.3%

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

      6. unsub-neg 65.3%

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

      7. *-commutative 65.3%

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

   7. Simplified 65.3%

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

   if 3.9000000000000001e273 < y0

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in x around inf 40.0%

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

   5. Taylor expanded in c around inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. +-commutative 60.6%

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

      3. mul-1-neg 60.6%

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

      4. unsub-neg 60.6%

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

   7. Simplified 60.6%

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

      1. flip-- 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

      4. *-commutative 80.0%

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

   9. Applied egg-rr 80.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.9 \cdot 10^{+60}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -2 \cdot 10^{-42}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -7.6 \cdot 10^{-118}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq -1.45 \cdot 10^{-233}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -3.3 \cdot 10^{-286}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1 - t \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.3 \cdot 10^{-262}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;y0 \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{+180}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+273}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{\left(y0 \cdot y2\right) \cdot \left(y0 \cdot y2\right) - \left(y \cdot i\right) \cdot \left(y \cdot i\right)}{y0 \cdot y2 + y \cdot i}\right)\\ \end{array} \]

Alternative 7: 38.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot y3 - k \cdot y2\\ t_2 := y \cdot k - t \cdot j\\ t_3 := i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot t_2\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_4 := y5 \cdot \left(i \cdot t_2 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot t_1\right)\right)\\ t_5 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-116}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-280}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-151}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot t_1 + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+24}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 10^{+250}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+257}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j y3) (* k y2)))
        (t_2 (- (* y k) (* t j)))
        (t_3
         (*
          i
          (-
           (+ (* y1 (- (* x j) (* z k))) (* y5 t_2))
           (* c (- (* x y) (* z t))))))
        (t_4 (* y5 (+ (* i t_2) (+ (* a (- (* t y2) (* y y3))) (* y0 t_1)))))
        (t_5
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= i -8.5e+159)
     t_3
     (if (<= i -2.15e-116)
       t_4
       (if (<= i -2.8e-280)
         t_5
         (if (<= i 4e-151)
           (*
            y0
            (+
             (+ (* y5 t_1) (* c (- (* x y2) (* z y3))))
             (* b (- (* z k) (* x j)))))
           (if (<= i 1.02e+24)
             (* y3 (+ (* y (- (* c y4) (* a y5))) (* z (- (* a y1) (* c y0)))))
             (if (<= i 4e+153)
               (* x (* b (- (* y a) (* j y0))))
               (if (<= i 4.2e+191)
                 (* t (* z (- (* c i) (* a b))))
                 (if (<= i 1e+250) t_5 (if (<= i 6.2e+257) t_4 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y3) - (k * y2);
	double t_2 = (y * k) - (t * j);
	double t_3 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * ((x * y) - (z * t))));
	double t_4 = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (i <= -8.5e+159) {
		tmp = t_3;
	} else if (i <= -2.15e-116) {
		tmp = t_4;
	} else if (i <= -2.8e-280) {
		tmp = t_5;
	} else if (i <= 4e-151) {
		tmp = y0 * (((y5 * t_1) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (i <= 1.02e+24) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (i <= 4e+153) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (i <= 4.2e+191) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= 1e+250) {
		tmp = t_5;
	} else if (i <= 6.2e+257) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (j * y3) - (k * y2)
    t_2 = (y * k) - (t * j)
    t_3 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * ((x * y) - (z * t))))
    t_4 = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)))
    t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (i <= (-8.5d+159)) then
        tmp = t_3
    else if (i <= (-2.15d-116)) then
        tmp = t_4
    else if (i <= (-2.8d-280)) then
        tmp = t_5
    else if (i <= 4d-151) then
        tmp = y0 * (((y5 * t_1) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
    else if (i <= 1.02d+24) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
    else if (i <= 4d+153) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (i <= 4.2d+191) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (i <= 1d+250) then
        tmp = t_5
    else if (i <= 6.2d+257) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * y3) - (k * y2);
	double t_2 = (y * k) - (t * j);
	double t_3 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * ((x * y) - (z * t))));
	double t_4 = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	double t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (i <= -8.5e+159) {
		tmp = t_3;
	} else if (i <= -2.15e-116) {
		tmp = t_4;
	} else if (i <= -2.8e-280) {
		tmp = t_5;
	} else if (i <= 4e-151) {
		tmp = y0 * (((y5 * t_1) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (i <= 1.02e+24) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (i <= 4e+153) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (i <= 4.2e+191) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (i <= 1e+250) {
		tmp = t_5;
	} else if (i <= 6.2e+257) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (j * y3) - (k * y2)
	t_2 = (y * k) - (t * j)
	t_3 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * ((x * y) - (z * t))))
	t_4 = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)))
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if i <= -8.5e+159:
		tmp = t_3
	elif i <= -2.15e-116:
		tmp = t_4
	elif i <= -2.8e-280:
		tmp = t_5
	elif i <= 4e-151:
		tmp = y0 * (((y5 * t_1) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
	elif i <= 1.02e+24:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
	elif i <= 4e+153:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif i <= 4.2e+191:
		tmp = t * (z * ((c * i) - (a * b)))
	elif i <= 1e+250:
		tmp = t_5
	elif i <= 6.2e+257:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * y3) - Float64(k * y2))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * t_2)) - Float64(c * Float64(Float64(x * y) - Float64(z * t)))))
	t_4 = Float64(y5 * Float64(Float64(i * t_2) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * t_1))))
	t_5 = 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)))))
	tmp = 0.0
	if (i <= -8.5e+159)
		tmp = t_3;
	elseif (i <= -2.15e-116)
		tmp = t_4;
	elseif (i <= -2.8e-280)
		tmp = t_5;
	elseif (i <= 4e-151)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * t_1) + Float64(c * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 1.02e+24)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))));
	elseif (i <= 4e+153)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (i <= 4.2e+191)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (i <= 1e+250)
		tmp = t_5;
	elseif (i <= 6.2e+257)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (j * y3) - (k * y2);
	t_2 = (y * k) - (t * j);
	t_3 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * ((x * y) - (z * t))));
	t_4 = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * t_1)));
	t_5 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (i <= -8.5e+159)
		tmp = t_3;
	elseif (i <= -2.15e-116)
		tmp = t_4;
	elseif (i <= -2.8e-280)
		tmp = t_5;
	elseif (i <= 4e-151)
		tmp = y0 * (((y5 * t_1) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	elseif (i <= 1.02e+24)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	elseif (i <= 4e+153)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (i <= 4.2e+191)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (i <= 1e+250)
		tmp = t_5;
	elseif (i <= 6.2e+257)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y5 * N[(N[(i * t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.5e+159], t$95$3, If[LessEqual[i, -2.15e-116], t$95$4, If[LessEqual[i, -2.8e-280], t$95$5, If[LessEqual[i, 4e-151], N[(y0 * N[(N[(N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.02e+24], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+153], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e+191], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1e+250], t$95$5, If[LessEqual[i, 6.2e+257], t$95$4, t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -8.50000000000000076e159 or 6.2000000000000001e257 < i

   1. Initial program 18.2%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in i around -inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate--l+ 66.5%

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

   6. Simplified 66.5%

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

   if -8.50000000000000076e159 < i < -2.1499999999999999e-116 or 9.9999999999999992e249 < i < 6.2000000000000001e257

   1. Initial program 31.6%

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

   3. Simplified 36.6%

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

   4. Taylor expanded in y5 around -inf 54.5%

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

   if -2.1499999999999999e-116 < i < -2.80000000000000017e-280 or 4.2000000000000001e191 < i < 9.9999999999999992e249

   1. Initial program 46.3%

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

   3. Simplified 46.3%

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

   4. Taylor expanded in x around inf 66.1%

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

   if -2.80000000000000017e-280 < i < 3.9999999999999998e-151

   1. Initial program 30.6%

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

   3. Simplified 30.6%

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

   4. Taylor expanded in y0 around inf 56.3%

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

   if 3.9999999999999998e-151 < i < 1.02000000000000004e24

   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 y3 around -inf 57.4%

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

   5. Taylor expanded in j around 0 68.7%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot z - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot y3\right) \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if 1.02000000000000004e24 < i < 4e153

   1. Initial program 33.5%

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

   3. Simplified 33.5%

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

   4. Taylor expanded in x around inf 61.4%

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

      1. add-cbrt-cube 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 66.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 66.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 61.8%

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

       1. *-commutative 61.8%

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

       2. *-commutative 61.8%

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

       3. associate-*l* 67.2%

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

   11. Simplified 67.2%

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

   if 4e153 < i < 4.2000000000000001e191

   1. Initial program 15.4%

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

   3. Simplified 15.4%

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

   4. Taylor expanded in z around -inf 54.0%

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

      1. mul-1-neg 54.0%

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

      2. associate--l+ 54.0%

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

   6. Simplified 54.0%

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

   7. Taylor expanded in t around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. *-commutative 69.6%

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

   9. Simplified 69.6%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+159}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-116}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-151}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+24}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+153}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 10^{+250}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+257}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 8: 36.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y1 - c \cdot y0\\ t_2 := c \cdot i - a \cdot b\\ t_3 := z \cdot t_2\\ t_4 := y \cdot k - t \cdot j\\ t_5 := y5 \cdot \left(i \cdot t_4 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -2.05 \cdot 10^{-43}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot t_1\right)\\ \mathbf{elif}\;y0 \leq -6.6 \cdot 10^{-204}:\\ \;\;\;\;t \cdot \left(t_3 + \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-11}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq 1950000000:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot t_4\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq 2.45 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(y3 \cdot t_1 + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot t_2\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot t_3\\ \mathbf{elif}\;y0 \leq 2.8 \cdot 10^{+179}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+273}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{\left(y0 \cdot y2\right) \cdot \left(y0 \cdot y2\right) - \left(y \cdot i\right) \cdot \left(y \cdot i\right)}{y0 \cdot y2 + y \cdot i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y1) (* c y0)))
        (t_2 (- (* c i) (* a b)))
        (t_3 (* z t_2))
        (t_4 (- (* y k) (* t j)))
        (t_5
         (*
          y5
          (+
           (* i t_4)
           (+ (* a (- (* t y2) (* y y3))) (* y0 (- (* j y3) (* k y2))))))))
   (if (<= y0 -1.05e+61)
     (* j (* y0 (- (* y3 y5) (* x b))))
     (if (<= y0 -2.05e-43)
       (* y3 (+ (* y (- (* c y4) (* a y5))) (* z t_1)))
       (if (<= y0 -6.6e-204)
         (*
          t
          (+ t_3 (+ (* y2 (- (* a y5) (* c y4))) (* j (- (* b y4) (* i y5))))))
         (if (<= y0 1.2e-96)
           (*
            x
            (+
             (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
             (* j (- (* i y1) (* b y0)))))
           (if (<= y0 9e-11)
             t_5
             (if (<= y0 1950000000.0)
               (*
                i
                (-
                 (+ (* y1 (- (* x j) (* z k))) (* y5 t_4))
                 (* c (- (* x y) (* z t)))))
               (if (<= y0 2.45e+67)
                 (* z (+ (* y3 t_1) (+ (* k (- (* b y0) (* i y1))) (* t t_2))))
                 (if (<= y0 8e+95)
                   (* t t_3)
                   (if (<= y0 2.8e+179)
                     t_5
                     (if (<= y0 3.9e+273)
                       (* y0 (* y2 (- (* x c) (* k y5))))
                       (*
                        x
                        (*
                         c
                         (/
                          (- (* (* y0 y2) (* y0 y2)) (* (* y i) (* y i)))
                          (+ (* y0 y2) (* y i)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = (c * i) - (a * b);
	double t_3 = z * t_2;
	double t_4 = (y * k) - (t * j);
	double t_5 = y5 * ((i * t_4) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y0 <= -1.05e+61) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y0 <= -2.05e-43) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * t_1));
	} else if (y0 <= -6.6e-204) {
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	} else if (y0 <= 1.2e-96) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= 9e-11) {
		tmp = t_5;
	} else if (y0 <= 1950000000.0) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_4)) - (c * ((x * y) - (z * t))));
	} else if (y0 <= 2.45e+67) {
		tmp = z * ((y3 * t_1) + ((k * ((b * y0) - (i * y1))) + (t * t_2)));
	} else if (y0 <= 8e+95) {
		tmp = t * t_3;
	} else if (y0 <= 2.8e+179) {
		tmp = t_5;
	} else if (y0 <= 3.9e+273) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (a * y1) - (c * y0)
    t_2 = (c * i) - (a * b)
    t_3 = z * t_2
    t_4 = (y * k) - (t * j)
    t_5 = y5 * ((i * t_4) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    if (y0 <= (-1.05d+61)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y0 <= (-2.05d-43)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * t_1))
    else if (y0 <= (-6.6d-204)) then
        tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))))
    else if (y0 <= 1.2d-96) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (y0 <= 9d-11) then
        tmp = t_5
    else if (y0 <= 1950000000.0d0) then
        tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_4)) - (c * ((x * y) - (z * t))))
    else if (y0 <= 2.45d+67) then
        tmp = z * ((y3 * t_1) + ((k * ((b * y0) - (i * y1))) + (t * t_2)))
    else if (y0 <= 8d+95) then
        tmp = t * t_3
    else if (y0 <= 2.8d+179) then
        tmp = t_5
    else if (y0 <= 3.9d+273) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else
        tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = (c * i) - (a * b);
	double t_3 = z * t_2;
	double t_4 = (y * k) - (t * j);
	double t_5 = y5 * ((i * t_4) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	double tmp;
	if (y0 <= -1.05e+61) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y0 <= -2.05e-43) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * t_1));
	} else if (y0 <= -6.6e-204) {
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	} else if (y0 <= 1.2e-96) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (y0 <= 9e-11) {
		tmp = t_5;
	} else if (y0 <= 1950000000.0) {
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_4)) - (c * ((x * y) - (z * t))));
	} else if (y0 <= 2.45e+67) {
		tmp = z * ((y3 * t_1) + ((k * ((b * y0) - (i * y1))) + (t * t_2)));
	} else if (y0 <= 8e+95) {
		tmp = t * t_3;
	} else if (y0 <= 2.8e+179) {
		tmp = t_5;
	} else if (y0 <= 3.9e+273) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y1) - (c * y0)
	t_2 = (c * i) - (a * b)
	t_3 = z * t_2
	t_4 = (y * k) - (t * j)
	t_5 = y5 * ((i * t_4) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	tmp = 0
	if y0 <= -1.05e+61:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y0 <= -2.05e-43:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * t_1))
	elif y0 <= -6.6e-204:
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))))
	elif y0 <= 1.2e-96:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif y0 <= 9e-11:
		tmp = t_5
	elif y0 <= 1950000000.0:
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_4)) - (c * ((x * y) - (z * t))))
	elif y0 <= 2.45e+67:
		tmp = z * ((y3 * t_1) + ((k * ((b * y0) - (i * y1))) + (t * t_2)))
	elif y0 <= 8e+95:
		tmp = t * t_3
	elif y0 <= 2.8e+179:
		tmp = t_5
	elif y0 <= 3.9e+273:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	else:
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y1) - Float64(c * y0))
	t_2 = Float64(Float64(c * i) - Float64(a * b))
	t_3 = Float64(z * t_2)
	t_4 = Float64(Float64(y * k) - Float64(t * j))
	t_5 = Float64(y5 * Float64(Float64(i * t_4) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))))
	tmp = 0.0
	if (y0 <= -1.05e+61)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y0 <= -2.05e-43)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(z * t_1)));
	elseif (y0 <= -6.6e-204)
		tmp = Float64(t * Float64(t_3 + Float64(Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5))))));
	elseif (y0 <= 1.2e-96)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (y0 <= 9e-11)
		tmp = t_5;
	elseif (y0 <= 1950000000.0)
		tmp = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * t_4)) - Float64(c * Float64(Float64(x * y) - Float64(z * t)))));
	elseif (y0 <= 2.45e+67)
		tmp = Float64(z * Float64(Float64(y3 * t_1) + Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(t * t_2))));
	elseif (y0 <= 8e+95)
		tmp = Float64(t * t_3);
	elseif (y0 <= 2.8e+179)
		tmp = t_5;
	elseif (y0 <= 3.9e+273)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(x * Float64(c * Float64(Float64(Float64(Float64(y0 * y2) * Float64(y0 * y2)) - Float64(Float64(y * i) * Float64(y * i))) / Float64(Float64(y0 * y2) + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y1) - (c * y0);
	t_2 = (c * i) - (a * b);
	t_3 = z * t_2;
	t_4 = (y * k) - (t * j);
	t_5 = y5 * ((i * t_4) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	tmp = 0.0;
	if (y0 <= -1.05e+61)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y0 <= -2.05e-43)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * t_1));
	elseif (y0 <= -6.6e-204)
		tmp = t * (t_3 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	elseif (y0 <= 1.2e-96)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (y0 <= 9e-11)
		tmp = t_5;
	elseif (y0 <= 1950000000.0)
		tmp = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_4)) - (c * ((x * y) - (z * t))));
	elseif (y0 <= 2.45e+67)
		tmp = z * ((y3 * t_1) + ((k * ((b * y0) - (i * y1))) + (t * t_2)));
	elseif (y0 <= 8e+95)
		tmp = t * t_3;
	elseif (y0 <= 2.8e+179)
		tmp = t_5;
	elseif (y0 <= 3.9e+273)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	else
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y5 * N[(N[(i * t$95$4), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -1.05e+61], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.05e-43], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -6.6e-204], N[(t * N[(t$95$3 + N[(N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.2e-96], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9e-11], t$95$5, If[LessEqual[y0, 1950000000.0], N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.45e+67], N[(z * N[(N[(y3 * t$95$1), $MachinePrecision] + N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 8e+95], N[(t * t$95$3), $MachinePrecision], If[LessEqual[y0, 2.8e+179], t$95$5, If[LessEqual[y0, 3.9e+273], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(c * N[(N[(N[(N[(y0 * y2), $MachinePrecision] * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y0 * y2), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y0 < -1.0500000000000001e61

   1. Initial program 23.2%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 41.4%

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

   5. Taylor expanded in y0 around inf 57.9%

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

   if -1.0500000000000001e61 < y0 < -2.0499999999999999e-43

   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 y3 around -inf 52.8%

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

   5. Taylor expanded in j around 0 61.5%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot z - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot y3\right) \]
   6. Step-by-step derivation

      1. *-commutative 61.5%

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

      2. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   if -2.0499999999999999e-43 < y0 < -6.60000000000000018e-204

   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 36.5%

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

   4. Taylor expanded in t around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. mul-1-neg 57.6%

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

      3. sub-neg 57.6%

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

   6. Simplified 57.6%

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

   if -6.60000000000000018e-204 < y0 < 1.2000000000000001e-96

   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 32.8%

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

   4. Taylor expanded in x around inf 55.8%

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

   if 1.2000000000000001e-96 < y0 < 8.9999999999999999e-11 or 8.00000000000000016e95 < y0 < 2.8e179

   1. Initial program 26.7%

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

   3. Simplified 36.7%

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

   4. Taylor expanded in y5 around -inf 64.4%

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

   if 8.9999999999999999e-11 < y0 < 1.95e9

   1. Initial program 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in i around -inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. associate--l+ 80.8%

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

   6. Simplified 80.8%

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

   if 1.95e9 < y0 < 2.44999999999999995e67

   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 z around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. associate--l+ 85.7%

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

   6. Simplified 85.7%

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

   if 2.44999999999999995e67 < y0 < 8.00000000000000016e95

   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 z around -inf 14.3%

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

      1. mul-1-neg 14.3%

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

      2. associate--l+ 14.3%

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

   6. Simplified 14.3%

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

   7. Taylor expanded in t around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. *-commutative 71.7%

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

      3. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if 2.8e179 < y0 < 3.9000000000000001e273

   1. Initial program 28.0%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in y2 around inf 52.5%

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

   5. Taylor expanded in y0 around -inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

      4. *-commutative 65.3%

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

      5. mul-1-neg 65.3%

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

      6. unsub-neg 65.3%

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

      7. *-commutative 65.3%

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

   7. Simplified 65.3%

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

   if 3.9000000000000001e273 < y0

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in x around inf 40.0%

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

   5. Taylor expanded in c around inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. +-commutative 60.6%

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

      3. mul-1-neg 60.6%

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

      4. unsub-neg 60.6%

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

   7. Simplified 60.6%

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

      1. flip-- 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

      4. *-commutative 80.0%

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

   9. Applied egg-rr 80.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1.05 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -2.05 \cdot 10^{-43}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -6.6 \cdot 10^{-204}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-11}:\\ \;\;\;\;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}\;y0 \leq 1950000000:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq 2.45 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) + \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t \cdot \left(c \cdot i - a \cdot b\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 2.8 \cdot 10^{+179}:\\ \;\;\;\;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}\;y0 \leq 3.9 \cdot 10^{+273}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{\left(y0 \cdot y2\right) \cdot \left(y0 \cdot y2\right) - \left(y \cdot i\right) \cdot \left(y \cdot i\right)}{y0 \cdot y2 + y \cdot i}\right)\\ \end{array} \]

Alternative 9: 39.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot i - a \cdot b\right)\\ t_2 := y \cdot k - t \cdot j\\ t_3 := y \cdot \left(c \cdot y4 - a \cdot y5\right)\\ t_4 := x \cdot y - z \cdot t\\ t_5 := i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot t_2\right) - c \cdot t_4\right)\\ t_6 := z \cdot \left(a \cdot y1 - c \cdot y0\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+131}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(t_1 + \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.1 \cdot 10^{-271}:\\ \;\;\;\;y3 \cdot \left(\left(t_6 + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + t_3\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(\left(a \cdot t_4 + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;y3 \cdot \left(t_3 + t_6\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+188}:\\ \;\;\;\;t \cdot t_1\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+247}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+257}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_2 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* z (- (* c i) (* a b))))
        (t_2 (- (* y k) (* t j)))
        (t_3 (* y (- (* c y4) (* a y5))))
        (t_4 (- (* x y) (* z t)))
        (t_5 (* i (- (+ (* y1 (- (* x j) (* z k))) (* y5 t_2)) (* c t_4))))
        (t_6 (* z (- (* a y1) (* c y0)))))
   (if (<= i -1.25e+131)
     t_5
     (if (<= i -1.5e-147)
       (*
        t
        (+ t_1 (+ (* y2 (- (* a y5) (* c y4))) (* j (- (* b y4) (* i y5))))))
       (if (<= i 8.1e-271)
         (* y3 (+ (+ t_6 (* j (- (* y0 y5) (* y1 y4)))) t_3))
         (if (<= i 1.6e-155)
           (*
            b
            (+
             (+ (* a t_4) (* y4 (- (* t j) (* y k))))
             (* y0 (- (* z k) (* x j)))))
           (if (<= i 3.6e+26)
             (* y3 (+ t_3 t_6))
             (if (<= i 2.6e+150)
               (* x (* b (- (* y a) (* j y0))))
               (if (<= i 1.6e+188)
                 (* t t_1)
                 (if (<= i 3.1e+247)
                   (*
                    x
                    (+
                     (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
                     (* j (- (* i y1) (* b y0)))))
                   (if (<= i 5.6e+257)
                     (*
                      y5
                      (+
                       (* i t_2)
                       (+
                        (* a (- (* t y2) (* y y3)))
                        (* y0 (- (* j y3) (* k y2))))))
                     t_5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((c * i) - (a * b));
	double t_2 = (y * k) - (t * j);
	double t_3 = y * ((c * y4) - (a * y5));
	double t_4 = (x * y) - (z * t);
	double t_5 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * t_4));
	double t_6 = z * ((a * y1) - (c * y0));
	double tmp;
	if (i <= -1.25e+131) {
		tmp = t_5;
	} else if (i <= -1.5e-147) {
		tmp = t * (t_1 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	} else if (i <= 8.1e-271) {
		tmp = y3 * ((t_6 + (j * ((y0 * y5) - (y1 * y4)))) + t_3);
	} else if (i <= 1.6e-155) {
		tmp = b * (((a * t_4) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 3.6e+26) {
		tmp = y3 * (t_3 + t_6);
	} else if (i <= 2.6e+150) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (i <= 1.6e+188) {
		tmp = t * t_1;
	} else if (i <= 3.1e+247) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (i <= 5.6e+257) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = z * ((c * i) - (a * b))
    t_2 = (y * k) - (t * j)
    t_3 = y * ((c * y4) - (a * y5))
    t_4 = (x * y) - (z * t)
    t_5 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * t_4))
    t_6 = z * ((a * y1) - (c * y0))
    if (i <= (-1.25d+131)) then
        tmp = t_5
    else if (i <= (-1.5d-147)) then
        tmp = t * (t_1 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))))
    else if (i <= 8.1d-271) then
        tmp = y3 * ((t_6 + (j * ((y0 * y5) - (y1 * y4)))) + t_3)
    else if (i <= 1.6d-155) then
        tmp = b * (((a * t_4) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
    else if (i <= 3.6d+26) then
        tmp = y3 * (t_3 + t_6)
    else if (i <= 2.6d+150) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (i <= 1.6d+188) then
        tmp = t * t_1
    else if (i <= 3.1d+247) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    else if (i <= 5.6d+257) then
        tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = z * ((c * i) - (a * b));
	double t_2 = (y * k) - (t * j);
	double t_3 = y * ((c * y4) - (a * y5));
	double t_4 = (x * y) - (z * t);
	double t_5 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * t_4));
	double t_6 = z * ((a * y1) - (c * y0));
	double tmp;
	if (i <= -1.25e+131) {
		tmp = t_5;
	} else if (i <= -1.5e-147) {
		tmp = t * (t_1 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	} else if (i <= 8.1e-271) {
		tmp = y3 * ((t_6 + (j * ((y0 * y5) - (y1 * y4)))) + t_3);
	} else if (i <= 1.6e-155) {
		tmp = b * (((a * t_4) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	} else if (i <= 3.6e+26) {
		tmp = y3 * (t_3 + t_6);
	} else if (i <= 2.6e+150) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (i <= 1.6e+188) {
		tmp = t * t_1;
	} else if (i <= 3.1e+247) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	} else if (i <= 5.6e+257) {
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = z * ((c * i) - (a * b))
	t_2 = (y * k) - (t * j)
	t_3 = y * ((c * y4) - (a * y5))
	t_4 = (x * y) - (z * t)
	t_5 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * t_4))
	t_6 = z * ((a * y1) - (c * y0))
	tmp = 0
	if i <= -1.25e+131:
		tmp = t_5
	elif i <= -1.5e-147:
		tmp = t * (t_1 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))))
	elif i <= 8.1e-271:
		tmp = y3 * ((t_6 + (j * ((y0 * y5) - (y1 * y4)))) + t_3)
	elif i <= 1.6e-155:
		tmp = b * (((a * t_4) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))))
	elif i <= 3.6e+26:
		tmp = y3 * (t_3 + t_6)
	elif i <= 2.6e+150:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif i <= 1.6e+188:
		tmp = t * t_1
	elif i <= 3.1e+247:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	elif i <= 5.6e+257:
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(z * Float64(Float64(c * i) - Float64(a * b)))
	t_2 = Float64(Float64(y * k) - Float64(t * j))
	t_3 = Float64(y * Float64(Float64(c * y4) - Float64(a * y5)))
	t_4 = Float64(Float64(x * y) - Float64(z * t))
	t_5 = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * t_2)) - Float64(c * t_4)))
	t_6 = Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))
	tmp = 0.0
	if (i <= -1.25e+131)
		tmp = t_5;
	elseif (i <= -1.5e-147)
		tmp = Float64(t * Float64(t_1 + Float64(Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))) + Float64(j * Float64(Float64(b * y4) - Float64(i * y5))))));
	elseif (i <= 8.1e-271)
		tmp = Float64(y3 * Float64(Float64(t_6 + Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4)))) + t_3));
	elseif (i <= 1.6e-155)
		tmp = Float64(b * Float64(Float64(Float64(a * t_4) + Float64(y4 * Float64(Float64(t * j) - Float64(y * k)))) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 3.6e+26)
		tmp = Float64(y3 * Float64(t_3 + t_6));
	elseif (i <= 2.6e+150)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (i <= 1.6e+188)
		tmp = Float64(t * t_1);
	elseif (i <= 3.1e+247)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))));
	elseif (i <= 5.6e+257)
		tmp = Float64(y5 * Float64(Float64(i * t_2) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * Float64(Float64(j * y3) - Float64(k * y2))))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = z * ((c * i) - (a * b));
	t_2 = (y * k) - (t * j);
	t_3 = y * ((c * y4) - (a * y5));
	t_4 = (x * y) - (z * t);
	t_5 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_2)) - (c * t_4));
	t_6 = z * ((a * y1) - (c * y0));
	tmp = 0.0;
	if (i <= -1.25e+131)
		tmp = t_5;
	elseif (i <= -1.5e-147)
		tmp = t * (t_1 + ((y2 * ((a * y5) - (c * y4))) + (j * ((b * y4) - (i * y5)))));
	elseif (i <= 8.1e-271)
		tmp = y3 * ((t_6 + (j * ((y0 * y5) - (y1 * y4)))) + t_3);
	elseif (i <= 1.6e-155)
		tmp = b * (((a * t_4) + (y4 * ((t * j) - (y * k)))) + (y0 * ((z * k) - (x * j))));
	elseif (i <= 3.6e+26)
		tmp = y3 * (t_3 + t_6);
	elseif (i <= 2.6e+150)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (i <= 1.6e+188)
		tmp = t * t_1;
	elseif (i <= 3.1e+247)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	elseif (i <= 5.6e+257)
		tmp = y5 * ((i * t_2) + ((a * ((t * y2) - (y * y3))) + (y0 * ((j * y3) - (k * y2)))));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e+131], t$95$5, If[LessEqual[i, -1.5e-147], N[(t * N[(t$95$1 + N[(N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.1e-271], N[(y3 * N[(N[(t$95$6 + N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e-155], N[(b * N[(N[(N[(a * t$95$4), $MachinePrecision] + N[(y4 * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.6e+26], N[(y3 * N[(t$95$3 + t$95$6), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+150], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e+188], N[(t * t$95$1), $MachinePrecision], If[LessEqual[i, 3.1e+247], N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.6e+257], N[(y5 * N[(N[(i * t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if i < -1.24999999999999999e131 or 5.5999999999999996e257 < i

   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 i around -inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. associate--l+ 64.4%

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

   6. Simplified 64.4%

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

   if -1.24999999999999999e131 < i < -1.5000000000000001e-147

   1. Initial program 32.2%

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

   3. Simplified 37.3%

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

   4. Taylor expanded in t around inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. mul-1-neg 50.3%

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

      3. sub-neg 50.3%

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

   6. Simplified 50.3%

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

   if -1.5000000000000001e-147 < i < 8.09999999999999958e-271

   1. Initial program 37.1%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in y3 around -inf 58.4%

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

   if 8.09999999999999958e-271 < i < 1.60000000000000006e-155

   1. Initial program 43.8%

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

   3. Simplified 43.8%

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

   4. Taylor expanded in b around inf 62.5%

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

   if 1.60000000000000006e-155 < i < 3.60000000000000024e26

   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 y3 around -inf 57.4%

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

   5. Taylor expanded in j around 0 68.7%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot z - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot y3\right) \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

   7. Simplified 68.7%

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

   if 3.60000000000000024e26 < i < 2.60000000000000006e150

   1. Initial program 33.5%

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

   3. Simplified 33.5%

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

   4. Taylor expanded in x around inf 61.4%

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

      1. add-cbrt-cube 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 66.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 66.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 66.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 61.8%

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

       1. *-commutative 61.8%

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

       2. *-commutative 61.8%

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

       3. associate-*l* 67.2%

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

   11. Simplified 67.2%

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

   if 2.60000000000000006e150 < i < 1.59999999999999985e188

   1. Initial program 15.4%

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

   3. Simplified 15.4%

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

   4. Taylor expanded in z around -inf 54.0%

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

      1. mul-1-neg 54.0%

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

      2. associate--l+ 54.0%

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

   6. Simplified 54.0%

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

   7. Taylor expanded in t around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. *-commutative 69.6%

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

   9. Simplified 69.6%

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

   if 1.59999999999999985e188 < i < 3.0999999999999998e247

   1. Initial program 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in x around inf 77.8%

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

   if 3.0999999999999998e247 < i < 5.5999999999999996e257

   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%

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

   4. Taylor expanded in y5 around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(i \cdot \left(t \cdot j - k \cdot y\right) + \left(\left(y \cdot y3 - t \cdot y2\right) \cdot a + y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+131}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right) + \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right) + j \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.1 \cdot 10^{-271}:\\ \;\;\;\;y3 \cdot \left(\left(z \cdot \left(a \cdot y1 - c \cdot y0\right) + j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right)\right) + y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+188}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+247}:\\ \;\;\;\;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}\;i \leq 5.6 \cdot 10^{+257}:\\ \;\;\;\;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{else}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 10: 40.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot k - t \cdot j\\ t_2 := i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot t_1\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_3 := j \cdot y3 - k \cdot y2\\ t_4 := i \cdot y1 - b \cdot y0\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-116}:\\ \;\;\;\;y5 \cdot \left(i \cdot t_1 + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot t_3\right)\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot t_4\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-149}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot t_3 + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+36}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot t_4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* y k) (* t j)))
        (t_2
         (*
          i
          (-
           (+ (* y1 (- (* x j) (* z k))) (* y5 t_1))
           (* c (- (* x y) (* z t))))))
        (t_3 (- (* j y3) (* k y2)))
        (t_4 (- (* i y1) (* b y0))))
   (if (<= i -1.4e+160)
     t_2
     (if (<= i -1.65e-116)
       (* y5 (+ (* i t_1) (+ (* a (- (* t y2) (* y y3))) (* y0 t_3))))
       (if (<= i -1.05e-283)
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j t_4)))
         (if (<= i 1.2e-149)
           (*
            y0
            (+
             (+ (* y5 t_3) (* c (- (* x y2) (* z y3))))
             (* b (- (* z k) (* x j)))))
           (if (<= i 1.05e+36)
             (* y3 (+ (* y (- (* c y4) (* a y5))) (* z (- (* a y1) (* c y0)))))
             (if (<= i 4e+174)
               (*
                j
                (+
                 (+ (* y3 (- (* y0 y5) (* y1 y4))) (* t (- (* b y4) (* i y5))))
                 (* x t_4)))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_1)) - (c * ((x * y) - (z * t))));
	double t_3 = (j * y3) - (k * y2);
	double t_4 = (i * y1) - (b * y0);
	double tmp;
	if (i <= -1.4e+160) {
		tmp = t_2;
	} else if (i <= -1.65e-116) {
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * t_3)));
	} else if (i <= -1.05e-283) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_4));
	} else if (i <= 1.2e-149) {
		tmp = y0 * (((y5 * t_3) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (i <= 1.05e+36) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (i <= 4e+174) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_4));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (y * k) - (t * j)
    t_2 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_1)) - (c * ((x * y) - (z * t))))
    t_3 = (j * y3) - (k * y2)
    t_4 = (i * y1) - (b * y0)
    if (i <= (-1.4d+160)) then
        tmp = t_2
    else if (i <= (-1.65d-116)) then
        tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * t_3)))
    else if (i <= (-1.05d-283)) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_4))
    else if (i <= 1.2d-149) then
        tmp = y0 * (((y5 * t_3) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
    else if (i <= 1.05d+36) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
    else if (i <= 4d+174) then
        tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_4))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y * k) - (t * j);
	double t_2 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_1)) - (c * ((x * y) - (z * t))));
	double t_3 = (j * y3) - (k * y2);
	double t_4 = (i * y1) - (b * y0);
	double tmp;
	if (i <= -1.4e+160) {
		tmp = t_2;
	} else if (i <= -1.65e-116) {
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * t_3)));
	} else if (i <= -1.05e-283) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_4));
	} else if (i <= 1.2e-149) {
		tmp = y0 * (((y5 * t_3) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	} else if (i <= 1.05e+36) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (i <= 4e+174) {
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_4));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (y * k) - (t * j)
	t_2 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_1)) - (c * ((x * y) - (z * t))))
	t_3 = (j * y3) - (k * y2)
	t_4 = (i * y1) - (b * y0)
	tmp = 0
	if i <= -1.4e+160:
		tmp = t_2
	elif i <= -1.65e-116:
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * t_3)))
	elif i <= -1.05e-283:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_4))
	elif i <= 1.2e-149:
		tmp = y0 * (((y5 * t_3) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))))
	elif i <= 1.05e+36:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
	elif i <= 4e+174:
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_4))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(y * k) - Float64(t * j))
	t_2 = Float64(i * Float64(Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(y5 * t_1)) - Float64(c * Float64(Float64(x * y) - Float64(z * t)))))
	t_3 = Float64(Float64(j * y3) - Float64(k * y2))
	t_4 = Float64(Float64(i * y1) - Float64(b * y0))
	tmp = 0.0
	if (i <= -1.4e+160)
		tmp = t_2;
	elseif (i <= -1.65e-116)
		tmp = Float64(y5 * Float64(Float64(i * t_1) + Float64(Float64(a * Float64(Float64(t * y2) - Float64(y * y3))) + Float64(y0 * t_3))));
	elseif (i <= -1.05e-283)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) + Float64(j * t_4)));
	elseif (i <= 1.2e-149)
		tmp = Float64(y0 * Float64(Float64(Float64(y5 * t_3) + Float64(c * Float64(Float64(x * y2) - Float64(z * y3)))) + Float64(b * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (i <= 1.05e+36)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))));
	elseif (i <= 4e+174)
		tmp = Float64(j * Float64(Float64(Float64(y3 * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) + Float64(x * t_4)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (y * k) - (t * j);
	t_2 = i * (((y1 * ((x * j) - (z * k))) + (y5 * t_1)) - (c * ((x * y) - (z * t))));
	t_3 = (j * y3) - (k * y2);
	t_4 = (i * y1) - (b * y0);
	tmp = 0.0;
	if (i <= -1.4e+160)
		tmp = t_2;
	elseif (i <= -1.65e-116)
		tmp = y5 * ((i * t_1) + ((a * ((t * y2) - (y * y3))) + (y0 * t_3)));
	elseif (i <= -1.05e-283)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * t_4));
	elseif (i <= 1.2e-149)
		tmp = y0 * (((y5 * t_3) + (c * ((x * y2) - (z * y3)))) + (b * ((z * k) - (x * j))));
	elseif (i <= 1.05e+36)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	elseif (i <= 4e+174)
		tmp = j * (((y3 * ((y0 * y5) - (y1 * y4))) + (t * ((b * y4) - (i * y5)))) + (x * t_4));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * y3), $MachinePrecision] - N[(k * y2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+160], t$95$2, If[LessEqual[i, -1.65e-116], N[(y5 * N[(N[(i * t$95$1), $MachinePrecision] + N[(N[(a * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.05e-283], 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 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e-149], N[(y0 * N[(N[(N[(y5 * t$95$3), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e+36], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+174], N[(j * N[(N[(N[(y3 * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.4e160 or 4.00000000000000028e174 < i

   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 i around -inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. associate--l+ 67.0%

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

   6. Simplified 67.0%

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

   if -1.4e160 < i < -1.65e-116

   1. Initial program 33.9%

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

   3. Simplified 39.3%

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

   4. Taylor expanded in y5 around -inf 51.2%

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

   if -1.65e-116 < i < -1.04999999999999999e-283

   1. Initial program 43.8%

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

   3. Simplified 43.8%

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

   4. Taylor expanded in x around inf 62.8%

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

   if -1.04999999999999999e-283 < i < 1.2000000000000001e-149

   1. Initial program 30.6%

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

   3. Simplified 30.6%

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

   4. Taylor expanded in y0 around inf 56.3%

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

   if 1.2000000000000001e-149 < i < 1.05000000000000002e36

   1. Initial program 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in y3 around -inf 55.8%

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

   5. Taylor expanded in j around 0 66.8%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot z - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot y3\right) \]
   6. Step-by-step derivation

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   7. Simplified 66.8%

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

   if 1.05000000000000002e36 < i < 4.00000000000000028e174

   1. Initial program 21.0%

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

   3. Simplified 21.0%

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

   4. Taylor expanded in j around inf 70.9%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+160}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-116}:\\ \;\;\;\;y5 \cdot \left(i \cdot \left(y \cdot k - t \cdot j\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + y0 \cdot \left(j \cdot y3 - k \cdot y2\right)\right)\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-149}:\\ \;\;\;\;y0 \cdot \left(\left(y5 \cdot \left(j \cdot y3 - k \cdot y2\right) + c \cdot \left(x \cdot y2 - z \cdot y3\right)\right) + b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+36}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(\left(y3 \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(y1 \cdot \left(x \cdot j - z \cdot k\right) + y5 \cdot \left(y \cdot k - t \cdot j\right)\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 35.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := i \cdot y1 - b \cdot y0\\ \mathbf{if}\;y0 \leq -3 \cdot 10^{+60}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.16 \cdot 10^{-42}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.85 \cdot 10^{-204}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_1 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot t_2\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(x \cdot t_2\right)\\ \mathbf{elif}\;y0 \leq 1.92 \cdot 10^{+180}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+273}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{\left(y0 \cdot y2\right) \cdot \left(y0 \cdot y2\right) - \left(y \cdot i\right) \cdot \left(y \cdot i\right)}{y0 \cdot y2 + y \cdot i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1))) (t_2 (- (* i y1) (* b y0))))
   (if (<= y0 -3e+60)
     (* j (* y0 (- (* y3 y5) (* x b))))
     (if (<= y0 -1.16e-42)
       (* y3 (+ (* y (- (* c y4) (* a y5))) (* z (- (* a y1) (* c y0)))))
       (if (<= y0 -1.85e-204)
         (*
          y2
          (+
           (+ (* x t_1) (* k (- (* y1 y4) (* y0 y5))))
           (* t (- (* a y5) (* c y4)))))
         (if (<= y0 1.6e-18)
           (* x (+ (+ (* y (- (* a b) (* c i))) (* y2 t_1)) (* j t_2)))
           (if (<= y0 6.5e+121)
             (* j (* x t_2))
             (if (<= y0 1.92e+180)
               (* (* z y0) (- (* b k) (* c y3)))
               (if (<= y0 3.9e+273)
                 (* y0 (* y2 (- (* x c) (* k y5))))
                 (*
                  x
                  (*
                   c
                   (/
                    (- (* (* y0 y2) (* y0 y2)) (* (* y i) (* y i)))
                    (+ (* y0 y2) (* y i))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double tmp;
	if (y0 <= -3e+60) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y0 <= -1.16e-42) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (y0 <= -1.85e-204) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 1.6e-18) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	} else if (y0 <= 6.5e+121) {
		tmp = j * (x * t_2);
	} else if (y0 <= 1.92e+180) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= 3.9e+273) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * y0) - (a * y1)
    t_2 = (i * y1) - (b * y0)
    if (y0 <= (-3d+60)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (y0 <= (-1.16d-42)) then
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
    else if (y0 <= (-1.85d-204)) then
        tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y0 <= 1.6d-18) then
        tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
    else if (y0 <= 6.5d+121) then
        tmp = j * (x * t_2)
    else if (y0 <= 1.92d+180) then
        tmp = (z * y0) * ((b * k) - (c * y3))
    else if (y0 <= 3.9d+273) then
        tmp = y0 * (y2 * ((x * c) - (k * y5)))
    else
        tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = (i * y1) - (b * y0);
	double tmp;
	if (y0 <= -3e+60) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (y0 <= -1.16e-42) {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	} else if (y0 <= -1.85e-204) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y0 <= 1.6e-18) {
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	} else if (y0 <= 6.5e+121) {
		tmp = j * (x * t_2);
	} else if (y0 <= 1.92e+180) {
		tmp = (z * y0) * ((b * k) - (c * y3));
	} else if (y0 <= 3.9e+273) {
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	} else {
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	}
	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 = (i * y1) - (b * y0)
	tmp = 0
	if y0 <= -3e+60:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif y0 <= -1.16e-42:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))))
	elif y0 <= -1.85e-204:
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y0 <= 1.6e-18:
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2))
	elif y0 <= 6.5e+121:
		tmp = j * (x * t_2)
	elif y0 <= 1.92e+180:
		tmp = (z * y0) * ((b * k) - (c * y3))
	elif y0 <= 3.9e+273:
		tmp = y0 * (y2 * ((x * c) - (k * y5)))
	else:
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(Float64(i * y1) - Float64(b * y0))
	tmp = 0.0
	if (y0 <= -3e+60)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (y0 <= -1.16e-42)
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(z * Float64(Float64(a * y1) - Float64(c * y0)))));
	elseif (y0 <= -1.85e-204)
		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 (y0 <= 1.6e-18)
		tmp = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * t_2)));
	elseif (y0 <= 6.5e+121)
		tmp = Float64(j * Float64(x * t_2));
	elseif (y0 <= 1.92e+180)
		tmp = Float64(Float64(z * y0) * Float64(Float64(b * k) - Float64(c * y3)));
	elseif (y0 <= 3.9e+273)
		tmp = Float64(y0 * Float64(y2 * Float64(Float64(x * c) - Float64(k * y5))));
	else
		tmp = Float64(x * Float64(c * Float64(Float64(Float64(Float64(y0 * y2) * Float64(y0 * y2)) - Float64(Float64(y * i) * Float64(y * i))) / Float64(Float64(y0 * y2) + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = (i * y1) - (b * y0);
	tmp = 0.0;
	if (y0 <= -3e+60)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (y0 <= -1.16e-42)
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + (z * ((a * y1) - (c * y0))));
	elseif (y0 <= -1.85e-204)
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y0 <= 1.6e-18)
		tmp = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * t_2));
	elseif (y0 <= 6.5e+121)
		tmp = j * (x * t_2);
	elseif (y0 <= 1.92e+180)
		tmp = (z * y0) * ((b * k) - (c * y3));
	elseif (y0 <= 3.9e+273)
		tmp = y0 * (y2 * ((x * c) - (k * y5)));
	else
		tmp = x * (c * ((((y0 * y2) * (y0 * y2)) - ((y * i) * (y * i))) / ((y0 * y2) + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -3e+60], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.16e-42], N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.85e-204], 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[y0, 1.6e-18], 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 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.5e+121], N[(j * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.92e+180], N[(N[(z * y0), $MachinePrecision] * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 3.9e+273], N[(y0 * N[(y2 * N[(N[(x * c), $MachinePrecision] - N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(c * N[(N[(N[(N[(y0 * y2), $MachinePrecision] * N[(y0 * y2), $MachinePrecision]), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y0 * y2), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -2.9999999999999998e60

   1. Initial program 23.2%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in j around inf 41.4%

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

   5. Taylor expanded in y0 around inf 57.9%

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

   if -2.9999999999999998e60 < y0 < -1.1600000000000001e-42

   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 y3 around -inf 52.8%

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

   5. Taylor expanded in j around 0 61.5%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot z - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \cdot y3\right) \]
   6. Step-by-step derivation

      1. *-commutative 61.5%

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

      2. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   if -1.1600000000000001e-42 < y0 < -1.8499999999999999e-204

   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 27.4%

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

   4. Taylor expanded in y2 around inf 54.8%

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

   if -1.8499999999999999e-204 < y0 < 1.6e-18

   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 x around inf 54.0%

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

   if 1.6e-18 < y0 < 6.50000000000000019e121

   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%

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

   4. Taylor expanded in j around inf 41.1%

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

   5. Taylor expanded in x around inf 53.5%

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

   if 6.50000000000000019e121 < y0 < 1.9200000000000001e180

   1. Initial program 21.4%

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

   3. Simplified 21.4%

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

   4. Taylor expanded in z around -inf 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate--l+ 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in y0 around inf 51.5%

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

      1. associate-*r* 71.8%

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

      2. *-commutative 71.8%

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

   9. Simplified 71.8%

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

   if 1.9200000000000001e180 < y0 < 3.9000000000000001e273

   1. Initial program 28.0%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in y2 around inf 52.5%

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

   5. Taylor expanded in y0 around -inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

      4. *-commutative 65.3%

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

      5. mul-1-neg 65.3%

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

      6. unsub-neg 65.3%

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

      7. *-commutative 65.3%

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

   7. Simplified 65.3%

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

   if 3.9000000000000001e273 < y0

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in x around inf 40.0%

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

   5. Taylor expanded in c around inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. +-commutative 60.6%

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

      3. mul-1-neg 60.6%

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

      4. unsub-neg 60.6%

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

   7. Simplified 60.6%

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

      1. flip-- 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

      4. *-commutative 80.0%

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

   9. Applied egg-rr 80.0%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -3 \cdot 10^{+60}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq -1.16 \cdot 10^{-42}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq -1.85 \cdot 10^{-204}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 6.5 \cdot 10^{+121}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y0 \leq 1.92 \cdot 10^{+180}:\\ \;\;\;\;\left(z \cdot y0\right) \cdot \left(b \cdot k - c \cdot y3\right)\\ \mathbf{elif}\;y0 \leq 3.9 \cdot 10^{+273}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \left(x \cdot c - k \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{\left(y0 \cdot y2\right) \cdot \left(y0 \cdot y2\right) - \left(y \cdot i\right) \cdot \left(y \cdot i\right)}{y0 \cdot y2 + y \cdot i}\right)\\ \end{array} \]

Alternative 12: 31.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ t_3 := y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-217}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-269}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-230}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (- (* y y3) (* t y2)))))
        (t_2 (* j (* y0 (- (* y3 y5) (* x b)))))
        (t_3 (* y2 (* a (- (* t y5) (* x y1))))))
   (if (<= c -4e+149)
     t_1
     (if (<= c -3.2e-200)
       (* x (* b (- (* y a) (* j y0))))
       (if (<= c -8.5e-217)
         (* y1 (* (* x y2) (- a)))
         (if (<= c -1e-281)
           t_2
           (if (<= c 1.7e-269)
             (* y4 (* b (- (* t j) (* y k))))
             (if (<= c 2.8e-230)
               t_3
               (if (<= c 3.2e-144)
                 (* y4 (* k (- (* y1 y2) (* y b))))
                 (if (<= c 1.2e-8) t_3 (if (<= c 9.2e+126) 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 = y4 * (c * ((y * y3) - (t * y2)));
	double t_2 = j * (y0 * ((y3 * y5) - (x * b)));
	double t_3 = y2 * (a * ((t * y5) - (x * y1)));
	double tmp;
	if (c <= -4e+149) {
		tmp = t_1;
	} else if (c <= -3.2e-200) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (c <= -8.5e-217) {
		tmp = y1 * ((x * y2) * -a);
	} else if (c <= -1e-281) {
		tmp = t_2;
	} else if (c <= 1.7e-269) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (c <= 2.8e-230) {
		tmp = t_3;
	} else if (c <= 3.2e-144) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (c <= 1.2e-8) {
		tmp = t_3;
	} else if (c <= 9.2e+126) {
		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) :: t_3
    real(8) :: tmp
    t_1 = y4 * (c * ((y * y3) - (t * y2)))
    t_2 = j * (y0 * ((y3 * y5) - (x * b)))
    t_3 = y2 * (a * ((t * y5) - (x * y1)))
    if (c <= (-4d+149)) then
        tmp = t_1
    else if (c <= (-3.2d-200)) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (c <= (-8.5d-217)) then
        tmp = y1 * ((x * y2) * -a)
    else if (c <= (-1d-281)) then
        tmp = t_2
    else if (c <= 1.7d-269) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (c <= 2.8d-230) then
        tmp = t_3
    else if (c <= 3.2d-144) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (c <= 1.2d-8) then
        tmp = t_3
    else if (c <= 9.2d+126) 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 = y4 * (c * ((y * y3) - (t * y2)));
	double t_2 = j * (y0 * ((y3 * y5) - (x * b)));
	double t_3 = y2 * (a * ((t * y5) - (x * y1)));
	double tmp;
	if (c <= -4e+149) {
		tmp = t_1;
	} else if (c <= -3.2e-200) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (c <= -8.5e-217) {
		tmp = y1 * ((x * y2) * -a);
	} else if (c <= -1e-281) {
		tmp = t_2;
	} else if (c <= 1.7e-269) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (c <= 2.8e-230) {
		tmp = t_3;
	} else if (c <= 3.2e-144) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (c <= 1.2e-8) {
		tmp = t_3;
	} else if (c <= 9.2e+126) {
		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 = y4 * (c * ((y * y3) - (t * y2)))
	t_2 = j * (y0 * ((y3 * y5) - (x * b)))
	t_3 = y2 * (a * ((t * y5) - (x * y1)))
	tmp = 0
	if c <= -4e+149:
		tmp = t_1
	elif c <= -3.2e-200:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif c <= -8.5e-217:
		tmp = y1 * ((x * y2) * -a)
	elif c <= -1e-281:
		tmp = t_2
	elif c <= 1.7e-269:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif c <= 2.8e-230:
		tmp = t_3
	elif c <= 3.2e-144:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif c <= 1.2e-8:
		tmp = t_3
	elif c <= 9.2e+126:
		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(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))))
	t_2 = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))))
	t_3 = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))))
	tmp = 0.0
	if (c <= -4e+149)
		tmp = t_1;
	elseif (c <= -3.2e-200)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (c <= -8.5e-217)
		tmp = Float64(y1 * Float64(Float64(x * y2) * Float64(-a)));
	elseif (c <= -1e-281)
		tmp = t_2;
	elseif (c <= 1.7e-269)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (c <= 2.8e-230)
		tmp = t_3;
	elseif (c <= 3.2e-144)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (c <= 1.2e-8)
		tmp = t_3;
	elseif (c <= 9.2e+126)
		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 = y4 * (c * ((y * y3) - (t * y2)));
	t_2 = j * (y0 * ((y3 * y5) - (x * b)));
	t_3 = y2 * (a * ((t * y5) - (x * y1)));
	tmp = 0.0;
	if (c <= -4e+149)
		tmp = t_1;
	elseif (c <= -3.2e-200)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (c <= -8.5e-217)
		tmp = y1 * ((x * y2) * -a);
	elseif (c <= -1e-281)
		tmp = t_2;
	elseif (c <= 1.7e-269)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (c <= 2.8e-230)
		tmp = t_3;
	elseif (c <= 3.2e-144)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (c <= 1.2e-8)
		tmp = t_3;
	elseif (c <= 9.2e+126)
		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[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e+149], t$95$1, If[LessEqual[c, -3.2e-200], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.5e-217], N[(y1 * N[(N[(x * y2), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1e-281], t$95$2, If[LessEqual[c, 1.7e-269], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e-230], t$95$3, If[LessEqual[c, 3.2e-144], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.2e-8], t$95$3, If[LessEqual[c, 9.2e+126], t$95$2, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -4.0000000000000002e149 or 9.2000000000000002e126 < c

   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 y4 around inf 40.8%

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

   5. Taylor expanded in c around inf 57.6%

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

      1. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   if -4.0000000000000002e149 < c < -3.19999999999999983e-200

   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 x around inf 54.2%

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

      1. add-cbrt-cube 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 55.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 55.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 34.1%

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

       1. *-commutative 34.1%

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

       2. *-commutative 34.1%

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

       3. associate-*l* 45.4%

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

   11. Simplified 45.4%

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

   if -3.19999999999999983e-200 < c < -8.4999999999999994e-217

   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 x around inf 57.3%

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

   5. Taylor expanded in y1 around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. associate-*r* 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in a around inf 57.8%

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

   if -8.4999999999999994e-217 < c < -1e-281 or 1.19999999999999999e-8 < c < 9.2000000000000002e126

   1. Initial program 35.2%

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

   3. Simplified 40.2%

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

   4. Taylor expanded in j around inf 50.4%

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

   5. Taylor expanded in y0 around inf 55.7%

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

   if -1e-281 < c < 1.6999999999999999e-269

   1. Initial program 9.2%

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

   3. Simplified 9.2%

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

   4. Taylor expanded in y4 around inf 26.8%

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

   5. Taylor expanded in b around inf 52.4%

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

   if 1.6999999999999999e-269 < c < 2.8000000000000001e-230 or 3.19999999999999973e-144 < c < 1.19999999999999999e-8

   1. Initial program 47.1%

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

   3. Simplified 47.1%

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

   4. Taylor expanded in y2 around inf 48.3%

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

   5. Taylor expanded in a around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. *-commutative 51.1%

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

      3. associate-*l* 53.9%

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

      4. cancel-sign-sub-inv 53.9%

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

      5. metadata-eval 53.9%

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

      6. *-lft-identity 53.9%

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

      7. +-commutative 53.9%

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

      8. mul-1-neg 53.9%

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

      9. unsub-neg 53.9%

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

      10. *-commutative 53.9%

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

   7. Simplified 53.9%

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

   if 2.8000000000000001e-230 < c < 3.19999999999999973e-144

   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 54.5%

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

   5. Taylor expanded in k around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. +-commutative 48.7%

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

      3. mul-1-neg 48.7%

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

      4. unsub-neg 48.7%

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

      5. *-commutative 48.7%

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

   7. Simplified 48.7%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+149}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-217}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-281}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-269}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-230}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-8}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 13: 30.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-217}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-270}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-230}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-127}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (- (* y y3) (* t y2))))))
   (if (<= c -2.6e+151)
     t_1
     (if (<= c -2.6e-200)
       (* x (* b (- (* y a) (* j y0))))
       (if (<= c -7.6e-217)
         (* y1 (* (* x y2) (- a)))
         (if (<= c -6.8e-282)
           (* j (* y0 (- (* y3 y5) (* x b))))
           (if (<= c 1.65e-270)
             (* y4 (* b (- (* t j) (* y k))))
             (if (<= c 2.8e-230)
               (* y2 (* a (- (* t y5) (* x y1))))
               (if (<= c 2.65e-127)
                 (* y4 (* k (- (* y1 y2) (* y b))))
                 (if (<= c 4.5e+166)
                   (* j (* x (- (* i y1) (* b 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 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -2.6e+151) {
		tmp = t_1;
	} else if (c <= -2.6e-200) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (c <= -7.6e-217) {
		tmp = y1 * ((x * y2) * -a);
	} else if (c <= -6.8e-282) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (c <= 1.65e-270) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (c <= 2.8e-230) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (c <= 2.65e-127) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (c <= 4.5e+166) {
		tmp = j * (x * ((i * y1) - (b * 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 * ((y * y3) - (t * y2)))
    if (c <= (-2.6d+151)) then
        tmp = t_1
    else if (c <= (-2.6d-200)) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (c <= (-7.6d-217)) then
        tmp = y1 * ((x * y2) * -a)
    else if (c <= (-6.8d-282)) then
        tmp = j * (y0 * ((y3 * y5) - (x * b)))
    else if (c <= 1.65d-270) then
        tmp = y4 * (b * ((t * j) - (y * k)))
    else if (c <= 2.8d-230) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (c <= 2.65d-127) then
        tmp = y4 * (k * ((y1 * y2) - (y * b)))
    else if (c <= 4.5d+166) then
        tmp = j * (x * ((i * y1) - (b * 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 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -2.6e+151) {
		tmp = t_1;
	} else if (c <= -2.6e-200) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (c <= -7.6e-217) {
		tmp = y1 * ((x * y2) * -a);
	} else if (c <= -6.8e-282) {
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	} else if (c <= 1.65e-270) {
		tmp = y4 * (b * ((t * j) - (y * k)));
	} else if (c <= 2.8e-230) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (c <= 2.65e-127) {
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	} else if (c <= 4.5e+166) {
		tmp = j * (x * ((i * y1) - (b * 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 * ((y * y3) - (t * y2)))
	tmp = 0
	if c <= -2.6e+151:
		tmp = t_1
	elif c <= -2.6e-200:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif c <= -7.6e-217:
		tmp = y1 * ((x * y2) * -a)
	elif c <= -6.8e-282:
		tmp = j * (y0 * ((y3 * y5) - (x * b)))
	elif c <= 1.65e-270:
		tmp = y4 * (b * ((t * j) - (y * k)))
	elif c <= 2.8e-230:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif c <= 2.65e-127:
		tmp = y4 * (k * ((y1 * y2) - (y * b)))
	elif c <= 4.5e+166:
		tmp = j * (x * ((i * y1) - (b * 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(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (c <= -2.6e+151)
		tmp = t_1;
	elseif (c <= -2.6e-200)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (c <= -7.6e-217)
		tmp = Float64(y1 * Float64(Float64(x * y2) * Float64(-a)));
	elseif (c <= -6.8e-282)
		tmp = Float64(j * Float64(y0 * Float64(Float64(y3 * y5) - Float64(x * b))));
	elseif (c <= 1.65e-270)
		tmp = Float64(y4 * Float64(b * Float64(Float64(t * j) - Float64(y * k))));
	elseif (c <= 2.8e-230)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (c <= 2.65e-127)
		tmp = Float64(y4 * Float64(k * Float64(Float64(y1 * y2) - Float64(y * b))));
	elseif (c <= 4.5e+166)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * 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 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (c <= -2.6e+151)
		tmp = t_1;
	elseif (c <= -2.6e-200)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (c <= -7.6e-217)
		tmp = y1 * ((x * y2) * -a);
	elseif (c <= -6.8e-282)
		tmp = j * (y0 * ((y3 * y5) - (x * b)));
	elseif (c <= 1.65e-270)
		tmp = y4 * (b * ((t * j) - (y * k)));
	elseif (c <= 2.8e-230)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (c <= 2.65e-127)
		tmp = y4 * (k * ((y1 * y2) - (y * b)));
	elseif (c <= 4.5e+166)
		tmp = j * (x * ((i * y1) - (b * 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[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.6e+151], t$95$1, If[LessEqual[c, -2.6e-200], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.6e-217], N[(y1 * N[(N[(x * y2), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.8e-282], N[(j * N[(y0 * N[(N[(y3 * y5), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e-270], N[(y4 * N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e-230], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.65e-127], N[(y4 * N[(k * N[(N[(y1 * y2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e+166], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -2.60000000000000013e151 or 4.5000000000000003e166 < c

   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 20.3%

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

   4. Taylor expanded in y4 around inf 40.8%

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

   5. Taylor expanded in c around inf 57.4%

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

      1. *-commutative 57.4%

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

   7. Simplified 57.4%

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

   if -2.60000000000000013e151 < c < -2.5999999999999999e-200

   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 x around inf 54.2%

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

      1. add-cbrt-cube 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 55.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 55.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 55.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 34.1%

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

       1. *-commutative 34.1%

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

       2. *-commutative 34.1%

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

       3. associate-*l* 45.4%

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

   11. Simplified 45.4%

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

   if -2.5999999999999999e-200 < c < -7.59999999999999974e-217

   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 x around inf 57.3%

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

   5. Taylor expanded in y1 around -inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. associate-*r* 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in a around inf 57.8%

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

   if -7.59999999999999974e-217 < c < -6.79999999999999997e-282

   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 35.3%

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

   4. Taylor expanded in j around inf 53.2%

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

   5. Taylor expanded in y0 around inf 65.1%

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

   if -6.79999999999999997e-282 < c < 1.65000000000000009e-270

   1. Initial program 9.2%

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

   3. Simplified 9.2%

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

   4. Taylor expanded in y4 around inf 26.8%

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

   5. Taylor expanded in b around inf 52.4%

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

   if 1.65000000000000009e-270 < c < 2.8000000000000001e-230

   1. Initial program 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in y2 around inf 50.9%

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

   5. Taylor expanded in a around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. *-commutative 70.4%

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

      3. associate-*l* 80.4%

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

      4. cancel-sign-sub-inv 80.4%

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

      5. metadata-eval 80.4%

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

      6. *-lft-identity 80.4%

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

      7. +-commutative 80.4%

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

      8. mul-1-neg 80.4%

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

      9. unsub-neg 80.4%

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

      10. *-commutative 80.4%

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

   7. Simplified 80.4%

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

   if 2.8000000000000001e-230 < c < 2.6500000000000001e-127

   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 y4 around inf 48.2%

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

   5. Taylor expanded in k around inf 49.0%

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

      1. *-commutative 49.0%

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

      2. +-commutative 49.0%

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

      3. mul-1-neg 49.0%

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

      4. unsub-neg 49.0%

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

      5. *-commutative 49.0%

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

   7. Simplified 49.0%

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

   if 2.6500000000000001e-127 < c < 4.5000000000000003e166

   1. Initial program 46.2%

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

   3. Simplified 48.1%

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

   4. Taylor expanded in j around inf 45.8%

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

   5. Taylor expanded in x around inf 42.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+151}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-217}:\\ \;\;\;\;y1 \cdot \left(\left(x \cdot y2\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(y0 \cdot \left(y3 \cdot y5 - x \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-270}:\\ \;\;\;\;y4 \cdot \left(b \cdot \left(t \cdot j - y \cdot k\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-230}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-127}:\\ \;\;\;\;y4 \cdot \left(k \cdot \left(y1 \cdot y2 - y \cdot b\right)\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 14: 30.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ t_2 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* x (- (* c y2) (* b j)))))
        (t_2 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= x -3.8e+179)
     (* y (* x (- (* a b) (* c i))))
     (if (<= x -7.5e-139)
       t_1
       (if (<= x 2.9e-185)
         t_2
         (if (<= x 3.8e-73)
           (* x (* b (- (* y a) (* j y0))))
           (if (<= x 1.5e+31)
             t_2
             (if (<= x 3.6e+177) (* y2 (* a (- (* t y5) (* x y1)))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (x * ((c * y2) - (b * j)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (x <= -3.8e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -7.5e-139) {
		tmp = t_1;
	} else if (x <= 2.9e-185) {
		tmp = t_2;
	} else if (x <= 3.8e-73) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (x <= 1.5e+31) {
		tmp = t_2;
	} else if (x <= 3.6e+177) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y0 * (x * ((c * y2) - (b * j)))
    t_2 = c * (y4 * ((y * y3) - (t * y2)))
    if (x <= (-3.8d+179)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (x <= (-7.5d-139)) then
        tmp = t_1
    else if (x <= 2.9d-185) then
        tmp = t_2
    else if (x <= 3.8d-73) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (x <= 1.5d+31) then
        tmp = t_2
    else if (x <= 3.6d+177) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (x * ((c * y2) - (b * j)));
	double t_2 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (x <= -3.8e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -7.5e-139) {
		tmp = t_1;
	} else if (x <= 2.9e-185) {
		tmp = t_2;
	} else if (x <= 3.8e-73) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (x <= 1.5e+31) {
		tmp = t_2;
	} else if (x <= 3.6e+177) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (x * ((c * y2) - (b * j)))
	t_2 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if x <= -3.8e+179:
		tmp = y * (x * ((a * b) - (c * i)))
	elif x <= -7.5e-139:
		tmp = t_1
	elif x <= 2.9e-185:
		tmp = t_2
	elif x <= 3.8e-73:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif x <= 1.5e+31:
		tmp = t_2
	elif x <= 3.6e+177:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))))
	t_2 = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (x <= -3.8e+179)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (x <= -7.5e-139)
		tmp = t_1;
	elseif (x <= 2.9e-185)
		tmp = t_2;
	elseif (x <= 3.8e-73)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (x <= 1.5e+31)
		tmp = t_2;
	elseif (x <= 3.6e+177)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (x * ((c * y2) - (b * j)));
	t_2 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (x <= -3.8e+179)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (x <= -7.5e-139)
		tmp = t_1;
	elseif (x <= 2.9e-185)
		tmp = t_2;
	elseif (x <= 3.8e-73)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (x <= 1.5e+31)
		tmp = t_2;
	elseif (x <= 3.6e+177)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+179], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-139], t$95$1, If[LessEqual[x, 2.9e-185], t$95$2, If[LessEqual[x, 3.8e-73], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+31], t$95$2, If[LessEqual[x, 3.6e+177], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.8e179

   1. Initial program 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in x around inf 51.5%

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

   5. Taylor expanded in y around inf 57.9%

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

   if -3.8e179 < x < -7.5000000000000001e-139 or 3.60000000000000003e177 < x

   1. Initial program 34.1%

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

   3. Simplified 34.1%

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

   4. Taylor expanded in x around inf 49.5%

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

   5. Taylor expanded in y0 around inf 41.7%

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

   if -7.5000000000000001e-139 < x < 2.89999999999999995e-185 or 3.8000000000000003e-73 < x < 1.49999999999999995e31

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in y4 around inf 38.9%

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

   5. Taylor expanded in c around inf 38.8%

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

   if 2.89999999999999995e-185 < x < 3.8000000000000003e-73

   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 x around inf 34.1%

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

      1. add-cbrt-cube 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 33.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 33.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 18.7%

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

       1. *-commutative 18.7%

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

       2. *-commutative 18.7%

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

       3. associate-*l* 39.7%

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

   11. Simplified 39.7%

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

   if 1.49999999999999995e31 < x < 3.60000000000000003e177

   1. Initial program 25.9%

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

   3. Simplified 25.9%

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

   4. Taylor expanded in y2 around inf 52.2%

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

   5. Taylor expanded in a around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*l* 78.2%

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

      4. cancel-sign-sub-inv 78.2%

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

      5. metadata-eval 78.2%

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

      6. *-lft-identity 78.2%

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

      7. +-commutative 78.2%

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

      8. mul-1-neg 78.2%

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

      9. unsub-neg 78.2%

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

      10. *-commutative 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-139}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-185}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+31}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+177}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \end{array} \]

Alternative 15: 30.5% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-139}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* c (* y4 (- (* y y3) (* t y2))))))
   (if (<= x -4.3e+179)
     (* y (* x (- (* a b) (* c i))))
     (if (<= x -2.6e-139)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= x 4.7e-184)
         t_1
         (if (<= x 3.3e-74)
           (* x (* b (- (* y a) (* j y0))))
           (if (<= x 6.8e+52) t_1 (* y2 (* x (- (* c y0) (* 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 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (x <= -4.3e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -2.6e-139) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= 4.7e-184) {
		tmp = t_1;
	} else if (x <= 3.3e-74) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (x <= 6.8e+52) {
		tmp = t_1;
	} else {
		tmp = y2 * (x * ((c * y0) - (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 = c * (y4 * ((y * y3) - (t * y2)))
    if (x <= (-4.3d+179)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (x <= (-2.6d-139)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (x <= 4.7d-184) then
        tmp = t_1
    else if (x <= 3.3d-74) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (x <= 6.8d+52) then
        tmp = t_1
    else
        tmp = y2 * (x * ((c * y0) - (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 = c * (y4 * ((y * y3) - (t * y2)));
	double tmp;
	if (x <= -4.3e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -2.6e-139) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= 4.7e-184) {
		tmp = t_1;
	} else if (x <= 3.3e-74) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (x <= 6.8e+52) {
		tmp = t_1;
	} else {
		tmp = y2 * (x * ((c * y0) - (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 = c * (y4 * ((y * y3) - (t * y2)))
	tmp = 0
	if x <= -4.3e+179:
		tmp = y * (x * ((a * b) - (c * i)))
	elif x <= -2.6e-139:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif x <= 4.7e-184:
		tmp = t_1
	elif x <= 3.3e-74:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif x <= 6.8e+52:
		tmp = t_1
	else:
		tmp = y2 * (x * ((c * y0) - (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(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (x <= -4.3e+179)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (x <= -2.6e-139)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (x <= 4.7e-184)
		tmp = t_1;
	elseif (x <= 3.3e-74)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (x <= 6.8e+52)
		tmp = t_1;
	else
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - 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 = c * (y4 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (x <= -4.3e+179)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (x <= -2.6e-139)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (x <= 4.7e-184)
		tmp = t_1;
	elseif (x <= 3.3e-74)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (x <= 6.8e+52)
		tmp = t_1;
	else
		tmp = y2 * (x * ((c * y0) - (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[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+179], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e-139], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7e-184], t$95$1, If[LessEqual[x, 3.3e-74], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+52], t$95$1, N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.2999999999999999e179

   1. Initial program 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in x around inf 51.5%

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

   5. Taylor expanded in y around inf 57.9%

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

   if -4.2999999999999999e179 < x < -2.5999999999999998e-139

   1. Initial program 36.0%

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

   3. Simplified 36.0%

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

   4. Taylor expanded in x around inf 44.1%

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

   5. Taylor expanded in y0 around inf 31.5%

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

   if -2.5999999999999998e-139 < x < 4.70000000000000019e-184 or 3.29999999999999996e-74 < x < 6.8e52

   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 30.3%

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

   4. Taylor expanded in y4 around inf 38.0%

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

   5. Taylor expanded in c around inf 39.1%

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

   if 4.70000000000000019e-184 < x < 3.29999999999999996e-74

   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 x around inf 34.1%

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

      1. add-cbrt-cube 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 33.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 33.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 18.7%

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

       1. *-commutative 18.7%

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

       2. *-commutative 18.7%

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

       3. associate-*l* 39.7%

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

   11. Simplified 39.7%

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

   if 6.8e52 < 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%

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

   4. Taylor expanded in x around inf 67.3%

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

      1. add-cbrt-cube 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 67.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 67.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in y2 around inf 69.9%

      \[\leadsto \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 69.9%

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

       2. associate-*l* 68.1%

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

   11. Simplified 68.1%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-139}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-184}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 16: 30.5% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-139}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (- (* y y3) (* t y2))))))
   (if (<= x -8.6e+178)
     (* y (* x (- (* a b) (* c i))))
     (if (<= x -7e-139)
       (* y0 (* x (- (* c y2) (* b j))))
       (if (<= x 5.2e-187)
         t_1
         (if (<= x 3e-74)
           (* x (* b (- (* y a) (* j y0))))
           (if (<= x 2.05e+55) t_1 (* y2 (* x (- (* c y0) (* 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 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (x <= -8.6e+178) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -7e-139) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= 5.2e-187) {
		tmp = t_1;
	} else if (x <= 3e-74) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (x <= 2.05e+55) {
		tmp = t_1;
	} else {
		tmp = y2 * (x * ((c * y0) - (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 * (c * ((y * y3) - (t * y2)))
    if (x <= (-8.6d+178)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (x <= (-7d-139)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (x <= 5.2d-187) then
        tmp = t_1
    else if (x <= 3d-74) then
        tmp = x * (b * ((y * a) - (j * y0)))
    else if (x <= 2.05d+55) then
        tmp = t_1
    else
        tmp = y2 * (x * ((c * y0) - (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 * (c * ((y * y3) - (t * y2)));
	double tmp;
	if (x <= -8.6e+178) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -7e-139) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= 5.2e-187) {
		tmp = t_1;
	} else if (x <= 3e-74) {
		tmp = x * (b * ((y * a) - (j * y0)));
	} else if (x <= 2.05e+55) {
		tmp = t_1;
	} else {
		tmp = y2 * (x * ((c * y0) - (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 * (c * ((y * y3) - (t * y2)))
	tmp = 0
	if x <= -8.6e+178:
		tmp = y * (x * ((a * b) - (c * i)))
	elif x <= -7e-139:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif x <= 5.2e-187:
		tmp = t_1
	elif x <= 3e-74:
		tmp = x * (b * ((y * a) - (j * y0)))
	elif x <= 2.05e+55:
		tmp = t_1
	else:
		tmp = y2 * (x * ((c * y0) - (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(c * Float64(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (x <= -8.6e+178)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (x <= -7e-139)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (x <= 5.2e-187)
		tmp = t_1;
	elseif (x <= 3e-74)
		tmp = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))));
	elseif (x <= 2.05e+55)
		tmp = t_1;
	else
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - 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 * (c * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (x <= -8.6e+178)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (x <= -7e-139)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (x <= 5.2e-187)
		tmp = t_1;
	elseif (x <= 3e-74)
		tmp = x * (b * ((y * a) - (j * y0)));
	elseif (x <= 2.05e+55)
		tmp = t_1;
	else
		tmp = y2 * (x * ((c * y0) - (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[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+178], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-139], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-187], t$95$1, If[LessEqual[x, 3e-74], N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+55], t$95$1, N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.6000000000000004e178

   1. Initial program 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in x around inf 51.5%

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

   5. Taylor expanded in y around inf 57.9%

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

   if -8.6000000000000004e178 < x < -7.00000000000000002e-139

   1. Initial program 36.0%

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

   3. Simplified 36.0%

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

   4. Taylor expanded in x around inf 44.1%

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

   5. Taylor expanded in y0 around inf 31.5%

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

   if -7.00000000000000002e-139 < x < 5.1999999999999999e-187 or 3.00000000000000007e-74 < x < 2.04999999999999991e55

   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 30.3%

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

   4. Taylor expanded in y4 around inf 38.0%

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

   5. Taylor expanded in c around inf 43.1%

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

      1. *-commutative 43.1%

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

   7. Simplified 43.1%

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

   if 5.1999999999999999e-187 < x < 3.00000000000000007e-74

   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 x around inf 34.1%

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

      1. add-cbrt-cube 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 33.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 33.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 33.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 18.7%

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

       1. *-commutative 18.7%

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

       2. *-commutative 18.7%

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

       3. associate-*l* 39.7%

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

   11. Simplified 39.7%

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

   if 2.04999999999999991e55 < 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%

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

   4. Taylor expanded in x around inf 67.3%

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

      1. add-cbrt-cube 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 67.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 67.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in y2 around inf 69.9%

      \[\leadsto \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 69.9%

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

       2. associate-*l* 68.1%

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

   11. Simplified 68.1%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-139}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-187}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+55}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 17: 31.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-37}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-139}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 15200000000000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.16e+179)
   (* y (* x (- (* a b) (* c i))))
   (if (<= x -1.5e-37)
     (* y0 (* x (- (* c y2) (* b j))))
     (if (<= x -6.5e-139)
       (* j (* b (- (* t y4) (* x y0))))
       (if (<= x 1.35e-183)
         (* y4 (* c (- (* y y3) (* t y2))))
         (if (<= x 15200000000000.0)
           (* y4 (* y1 (- (* k y2) (* j y3))))
           (* y2 (* x (- (* c y0) (* 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 (x <= -1.16e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -1.5e-37) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= -6.5e-139) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (x <= 1.35e-183) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 15200000000000.0) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y2 * (x * ((c * y0) - (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 (x <= (-1.16d+179)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (x <= (-1.5d-37)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (x <= (-6.5d-139)) then
        tmp = j * (b * ((t * y4) - (x * y0)))
    else if (x <= 1.35d-183) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (x <= 15200000000000.0d0) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else
        tmp = y2 * (x * ((c * y0) - (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 (x <= -1.16e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -1.5e-37) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= -6.5e-139) {
		tmp = j * (b * ((t * y4) - (x * y0)));
	} else if (x <= 1.35e-183) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 15200000000000.0) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y2 * (x * ((c * y0) - (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 x <= -1.16e+179:
		tmp = y * (x * ((a * b) - (c * i)))
	elif x <= -1.5e-37:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif x <= -6.5e-139:
		tmp = j * (b * ((t * y4) - (x * y0)))
	elif x <= 1.35e-183:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif x <= 15200000000000.0:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	else:
		tmp = y2 * (x * ((c * y0) - (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 (x <= -1.16e+179)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (x <= -1.5e-37)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (x <= -6.5e-139)
		tmp = Float64(j * Float64(b * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (x <= 1.35e-183)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 15200000000000.0)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - 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 (x <= -1.16e+179)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (x <= -1.5e-37)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (x <= -6.5e-139)
		tmp = j * (b * ((t * y4) - (x * y0)));
	elseif (x <= 1.35e-183)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (x <= 15200000000000.0)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	else
		tmp = y2 * (x * ((c * y0) - (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[x, -1.16e+179], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e-37], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-139], N[(j * N[(b * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-183], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 15200000000000.0], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.16e179

   1. Initial program 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in x around inf 51.5%

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

   5. Taylor expanded in y around inf 57.9%

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

   if -1.16e179 < x < -1.5e-37

   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 x around inf 41.8%

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

   5. Taylor expanded in y0 around inf 32.7%

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

   if -1.5e-37 < x < -6.5e-139

   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 36.0%

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

   4. Taylor expanded in j around inf 57.6%

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

   5. Taylor expanded in b around inf 44.3%

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

   if -6.5e-139 < x < 1.35000000000000004e-183

   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 33.5%

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

   5. Taylor expanded in c around inf 45.2%

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

      1. *-commutative 45.2%

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

   7. Simplified 45.2%

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

   if 1.35000000000000004e-183 < x < 1.52e13

   1. Initial program 23.0%

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

   3. Simplified 23.0%

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

   4. Taylor expanded in y4 around inf 46.4%

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

   5. Taylor expanded in y1 around inf 38.2%

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

   if 1.52e13 < x

   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 x around inf 63.4%

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

      1. add-cbrt-cube 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 63.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 63.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in y2 around inf 64.0%

      \[\leadsto \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 64.0%

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

       2. associate-*l* 62.5%

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

   11. Simplified 62.5%

       \[\leadsto \color{blue}{y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-37}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-139}:\\ \;\;\;\;j \cdot \left(b \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 15200000000000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 18: 30.8% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-140}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-184}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 42000000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -2.45e+179)
   (* y (* x (- (* a b) (* c i))))
   (if (<= x -8.5e-140)
     (* y0 (* x (- (* c y2) (* b j))))
     (if (<= x 8.8e-184)
       (* y4 (* c (- (* y y3) (* t y2))))
       (if (<= x 42000000.0)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (* y2 (* x (- (* c y0) (* 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 (x <= -2.45e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -8.5e-140) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= 8.8e-184) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 42000000.0) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y2 * (x * ((c * y0) - (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 (x <= (-2.45d+179)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (x <= (-8.5d-140)) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (x <= 8.8d-184) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (x <= 42000000.0d0) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else
        tmp = y2 * (x * ((c * y0) - (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 (x <= -2.45e+179) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -8.5e-140) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (x <= 8.8e-184) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 42000000.0) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y2 * (x * ((c * y0) - (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 x <= -2.45e+179:
		tmp = y * (x * ((a * b) - (c * i)))
	elif x <= -8.5e-140:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif x <= 8.8e-184:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif x <= 42000000.0:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	else:
		tmp = y2 * (x * ((c * y0) - (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 (x <= -2.45e+179)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (x <= -8.5e-140)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (x <= 8.8e-184)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 42000000.0)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - 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 (x <= -2.45e+179)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (x <= -8.5e-140)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (x <= 8.8e-184)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (x <= 42000000.0)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	else
		tmp = y2 * (x * ((c * y0) - (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[x, -2.45e+179], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-140], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e-184], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 42000000.0], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.4499999999999999e179

   1. Initial program 18.5%

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

   3. Simplified 18.5%

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

   4. Taylor expanded in x around inf 51.5%

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

   5. Taylor expanded in y around inf 57.9%

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

   if -2.4499999999999999e179 < x < -8.49999999999999997e-140

   1. Initial program 36.0%

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

   3. Simplified 36.0%

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

   4. Taylor expanded in x around inf 44.1%

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

   5. Taylor expanded in y0 around inf 31.5%

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

   if -8.49999999999999997e-140 < x < 8.79999999999999967e-184

   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 33.5%

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

   5. Taylor expanded in c around inf 45.2%

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

      1. *-commutative 45.2%

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

   7. Simplified 45.2%

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

   if 8.79999999999999967e-184 < x < 4.2e7

   1. Initial program 23.0%

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

   3. Simplified 23.0%

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

   4. Taylor expanded in y4 around inf 46.4%

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

   5. Taylor expanded in y1 around inf 38.2%

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

   if 4.2e7 < x

   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 x around inf 63.4%

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

      1. add-cbrt-cube 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 63.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 63.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in y2 around inf 64.0%

      \[\leadsto \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 64.0%

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

       2. associate-*l* 62.5%

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

   11. Simplified 62.5%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-140}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-184}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 42000000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 19: 31.4% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-215}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-184}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6500000000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -4.2e+172)
   (* y (* x (- (* a b) (* c i))))
   (if (<= x -8e-215)
     (* y5 (* y2 (- (* t a) (* k y0))))
     (if (<= x 7.2e-184)
       (* y4 (* c (- (* y y3) (* t y2))))
       (if (<= x 6500000000.0)
         (* y4 (* y1 (- (* k y2) (* j y3))))
         (* y2 (* x (- (* c y0) (* 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 (x <= -4.2e+172) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -8e-215) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (x <= 7.2e-184) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 6500000000.0) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y2 * (x * ((c * y0) - (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 (x <= (-4.2d+172)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (x <= (-8d-215)) then
        tmp = y5 * (y2 * ((t * a) - (k * y0)))
    else if (x <= 7.2d-184) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (x <= 6500000000.0d0) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else
        tmp = y2 * (x * ((c * y0) - (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 (x <= -4.2e+172) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -8e-215) {
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	} else if (x <= 7.2e-184) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 6500000000.0) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = y2 * (x * ((c * y0) - (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 x <= -4.2e+172:
		tmp = y * (x * ((a * b) - (c * i)))
	elif x <= -8e-215:
		tmp = y5 * (y2 * ((t * a) - (k * y0)))
	elif x <= 7.2e-184:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif x <= 6500000000.0:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	else:
		tmp = y2 * (x * ((c * y0) - (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 (x <= -4.2e+172)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (x <= -8e-215)
		tmp = Float64(y5 * Float64(y2 * Float64(Float64(t * a) - Float64(k * y0))));
	elseif (x <= 7.2e-184)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 6500000000.0)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - 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 (x <= -4.2e+172)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (x <= -8e-215)
		tmp = y5 * (y2 * ((t * a) - (k * y0)));
	elseif (x <= 7.2e-184)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (x <= 6500000000.0)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	else
		tmp = y2 * (x * ((c * y0) - (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[x, -4.2e+172], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-215], N[(y5 * N[(y2 * N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-184], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6500000000.0], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.2000000000000003e172

   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 20.3%

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

   4. Taylor expanded in x around inf 51.6%

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

   5. Taylor expanded in y around inf 57.5%

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

   if -4.2000000000000003e172 < x < -8.00000000000000033e-215

   1. Initial program 32.7%

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

   3. Simplified 32.7%

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

   4. Taylor expanded in y2 around inf 33.6%

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

   5. Taylor expanded in y5 around inf 30.7%

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

      1. *-commutative 30.7%

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

      2. associate-*l* 30.6%

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

      3. cancel-sign-sub-inv 30.6%

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

      4. metadata-eval 30.6%

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

      5. *-lft-identity 30.6%

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

      6. +-commutative 30.6%

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

      7. mul-1-neg 30.6%

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

      8. unsub-neg 30.6%

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

   7. Simplified 30.6%

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

   if -8.00000000000000033e-215 < x < 7.2000000000000002e-184

   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 40.3%

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

   5. Taylor expanded in c around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if 7.2000000000000002e-184 < x < 6.5e9

   1. Initial program 23.0%

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

   3. Simplified 23.0%

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

   4. Taylor expanded in y4 around inf 46.4%

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

   5. Taylor expanded in y1 around inf 38.2%

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

   if 6.5e9 < x

   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 x around inf 63.4%

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

      1. add-cbrt-cube 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 63.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 63.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 63.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in y2 around inf 64.0%

      \[\leadsto \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 64.0%

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

       2. associate-*l* 62.5%

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

   11. Simplified 62.5%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-215}:\\ \;\;\;\;y5 \cdot \left(y2 \cdot \left(t \cdot a - k \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-184}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 6500000000:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 20: 31.5% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* j (* t (- (* b y4) (* i y5))))))
   (if (<= x -1.6e+161)
     (* y (* x (- (* a b) (* c i))))
     (if (<= x -6.8e-215)
       t_1
       (if (<= x 1.5e-183)
         (* y4 (* c (- (* y y3) (* t y2))))
         (if (<= x 4.3e+51) t_1 (* y2 (* x (- (* c y0) (* 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 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (x <= -1.6e+161) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -6.8e-215) {
		tmp = t_1;
	} else if (x <= 1.5e-183) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 4.3e+51) {
		tmp = t_1;
	} else {
		tmp = y2 * (x * ((c * y0) - (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 = j * (t * ((b * y4) - (i * y5)))
    if (x <= (-1.6d+161)) then
        tmp = y * (x * ((a * b) - (c * i)))
    else if (x <= (-6.8d-215)) then
        tmp = t_1
    else if (x <= 1.5d-183) then
        tmp = y4 * (c * ((y * y3) - (t * y2)))
    else if (x <= 4.3d+51) then
        tmp = t_1
    else
        tmp = y2 * (x * ((c * y0) - (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 = j * (t * ((b * y4) - (i * y5)));
	double tmp;
	if (x <= -1.6e+161) {
		tmp = y * (x * ((a * b) - (c * i)));
	} else if (x <= -6.8e-215) {
		tmp = t_1;
	} else if (x <= 1.5e-183) {
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	} else if (x <= 4.3e+51) {
		tmp = t_1;
	} else {
		tmp = y2 * (x * ((c * y0) - (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 = j * (t * ((b * y4) - (i * y5)))
	tmp = 0
	if x <= -1.6e+161:
		tmp = y * (x * ((a * b) - (c * i)))
	elif x <= -6.8e-215:
		tmp = t_1
	elif x <= 1.5e-183:
		tmp = y4 * (c * ((y * y3) - (t * y2)))
	elif x <= 4.3e+51:
		tmp = t_1
	else:
		tmp = y2 * (x * ((c * y0) - (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(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))))
	tmp = 0.0
	if (x <= -1.6e+161)
		tmp = Float64(y * Float64(x * Float64(Float64(a * b) - Float64(c * i))));
	elseif (x <= -6.8e-215)
		tmp = t_1;
	elseif (x <= 1.5e-183)
		tmp = Float64(y4 * Float64(c * Float64(Float64(y * y3) - Float64(t * y2))));
	elseif (x <= 4.3e+51)
		tmp = t_1;
	else
		tmp = Float64(y2 * Float64(x * Float64(Float64(c * y0) - 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 = j * (t * ((b * y4) - (i * y5)));
	tmp = 0.0;
	if (x <= -1.6e+161)
		tmp = y * (x * ((a * b) - (c * i)));
	elseif (x <= -6.8e-215)
		tmp = t_1;
	elseif (x <= 1.5e-183)
		tmp = y4 * (c * ((y * y3) - (t * y2)));
	elseif (x <= 4.3e+51)
		tmp = t_1;
	else
		tmp = y2 * (x * ((c * y0) - (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[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+161], N[(y * N[(x * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.8e-215], t$95$1, If[LessEqual[x, 1.5e-183], N[(y4 * N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+51], t$95$1, N[(y2 * N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.60000000000000001e161

   1. Initial program 18.7%

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

   3. Simplified 18.7%

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

   4. Taylor expanded in x around inf 50.2%

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

   5. Taylor expanded in y around inf 55.6%

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

   if -1.60000000000000001e161 < x < -6.80000000000000003e-215 or 1.4999999999999999e-183 < x < 4.2999999999999997e51

   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 35.1%

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

   4. Taylor expanded in j around inf 40.6%

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

   5. Taylor expanded in t around inf 36.9%

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

   if -6.80000000000000003e-215 < x < 1.4999999999999999e-183

   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 40.3%

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

   5. Taylor expanded in c around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if 4.2999999999999997e51 < 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%

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

   4. Taylor expanded in x around inf 67.3%

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

      1. add-cbrt-cube 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 67.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 67.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 67.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in y2 around inf 69.9%

      \[\leadsto \color{blue}{\left(c \cdot y0 - a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 69.9%

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

       2. associate-*l* 68.1%

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

   11. Simplified 68.1%

       \[\leadsto \color{blue}{y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(x \cdot \left(a \cdot b - c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-183}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y2 \cdot \left(x \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \end{array} \]

Alternative 21: 30.7% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.75 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-8}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y4 (* c (- (* y y3) (* t y2))))))
   (if (<= c -5.6e+146)
     t_1
     (if (<= c -3.75e-261)
       (* j (* y5 (- (* y0 y3) (* t i))))
       (if (<= c 5.5e-8)
         (* y2 (* a (- (* t y5) (* x y1))))
         (if (<= c 3.7e+166) (* j (* x (- (* i y1) (* b 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 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -5.6e+146) {
		tmp = t_1;
	} else if (c <= -3.75e-261) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (c <= 5.5e-8) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (c <= 3.7e+166) {
		tmp = j * (x * ((i * y1) - (b * 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 * ((y * y3) - (t * y2)))
    if (c <= (-5.6d+146)) then
        tmp = t_1
    else if (c <= (-3.75d-261)) then
        tmp = j * (y5 * ((y0 * y3) - (t * i)))
    else if (c <= 5.5d-8) then
        tmp = y2 * (a * ((t * y5) - (x * y1)))
    else if (c <= 3.7d+166) then
        tmp = j * (x * ((i * y1) - (b * 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 * ((y * y3) - (t * y2)));
	double tmp;
	if (c <= -5.6e+146) {
		tmp = t_1;
	} else if (c <= -3.75e-261) {
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	} else if (c <= 5.5e-8) {
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	} else if (c <= 3.7e+166) {
		tmp = j * (x * ((i * y1) - (b * 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 * ((y * y3) - (t * y2)))
	tmp = 0
	if c <= -5.6e+146:
		tmp = t_1
	elif c <= -3.75e-261:
		tmp = j * (y5 * ((y0 * y3) - (t * i)))
	elif c <= 5.5e-8:
		tmp = y2 * (a * ((t * y5) - (x * y1)))
	elif c <= 3.7e+166:
		tmp = j * (x * ((i * y1) - (b * 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(Float64(y * y3) - Float64(t * y2))))
	tmp = 0.0
	if (c <= -5.6e+146)
		tmp = t_1;
	elseif (c <= -3.75e-261)
		tmp = Float64(j * Float64(y5 * Float64(Float64(y0 * y3) - Float64(t * i))));
	elseif (c <= 5.5e-8)
		tmp = Float64(y2 * Float64(a * Float64(Float64(t * y5) - Float64(x * y1))));
	elseif (c <= 3.7e+166)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * 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 * ((y * y3) - (t * y2)));
	tmp = 0.0;
	if (c <= -5.6e+146)
		tmp = t_1;
	elseif (c <= -3.75e-261)
		tmp = j * (y5 * ((y0 * y3) - (t * i)));
	elseif (c <= 5.5e-8)
		tmp = y2 * (a * ((t * y5) - (x * y1)));
	elseif (c <= 3.7e+166)
		tmp = j * (x * ((i * y1) - (b * 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[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.6e+146], t$95$1, If[LessEqual[c, -3.75e-261], N[(j * N[(y5 * N[(N[(y0 * y3), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e-8], N[(y2 * N[(a * N[(N[(t * y5), $MachinePrecision] - N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e+166], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.6000000000000002e146 or 3.70000000000000022e166 < c

   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%

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

   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 58.0%

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

      1. *-commutative 58.0%

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

   7. Simplified 58.0%

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

   if -5.6000000000000002e146 < c < -3.7500000000000001e-261

   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 31.9%

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

   4. Taylor expanded in j around inf 34.8%

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

   5. Taylor expanded in y5 around inf 44.2%

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

      1. mul-1-neg 44.2%

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

      2. unsub-neg 44.2%

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

   7. Simplified 44.2%

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

   if -3.7500000000000001e-261 < c < 5.5000000000000003e-8

   1. Initial program 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in y2 around inf 47.9%

      \[\leadsto \color{blue}{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot x + k \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \cdot y2} \]

   5. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y1 \cdot x\right) - -1 \cdot \left(t \cdot y5\right)\right) \cdot \left(a \cdot y2\right)} \]
   6. Step-by-step derivation

      1. *-commutative 39.4%

         \[\leadsto \color{blue}{\left(a \cdot y2\right) \cdot \left(-1 \cdot \left(y1 \cdot x\right) - -1 \cdot \left(t \cdot y5\right)\right)} \]

      2. *-commutative 39.4%

         \[\leadsto \color{blue}{\left(y2 \cdot a\right)} \cdot \left(-1 \cdot \left(y1 \cdot x\right) - -1 \cdot \left(t \cdot y5\right)\right) \]

      3. associate-*l* 42.3%

         \[\leadsto \color{blue}{y2 \cdot \left(a \cdot \left(-1 \cdot \left(y1 \cdot x\right) - -1 \cdot \left(t \cdot y5\right)\right)\right)} \]

      4. cancel-sign-sub-inv 42.3%

         \[\leadsto y2 \cdot \left(a \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot x\right) + \left(--1\right) \cdot \left(t \cdot y5\right)\right)}\right) \]

      5. metadata-eval 42.3%

         \[\leadsto y2 \cdot \left(a \cdot \left(-1 \cdot \left(y1 \cdot x\right) + \color{blue}{1} \cdot \left(t \cdot y5\right)\right)\right) \]

      6. *-lft-identity 42.3%

         \[\leadsto y2 \cdot \left(a \cdot \left(-1 \cdot \left(y1 \cdot x\right) + \color{blue}{t \cdot y5}\right)\right) \]

      7. +-commutative 42.3%

         \[\leadsto y2 \cdot \left(a \cdot \color{blue}{\left(t \cdot y5 + -1 \cdot \left(y1 \cdot x\right)\right)}\right) \]

      8. mul-1-neg 42.3%

         \[\leadsto y2 \cdot \left(a \cdot \left(t \cdot y5 + \color{blue}{\left(-y1 \cdot x\right)}\right)\right) \]

      9. unsub-neg 42.3%

         \[\leadsto y2 \cdot \left(a \cdot \color{blue}{\left(t \cdot y5 - y1 \cdot x\right)}\right) \]

      10. *-commutative 42.3%

          \[\leadsto y2 \cdot \left(a \cdot \left(\color{blue}{y5 \cdot t} - y1 \cdot x\right)\right) \]

   7. Simplified 42.3%

      \[\leadsto \color{blue}{y2 \cdot \left(a \cdot \left(y5 \cdot t - y1 \cdot x\right)\right)} \]

   if 5.5000000000000003e-8 < c < 3.70000000000000022e166

   1. Initial program 43.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \mathsf{fma}\left(x, j, z \cdot \left(-k\right)\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   4. Taylor expanded in j around inf 54.1%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y4 \cdot y1 - y0 \cdot y5\right)\right) + t \cdot \left(y4 \cdot b - i \cdot y5\right)\right) - \left(y0 \cdot b - i \cdot y1\right) \cdot x\right) \cdot j} \]

   5. Taylor expanded in x around inf 54.3%

      \[\leadsto \color{blue}{\left(\left(i \cdot y1 - y0 \cdot b\right) \cdot x\right)} \cdot j \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{+146}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;c \leq -3.75 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(y5 \cdot \left(y0 \cdot y3 - t \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-8}:\\ \;\;\;\;y2 \cdot \left(a \cdot \left(t \cdot y5 - x \cdot y1\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \end{array} \]

Alternative 22: 28.5% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(j \cdot \left(b \cdot \left(-x\right)\right)\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -11500000000000:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+141}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* j (* b (- x))))))
   (if (<= b -4.4e+151)
     t_1
     (if (<= b -11500000000000.0)
       (* k (* y0 (* z b)))
       (if (<= b 8e+141) (* c (* y4 (- (* y y3) (* t y2)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * (b * -x));
	double tmp;
	if (b <= -4.4e+151) {
		tmp = t_1;
	} else if (b <= -11500000000000.0) {
		tmp = k * (y0 * (z * b));
	} else if (b <= 8e+141) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y0 * (j * (b * -x))
    if (b <= (-4.4d+151)) then
        tmp = t_1
    else if (b <= (-11500000000000.0d0)) then
        tmp = k * (y0 * (z * b))
    else if (b <= 8d+141) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = y0 * (j * (b * -x));
	double tmp;
	if (b <= -4.4e+151) {
		tmp = t_1;
	} else if (b <= -11500000000000.0) {
		tmp = k * (y0 * (z * b));
	} else if (b <= 8e+141) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = y0 * (j * (b * -x))
	tmp = 0
	if b <= -4.4e+151:
		tmp = t_1
	elif b <= -11500000000000.0:
		tmp = k * (y0 * (z * b))
	elif b <= 8e+141:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(y0 * Float64(j * Float64(b * Float64(-x))))
	tmp = 0.0
	if (b <= -4.4e+151)
		tmp = t_1;
	elseif (b <= -11500000000000.0)
		tmp = Float64(k * Float64(y0 * Float64(z * b)));
	elseif (b <= 8e+141)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = y0 * (j * (b * -x));
	tmp = 0.0;
	if (b <= -4.4e+151)
		tmp = t_1;
	elseif (b <= -11500000000000.0)
		tmp = k * (y0 * (z * b));
	elseif (b <= 8e+141)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(y0 * N[(j * N[(b * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+151], t$95$1, If[LessEqual[b, -11500000000000.0], N[(k * N[(y0 * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+141], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.40000000000000013e151 or 8.00000000000000014e141 < b

   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 x around inf 43.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 42.0%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 42.0%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 42.0%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 40.5%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 40.5%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 46.7%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 46.7%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around 0 43.0%

       \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]

   if -4.40000000000000013e151 < b < -1.15e13

   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 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 43.5%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 43.5%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 54.0%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around 0 47.9%

      \[\leadsto -\color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 47.9%

         \[\leadsto -\color{blue}{\left(-k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]

      2. *-commutative 47.9%

         \[\leadsto -\left(-\color{blue}{\left(y0 \cdot \left(b \cdot z\right)\right) \cdot k}\right) \]

      3. *-commutative 47.9%

         \[\leadsto -\left(-\left(y0 \cdot \color{blue}{\left(z \cdot b\right)}\right) \cdot k\right) \]

      4. distribute-rgt-neg-in 47.9%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(z \cdot b\right)\right) \cdot \left(-k\right)} \]

      5. *-commutative 47.9%

         \[\leadsto -\left(y0 \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-k\right) \]

   10. Simplified 47.9%

       \[\leadsto -\color{blue}{\left(y0 \cdot \left(b \cdot z\right)\right) \cdot \left(-k\right)} \]

   if -1.15e13 < b < 8.00000000000000014e141

   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 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 38.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 35.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+151}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(b \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;b \leq -11500000000000:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+141}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(b \cdot \left(-x\right)\right)\right)\\ \end{array} \]

Alternative 23: 32.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -11500000000000:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* b (- (* y a) (* j y0))))))
   (if (<= b -2.4e+148)
     t_1
     (if (<= b -11500000000000.0)
       (* k (* y0 (* z b)))
       (if (<= b 9.2e+77) (* c (* y4 (- (* y y3) (* t y2)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (b * ((y * a) - (j * y0)));
	double tmp;
	if (b <= -2.4e+148) {
		tmp = t_1;
	} else if (b <= -11500000000000.0) {
		tmp = k * (y0 * (z * b));
	} else if (b <= 9.2e+77) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (b * ((y * a) - (j * y0)))
    if (b <= (-2.4d+148)) then
        tmp = t_1
    else if (b <= (-11500000000000.0d0)) then
        tmp = k * (y0 * (z * b))
    else if (b <= 9.2d+77) then
        tmp = c * (y4 * ((y * y3) - (t * y2)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (b * ((y * a) - (j * y0)));
	double tmp;
	if (b <= -2.4e+148) {
		tmp = t_1;
	} else if (b <= -11500000000000.0) {
		tmp = k * (y0 * (z * b));
	} else if (b <= 9.2e+77) {
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (b * ((y * a) - (j * y0)))
	tmp = 0
	if b <= -2.4e+148:
		tmp = t_1
	elif b <= -11500000000000.0:
		tmp = k * (y0 * (z * b))
	elif b <= 9.2e+77:
		tmp = c * (y4 * ((y * y3) - (t * y2)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(b * Float64(Float64(y * a) - Float64(j * y0))))
	tmp = 0.0
	if (b <= -2.4e+148)
		tmp = t_1;
	elseif (b <= -11500000000000.0)
		tmp = Float64(k * Float64(y0 * Float64(z * b)));
	elseif (b <= 9.2e+77)
		tmp = Float64(c * Float64(y4 * Float64(Float64(y * y3) - Float64(t * y2))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (b * ((y * a) - (j * y0)));
	tmp = 0.0;
	if (b <= -2.4e+148)
		tmp = t_1;
	elseif (b <= -11500000000000.0)
		tmp = k * (y0 * (z * b));
	elseif (b <= 9.2e+77)
		tmp = c * (y4 * ((y * y3) - (t * y2)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(b * N[(N[(y * a), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+148], t$95$1, If[LessEqual[b, -11500000000000.0], N[(k * N[(y0 * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+77], N[(c * N[(y4 * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.39999999999999995e148 or 9.19999999999999979e77 < b

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 42.9%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 38.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 38.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 38.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 35.8%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.8%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 35.8%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 45.6%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 45.6%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   if -2.39999999999999995e148 < b < -1.15e13

   1. Initial program 28.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 46.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.5%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 46.5%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 46.5%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 57.7%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around 0 51.0%

      \[\leadsto -\color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto -\color{blue}{\left(-k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]

      2. *-commutative 51.0%

         \[\leadsto -\left(-\color{blue}{\left(y0 \cdot \left(b \cdot z\right)\right) \cdot k}\right) \]

      3. *-commutative 51.0%

         \[\leadsto -\left(-\left(y0 \cdot \color{blue}{\left(z \cdot b\right)}\right) \cdot k\right) \]

      4. distribute-rgt-neg-in 51.0%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(z \cdot b\right)\right) \cdot \left(-k\right)} \]

      5. *-commutative 51.0%

         \[\leadsto -\left(y0 \cdot \color{blue}{\left(b \cdot z\right)}\right) \cdot \left(-k\right) \]

   10. Simplified 51.0%

       \[\leadsto -\color{blue}{\left(y0 \cdot \left(b \cdot z\right)\right) \cdot \left(-k\right)} \]

   if -1.15e13 < b < 9.19999999999999979e77

   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 32.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 34.8%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 35.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq -11500000000000:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+77}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a - j \cdot y0\right)\right)\\ \end{array} \]

Alternative 24: 21.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y0 \leq -5.5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -7.8 \cdot 10^{-234}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(y1 \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+176}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* c (* y0 y2)))))
   (if (<= y0 -5.5e+71)
     t_1
     (if (<= y0 -7.8e-234)
       (* y4 (* c (* y y3)))
       (if (<= y0 9.5e-7)
         (* (* x y2) (* y1 (- a)))
         (if (<= y0 1.8e+176) (* k (* (* i y1) (- z))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (c * (y0 * y2));
	double tmp;
	if (y0 <= -5.5e+71) {
		tmp = t_1;
	} else if (y0 <= -7.8e-234) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 9.5e-7) {
		tmp = (x * y2) * (y1 * -a);
	} else if (y0 <= 1.8e+176) {
		tmp = k * ((i * y1) * -z);
	} 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 = x * (c * (y0 * y2))
    if (y0 <= (-5.5d+71)) then
        tmp = t_1
    else if (y0 <= (-7.8d-234)) then
        tmp = y4 * (c * (y * y3))
    else if (y0 <= 9.5d-7) then
        tmp = (x * y2) * (y1 * -a)
    else if (y0 <= 1.8d+176) then
        tmp = k * ((i * y1) * -z)
    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 = x * (c * (y0 * y2));
	double tmp;
	if (y0 <= -5.5e+71) {
		tmp = t_1;
	} else if (y0 <= -7.8e-234) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 9.5e-7) {
		tmp = (x * y2) * (y1 * -a);
	} else if (y0 <= 1.8e+176) {
		tmp = k * ((i * y1) * -z);
	} 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 = x * (c * (y0 * y2))
	tmp = 0
	if y0 <= -5.5e+71:
		tmp = t_1
	elif y0 <= -7.8e-234:
		tmp = y4 * (c * (y * y3))
	elif y0 <= 9.5e-7:
		tmp = (x * y2) * (y1 * -a)
	elif y0 <= 1.8e+176:
		tmp = k * ((i * y1) * -z)
	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(x * Float64(c * Float64(y0 * y2)))
	tmp = 0.0
	if (y0 <= -5.5e+71)
		tmp = t_1;
	elseif (y0 <= -7.8e-234)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (y0 <= 9.5e-7)
		tmp = Float64(Float64(x * y2) * Float64(y1 * Float64(-a)));
	elseif (y0 <= 1.8e+176)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	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 = x * (c * (y0 * y2));
	tmp = 0.0;
	if (y0 <= -5.5e+71)
		tmp = t_1;
	elseif (y0 <= -7.8e-234)
		tmp = y4 * (c * (y * y3));
	elseif (y0 <= 9.5e-7)
		tmp = (x * y2) * (y1 * -a);
	elseif (y0 <= 1.8e+176)
		tmp = k * ((i * y1) * -z);
	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[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -5.5e+71], t$95$1, If[LessEqual[y0, -7.8e-234], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.5e-7], N[(N[(x * y2), $MachinePrecision] * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.8e+176], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -5.5e71 or 1.79999999999999996e176 < y0

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 41.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 52.1%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.1%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 52.1%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 52.1%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 52.1%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 52.1%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 45.2%

      \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2\right)}\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   10. Simplified 45.2%

       \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   if -5.5e71 < y0 < -7.8000000000000002e-234

   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 y4 around inf 39.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 28.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 21.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 21.3%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

      2. associate-*l* 25.2%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   8. Simplified 25.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   if -7.8000000000000002e-234 < y0 < 9.5000000000000001e-7

   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 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in y1 around -inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. associate-*r* 41.0%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   7. Simplified 41.0%

      \[\leadsto \color{blue}{-\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   8. Taylor expanded in a around inf 26.7%

      \[\leadsto -\color{blue}{y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 30.3%

         \[\leadsto -\color{blue}{\left(y1 \cdot a\right) \cdot \left(x \cdot y2\right)} \]

      2. *-commutative 30.3%

         \[\leadsto -\color{blue}{\left(a \cdot y1\right)} \cdot \left(x \cdot y2\right) \]

   10. Simplified 30.3%

       \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if 9.5000000000000001e-7 < y0 < 1.79999999999999996e176

   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 z around -inf 45.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 45.6%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 49.0%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around inf 31.5%

      \[\leadsto -k \cdot \left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -7.8 \cdot 10^{-234}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(y1 \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{+176}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 25: 20.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -1550000000000:\\ \;\;\;\;x \cdot \left(-y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -9.6 \cdot 10^{-234}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(y1 \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y0 \leq 2.5 \cdot 10^{+178}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -1550000000000.0)
   (* x (- (* y0 (* b j))))
   (if (<= y0 -9.6e-234)
     (* y4 (* c (* y y3)))
     (if (<= y0 1.9e-5)
       (* (* x y2) (* y1 (- a)))
       (if (<= y0 2.5e+178) (* k (* (* i y1) (- z))) (* x (* c (* y0 y2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1550000000000.0) {
		tmp = x * -(y0 * (b * j));
	} else if (y0 <= -9.6e-234) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 1.9e-5) {
		tmp = (x * y2) * (y1 * -a);
	} else if (y0 <= 2.5e+178) {
		tmp = k * ((i * y1) * -z);
	} else {
		tmp = x * (c * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-1550000000000.0d0)) then
        tmp = x * -(y0 * (b * j))
    else if (y0 <= (-9.6d-234)) then
        tmp = y4 * (c * (y * y3))
    else if (y0 <= 1.9d-5) then
        tmp = (x * y2) * (y1 * -a)
    else if (y0 <= 2.5d+178) then
        tmp = k * ((i * y1) * -z)
    else
        tmp = x * (c * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -1550000000000.0) {
		tmp = x * -(y0 * (b * j));
	} else if (y0 <= -9.6e-234) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 1.9e-5) {
		tmp = (x * y2) * (y1 * -a);
	} else if (y0 <= 2.5e+178) {
		tmp = k * ((i * y1) * -z);
	} else {
		tmp = x * (c * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -1550000000000.0:
		tmp = x * -(y0 * (b * j))
	elif y0 <= -9.6e-234:
		tmp = y4 * (c * (y * y3))
	elif y0 <= 1.9e-5:
		tmp = (x * y2) * (y1 * -a)
	elif y0 <= 2.5e+178:
		tmp = k * ((i * y1) * -z)
	else:
		tmp = x * (c * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -1550000000000.0)
		tmp = Float64(x * Float64(-Float64(y0 * Float64(b * j))));
	elseif (y0 <= -9.6e-234)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (y0 <= 1.9e-5)
		tmp = Float64(Float64(x * y2) * Float64(y1 * Float64(-a)));
	elseif (y0 <= 2.5e+178)
		tmp = Float64(k * Float64(Float64(i * y1) * Float64(-z)));
	else
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -1550000000000.0)
		tmp = x * -(y0 * (b * j));
	elseif (y0 <= -9.6e-234)
		tmp = y4 * (c * (y * y3));
	elseif (y0 <= 1.9e-5)
		tmp = (x * y2) * (y1 * -a);
	elseif (y0 <= 2.5e+178)
		tmp = k * ((i * y1) * -z);
	else
		tmp = x * (c * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -1550000000000.0], N[(x * (-N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[y0, -9.6e-234], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.9e-5], N[(N[(x * y2), $MachinePrecision] * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.5e+178], N[(k * N[(N[(i * y1), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision], N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -1.55e12

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 38.9%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 38.7%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 38.7%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 38.7%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 36.9%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 36.9%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 36.9%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 46.5%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 46.5%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around 0 38.6%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(j \cdot b\right)\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 38.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(j \cdot b\right)\right)} \]

       2. neg-mul-1 38.6%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(j \cdot b\right)\right) \]

       3. *-commutative 38.6%

          \[\leadsto x \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(b \cdot j\right)}\right) \]

   14. Simplified 38.6%

       \[\leadsto x \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(b \cdot j\right)\right)} \]

   if -1.55e12 < y0 < -9.5999999999999996e-234

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 31.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 22.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 22.7%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

      2. associate-*l* 26.2%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   8. Simplified 26.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   if -9.5999999999999996e-234 < y0 < 1.9000000000000001e-5

   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 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in y1 around -inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. associate-*r* 41.0%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   7. Simplified 41.0%

      \[\leadsto \color{blue}{-\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   8. Taylor expanded in a around inf 26.7%

      \[\leadsto -\color{blue}{y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 30.3%

         \[\leadsto -\color{blue}{\left(y1 \cdot a\right) \cdot \left(x \cdot y2\right)} \]

      2. *-commutative 30.3%

         \[\leadsto -\color{blue}{\left(a \cdot y1\right)} \cdot \left(x \cdot y2\right) \]

   10. Simplified 30.3%

       \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if 1.9000000000000001e-5 < y0 < 2.49999999999999995e178

   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 z around -inf 45.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.6%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 45.6%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 49.0%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around inf 31.5%

      \[\leadsto -k \cdot \left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right) \]

   if 2.49999999999999995e178 < y0

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 59.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.7%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 59.7%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 59.7%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 59.7%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 47.8%

      \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2\right)}\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   10. Simplified 47.8%

       \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -1550000000000:\\ \;\;\;\;x \cdot \left(-y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -9.6 \cdot 10^{-234}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(y1 \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y0 \leq 2.5 \cdot 10^{+178}:\\ \;\;\;\;k \cdot \left(\left(i \cdot y1\right) \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 26: 21.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot \left(y0 \cdot \left(-j\right)\right)\right)\\ \mathbf{if}\;y0 \leq -21000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -9 \cdot 10^{-234}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{-9}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(y1 \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y0 \leq 7.2 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* b (* y0 (- j))))))
   (if (<= y0 -21000000000.0)
     t_1
     (if (<= y0 -9e-234)
       (* y4 (* c (* y y3)))
       (if (<= y0 5.2e-9)
         (* (* x y2) (* y1 (- a)))
         (if (<= y0 7.2e+177) t_1 (* x (* c (* y0 y2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (b * (y0 * -j));
	double tmp;
	if (y0 <= -21000000000.0) {
		tmp = t_1;
	} else if (y0 <= -9e-234) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 5.2e-9) {
		tmp = (x * y2) * (y1 * -a);
	} else if (y0 <= 7.2e+177) {
		tmp = t_1;
	} else {
		tmp = x * (c * (y0 * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (b * (y0 * -j))
    if (y0 <= (-21000000000.0d0)) then
        tmp = t_1
    else if (y0 <= (-9d-234)) then
        tmp = y4 * (c * (y * y3))
    else if (y0 <= 5.2d-9) then
        tmp = (x * y2) * (y1 * -a)
    else if (y0 <= 7.2d+177) then
        tmp = t_1
    else
        tmp = x * (c * (y0 * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (b * (y0 * -j));
	double tmp;
	if (y0 <= -21000000000.0) {
		tmp = t_1;
	} else if (y0 <= -9e-234) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 5.2e-9) {
		tmp = (x * y2) * (y1 * -a);
	} else if (y0 <= 7.2e+177) {
		tmp = t_1;
	} else {
		tmp = x * (c * (y0 * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (b * (y0 * -j))
	tmp = 0
	if y0 <= -21000000000.0:
		tmp = t_1
	elif y0 <= -9e-234:
		tmp = y4 * (c * (y * y3))
	elif y0 <= 5.2e-9:
		tmp = (x * y2) * (y1 * -a)
	elif y0 <= 7.2e+177:
		tmp = t_1
	else:
		tmp = x * (c * (y0 * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(b * Float64(y0 * Float64(-j))))
	tmp = 0.0
	if (y0 <= -21000000000.0)
		tmp = t_1;
	elseif (y0 <= -9e-234)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (y0 <= 5.2e-9)
		tmp = Float64(Float64(x * y2) * Float64(y1 * Float64(-a)));
	elseif (y0 <= 7.2e+177)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(c * Float64(y0 * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (b * (y0 * -j));
	tmp = 0.0;
	if (y0 <= -21000000000.0)
		tmp = t_1;
	elseif (y0 <= -9e-234)
		tmp = y4 * (c * (y * y3));
	elseif (y0 <= 5.2e-9)
		tmp = (x * y2) * (y1 * -a);
	elseif (y0 <= 7.2e+177)
		tmp = t_1;
	else
		tmp = x * (c * (y0 * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(b * N[(y0 * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -21000000000.0], t$95$1, If[LessEqual[y0, -9e-234], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.2e-9], N[(N[(x * y2), $MachinePrecision] * N[(y1 * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 7.2e+177], t$95$1, N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -2.1e10 or 5.2000000000000002e-9 < y0 < 7.20000000000000005e177

   1. Initial program 28.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 38.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 38.1%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 38.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 38.1%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 33.2%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.2%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 33.2%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 44.5%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 44.5%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around 0 35.5%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(j \cdot b\right)\right)\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 35.5%

          \[\leadsto x \cdot \color{blue}{\left(-y0 \cdot \left(j \cdot b\right)\right)} \]

       2. associate-*r* 41.0%

          \[\leadsto x \cdot \left(-\color{blue}{\left(y0 \cdot j\right) \cdot b}\right) \]

       3. distribute-rgt-neg-in 41.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(y0 \cdot j\right) \cdot \left(-b\right)\right)} \]

   14. Simplified 41.0%

       \[\leadsto x \cdot \color{blue}{\left(\left(y0 \cdot j\right) \cdot \left(-b\right)\right)} \]

   if -2.1e10 < y0 < -9.00000000000000018e-234

   1. Initial program 29.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 29.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 42.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 31.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 22.7%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 22.7%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

      2. associate-*l* 26.2%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   8. Simplified 26.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   if -9.00000000000000018e-234 < y0 < 5.2000000000000002e-9

   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 30.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in y1 around -inf 42.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 42.5%

         \[\leadsto \color{blue}{-y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. associate-*r* 41.0%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   7. Simplified 41.0%

      \[\leadsto \color{blue}{-\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   8. Taylor expanded in a around inf 26.7%

      \[\leadsto -\color{blue}{y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 30.3%

         \[\leadsto -\color{blue}{\left(y1 \cdot a\right) \cdot \left(x \cdot y2\right)} \]

      2. *-commutative 30.3%

         \[\leadsto -\color{blue}{\left(a \cdot y1\right)} \cdot \left(x \cdot y2\right) \]

   10. Simplified 30.3%

       \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if 7.20000000000000005e177 < y0

   1. Initial program 28.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 59.7%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.7%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 59.7%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 59.7%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 59.7%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 59.7%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 47.8%

      \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2\right)}\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   10. Simplified 47.8%

       \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -21000000000:\\ \;\;\;\;x \cdot \left(b \cdot \left(y0 \cdot \left(-j\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -9 \cdot 10^{-234}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{-9}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(y1 \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y0 \leq 7.2 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y0 \cdot \left(-j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 27: 20.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(-y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+49}:\\ \;\;\;\;k \cdot \left(-y1 \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(-a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -5.2e-137)
   (* x (- (* y0 (* b j))))
   (if (<= x 3.7e-194)
     (* c (* y4 (* t (- y2))))
     (if (<= x 1.85e+49)
       (* k (- (* y1 (* z i))))
       (if (<= x 2.8e+143) (* (* x y1) (- (* a y2))) (* c (* y2 (* x y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -5.2e-137) {
		tmp = x * -(y0 * (b * j));
	} else if (x <= 3.7e-194) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 1.85e+49) {
		tmp = k * -(y1 * (z * i));
	} else if (x <= 2.8e+143) {
		tmp = (x * y1) * -(a * y2);
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-5.2d-137)) then
        tmp = x * -(y0 * (b * j))
    else if (x <= 3.7d-194) then
        tmp = c * (y4 * (t * -y2))
    else if (x <= 1.85d+49) then
        tmp = k * -(y1 * (z * i))
    else if (x <= 2.8d+143) then
        tmp = (x * y1) * -(a * y2)
    else
        tmp = c * (y2 * (x * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -5.2e-137) {
		tmp = x * -(y0 * (b * j));
	} else if (x <= 3.7e-194) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 1.85e+49) {
		tmp = k * -(y1 * (z * i));
	} else if (x <= 2.8e+143) {
		tmp = (x * y1) * -(a * y2);
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -5.2e-137:
		tmp = x * -(y0 * (b * j))
	elif x <= 3.7e-194:
		tmp = c * (y4 * (t * -y2))
	elif x <= 1.85e+49:
		tmp = k * -(y1 * (z * i))
	elif x <= 2.8e+143:
		tmp = (x * y1) * -(a * y2)
	else:
		tmp = c * (y2 * (x * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -5.2e-137)
		tmp = Float64(x * Float64(-Float64(y0 * Float64(b * j))));
	elseif (x <= 3.7e-194)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (x <= 1.85e+49)
		tmp = Float64(k * Float64(-Float64(y1 * Float64(z * i))));
	elseif (x <= 2.8e+143)
		tmp = Float64(Float64(x * y1) * Float64(-Float64(a * y2)));
	else
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -5.2e-137)
		tmp = x * -(y0 * (b * j));
	elseif (x <= 3.7e-194)
		tmp = c * (y4 * (t * -y2));
	elseif (x <= 1.85e+49)
		tmp = k * -(y1 * (z * i));
	elseif (x <= 2.8e+143)
		tmp = (x * y1) * -(a * y2);
	else
		tmp = c * (y2 * (x * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -5.2e-137], N[(x * (-N[(y0 * N[(b * j), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 3.7e-194], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+49], N[(k * (-N[(y1 * N[(z * i), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 2.8e+143], N[(N[(x * y1), $MachinePrecision] * (-N[(a * y2), $MachinePrecision])), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.1999999999999999e-137

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 43.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 43.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 31.6%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 31.6%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 35.5%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 35.5%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around 0 27.9%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot \left(j \cdot b\right)\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 27.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot y0\right) \cdot \left(j \cdot b\right)\right)} \]

       2. neg-mul-1 27.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y0\right)} \cdot \left(j \cdot b\right)\right) \]

       3. *-commutative 27.9%

          \[\leadsto x \cdot \left(\left(-y0\right) \cdot \color{blue}{\left(b \cdot j\right)}\right) \]

   14. Simplified 27.9%

       \[\leadsto x \cdot \color{blue}{\left(\left(-y0\right) \cdot \left(b \cdot j\right)\right)} \]

   if -5.1999999999999999e-137 < x < 3.70000000000000008e-194

   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 34.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 40.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 31.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. neg-mul-1 31.9%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2\right)\right) \]

      3. *-commutative 31.9%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   8. Simplified 31.9%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t\right)\right)} \]

   if 3.70000000000000008e-194 < x < 1.85000000000000009e49

   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 z around -inf 32.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 32.4%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 32.4%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 33.3%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around inf 22.6%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 22.6%

         \[\leadsto -\color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right) \cdot k} \]

      2. associate-*r* 22.9%

         \[\leadsto -\color{blue}{\left(\left(i \cdot y1\right) \cdot z\right)} \cdot k \]

      3. *-commutative 22.9%

         \[\leadsto -\left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right) \cdot k \]

      4. associate-*r* 24.8%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right)} \cdot k \]

   10. Simplified 24.8%

       \[\leadsto -\color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right) \cdot k} \]

   if 1.85000000000000009e49 < x < 2.79999999999999998e143

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 68.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in y1 around -inf 59.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 59.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. associate-*r* 63.9%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{-\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   8. Taylor expanded in a around inf 50.4%

      \[\leadsto -\color{blue}{y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto -y1 \cdot \color{blue}{\left(\left(x \cdot y2\right) \cdot a\right)} \]

      2. associate-*r* 59.9%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(x \cdot y2\right)\right) \cdot a} \]

      3. associate-*r* 74.1%

         \[\leadsto -\color{blue}{\left(\left(y1 \cdot x\right) \cdot y2\right)} \cdot a \]

      4. associate-*l* 69.2%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(y2 \cdot a\right)} \]

      5. *-commutative 69.2%

         \[\leadsto -\left(y1 \cdot x\right) \cdot \color{blue}{\left(a \cdot y2\right)} \]

   10. Simplified 69.2%

       \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2\right)} \]

   if 2.79999999999999998e143 < x

   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 x around inf 66.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 63.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 63.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 63.9%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 63.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 58.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 61.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot x\right) \cdot y2\right)} \]

   10. Simplified 61.3%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x\right) \cdot y2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \left(-y0 \cdot \left(b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+49}:\\ \;\;\;\;k \cdot \left(-y1 \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(-a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]

Alternative 28: 20.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-137}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(j \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+53}:\\ \;\;\;\;k \cdot \left(-y1 \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(-a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -1.05e-137)
   (* y0 (* b (* j (- x))))
   (if (<= x 1.6e-194)
     (* c (* y4 (* t (- y2))))
     (if (<= x 4.6e+53)
       (* k (- (* y1 (* z i))))
       (if (<= x 6.3e+143) (* (* x y1) (- (* a y2))) (* c (* y2 (* x y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.05e-137) {
		tmp = y0 * (b * (j * -x));
	} else if (x <= 1.6e-194) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 4.6e+53) {
		tmp = k * -(y1 * (z * i));
	} else if (x <= 6.3e+143) {
		tmp = (x * y1) * -(a * y2);
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-1.05d-137)) then
        tmp = y0 * (b * (j * -x))
    else if (x <= 1.6d-194) then
        tmp = c * (y4 * (t * -y2))
    else if (x <= 4.6d+53) then
        tmp = k * -(y1 * (z * i))
    else if (x <= 6.3d+143) then
        tmp = (x * y1) * -(a * y2)
    else
        tmp = c * (y2 * (x * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.05e-137) {
		tmp = y0 * (b * (j * -x));
	} else if (x <= 1.6e-194) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 4.6e+53) {
		tmp = k * -(y1 * (z * i));
	} else if (x <= 6.3e+143) {
		tmp = (x * y1) * -(a * y2);
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.05e-137:
		tmp = y0 * (b * (j * -x))
	elif x <= 1.6e-194:
		tmp = c * (y4 * (t * -y2))
	elif x <= 4.6e+53:
		tmp = k * -(y1 * (z * i))
	elif x <= 6.3e+143:
		tmp = (x * y1) * -(a * y2)
	else:
		tmp = c * (y2 * (x * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -1.05e-137)
		tmp = Float64(y0 * Float64(b * Float64(j * Float64(-x))));
	elseif (x <= 1.6e-194)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (x <= 4.6e+53)
		tmp = Float64(k * Float64(-Float64(y1 * Float64(z * i))));
	elseif (x <= 6.3e+143)
		tmp = Float64(Float64(x * y1) * Float64(-Float64(a * y2)));
	else
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -1.05e-137)
		tmp = y0 * (b * (j * -x));
	elseif (x <= 1.6e-194)
		tmp = c * (y4 * (t * -y2));
	elseif (x <= 4.6e+53)
		tmp = k * -(y1 * (z * i));
	elseif (x <= 6.3e+143)
		tmp = (x * y1) * -(a * y2);
	else
		tmp = c * (y2 * (x * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -1.05e-137], N[(y0 * N[(b * N[(j * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-194], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+53], N[(k * (-N[(y1 * N[(z * i), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 6.3e+143], N[(N[(x * y1), $MachinePrecision] * (-N[(a * y2), $MachinePrecision])), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.04999999999999996e-137

   1. Initial program 30.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 30.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 47.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 43.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 43.8%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 43.8%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 31.6%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 31.6%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 35.5%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 35.5%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around 0 30.8%

       \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 30.8%

          \[\leadsto \color{blue}{\left(-1 \cdot y0\right) \cdot \left(j \cdot \left(b \cdot x\right)\right)} \]

       2. neg-mul-1 30.8%

          \[\leadsto \color{blue}{\left(-y0\right)} \cdot \left(j \cdot \left(b \cdot x\right)\right) \]

       3. *-commutative 30.8%

          \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(\left(b \cdot x\right) \cdot j\right)} \]

       4. associate-*r* 29.8%

          \[\leadsto \left(-y0\right) \cdot \color{blue}{\left(b \cdot \left(x \cdot j\right)\right)} \]

   14. Simplified 29.8%

       \[\leadsto \color{blue}{\left(-y0\right) \cdot \left(b \cdot \left(x \cdot j\right)\right)} \]

   if -1.04999999999999996e-137 < x < 1.6000000000000001e-194

   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 34.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 40.2%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 31.9%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 31.9%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. neg-mul-1 31.9%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2\right)\right) \]

      3. *-commutative 31.9%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   8. Simplified 31.9%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t\right)\right)} \]

   if 1.6000000000000001e-194 < x < 4.60000000000000039e53

   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 z around -inf 32.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 32.4%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 32.4%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 33.3%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around inf 22.6%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 22.6%

         \[\leadsto -\color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right) \cdot k} \]

      2. associate-*r* 22.9%

         \[\leadsto -\color{blue}{\left(\left(i \cdot y1\right) \cdot z\right)} \cdot k \]

      3. *-commutative 22.9%

         \[\leadsto -\left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right) \cdot k \]

      4. associate-*r* 24.8%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right)} \cdot k \]

   10. Simplified 24.8%

       \[\leadsto -\color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right) \cdot k} \]

   if 4.60000000000000039e53 < x < 6.30000000000000006e143

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 68.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in y1 around -inf 59.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 59.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. associate-*r* 63.9%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{-\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   8. Taylor expanded in a around inf 50.4%

      \[\leadsto -\color{blue}{y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto -y1 \cdot \color{blue}{\left(\left(x \cdot y2\right) \cdot a\right)} \]

      2. associate-*r* 59.9%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(x \cdot y2\right)\right) \cdot a} \]

      3. associate-*r* 74.1%

         \[\leadsto -\color{blue}{\left(\left(y1 \cdot x\right) \cdot y2\right)} \cdot a \]

      4. associate-*l* 69.2%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(y2 \cdot a\right)} \]

      5. *-commutative 69.2%

         \[\leadsto -\left(y1 \cdot x\right) \cdot \color{blue}{\left(a \cdot y2\right)} \]

   10. Simplified 69.2%

       \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2\right)} \]

   if 6.30000000000000006e143 < x

   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 x around inf 66.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 63.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 63.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 63.9%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 63.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 58.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 61.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot x\right) \cdot y2\right)} \]

   10. Simplified 61.3%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x\right) \cdot y2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-137}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(j \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+53}:\\ \;\;\;\;k \cdot \left(-y1 \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(-a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]

Alternative 29: 21.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-106}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(b \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(-y1 \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(-a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -6e-106)
   (* y0 (* j (* b (- x))))
   (if (<= x 8.2e-194)
     (* c (* y4 (* t (- y2))))
     (if (<= x 3.4e+58)
       (* k (- (* y1 (* z i))))
       (if (<= x 3.1e+143) (* (* x y1) (- (* a y2))) (* c (* y2 (* x y0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -6e-106) {
		tmp = y0 * (j * (b * -x));
	} else if (x <= 8.2e-194) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 3.4e+58) {
		tmp = k * -(y1 * (z * i));
	} else if (x <= 3.1e+143) {
		tmp = (x * y1) * -(a * y2);
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-6d-106)) then
        tmp = y0 * (j * (b * -x))
    else if (x <= 8.2d-194) then
        tmp = c * (y4 * (t * -y2))
    else if (x <= 3.4d+58) then
        tmp = k * -(y1 * (z * i))
    else if (x <= 3.1d+143) then
        tmp = (x * y1) * -(a * y2)
    else
        tmp = c * (y2 * (x * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -6e-106) {
		tmp = y0 * (j * (b * -x));
	} else if (x <= 8.2e-194) {
		tmp = c * (y4 * (t * -y2));
	} else if (x <= 3.4e+58) {
		tmp = k * -(y1 * (z * i));
	} else if (x <= 3.1e+143) {
		tmp = (x * y1) * -(a * y2);
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -6e-106:
		tmp = y0 * (j * (b * -x))
	elif x <= 8.2e-194:
		tmp = c * (y4 * (t * -y2))
	elif x <= 3.4e+58:
		tmp = k * -(y1 * (z * i))
	elif x <= 3.1e+143:
		tmp = (x * y1) * -(a * y2)
	else:
		tmp = c * (y2 * (x * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -6e-106)
		tmp = Float64(y0 * Float64(j * Float64(b * Float64(-x))));
	elseif (x <= 8.2e-194)
		tmp = Float64(c * Float64(y4 * Float64(t * Float64(-y2))));
	elseif (x <= 3.4e+58)
		tmp = Float64(k * Float64(-Float64(y1 * Float64(z * i))));
	elseif (x <= 3.1e+143)
		tmp = Float64(Float64(x * y1) * Float64(-Float64(a * y2)));
	else
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -6e-106)
		tmp = y0 * (j * (b * -x));
	elseif (x <= 8.2e-194)
		tmp = c * (y4 * (t * -y2));
	elseif (x <= 3.4e+58)
		tmp = k * -(y1 * (z * i));
	elseif (x <= 3.1e+143)
		tmp = (x * y1) * -(a * y2);
	else
		tmp = c * (y2 * (x * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -6e-106], N[(y0 * N[(j * N[(b * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-194], N[(c * N[(y4 * N[(t * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+58], N[(k * (-N[(y1 * N[(z * i), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 3.1e+143], N[(N[(x * y1), $MachinePrecision] * (-N[(a * y2), $MachinePrecision])), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.00000000000000037e-106

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 46.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 42.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 42.6%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 42.6%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 33.6%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.6%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 33.6%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 35.6%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 35.6%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around 0 32.6%

       \[\leadsto \color{blue}{-1 \cdot \left(y0 \cdot \left(j \cdot \left(b \cdot x\right)\right)\right)} \]

   if -6.00000000000000037e-106 < x < 8.2000000000000005e-194

   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 y4 around inf 34.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 36.6%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around 0 29.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 29.4%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(y4 \cdot \left(t \cdot y2\right)\right)} \]

      2. neg-mul-1 29.4%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(y4 \cdot \left(t \cdot y2\right)\right) \]

      3. *-commutative 29.4%

         \[\leadsto \left(-c\right) \cdot \left(y4 \cdot \color{blue}{\left(y2 \cdot t\right)}\right) \]

   8. Simplified 29.4%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(y4 \cdot \left(y2 \cdot t\right)\right)} \]

   if 8.2000000000000005e-194 < x < 3.4000000000000001e58

   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 z around -inf 32.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 32.4%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 32.4%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 33.3%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in i around inf 22.6%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 22.6%

         \[\leadsto -\color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right) \cdot k} \]

      2. associate-*r* 22.9%

         \[\leadsto -\color{blue}{\left(\left(i \cdot y1\right) \cdot z\right)} \cdot k \]

      3. *-commutative 22.9%

         \[\leadsto -\left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right) \cdot k \]

      4. associate-*r* 24.8%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right)} \cdot k \]

   10. Simplified 24.8%

       \[\leadsto -\color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right) \cdot k} \]

   if 3.4000000000000001e58 < x < 3.0999999999999999e143

   1. Initial program 31.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 68.3%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in y1 around -inf 59.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 59.6%

         \[\leadsto \color{blue}{-y1 \cdot \left(x \cdot \left(a \cdot y2 - i \cdot j\right)\right)} \]

      2. associate-*r* 63.9%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{-\left(y1 \cdot x\right) \cdot \left(a \cdot y2 - i \cdot j\right)} \]

   8. Taylor expanded in a around inf 50.4%

      \[\leadsto -\color{blue}{y1 \cdot \left(a \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto -y1 \cdot \color{blue}{\left(\left(x \cdot y2\right) \cdot a\right)} \]

      2. associate-*r* 59.9%

         \[\leadsto -\color{blue}{\left(y1 \cdot \left(x \cdot y2\right)\right) \cdot a} \]

      3. associate-*r* 74.1%

         \[\leadsto -\color{blue}{\left(\left(y1 \cdot x\right) \cdot y2\right)} \cdot a \]

      4. associate-*l* 69.2%

         \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(y2 \cdot a\right)} \]

      5. *-commutative 69.2%

         \[\leadsto -\left(y1 \cdot x\right) \cdot \color{blue}{\left(a \cdot y2\right)} \]

   10. Simplified 69.2%

       \[\leadsto -\color{blue}{\left(y1 \cdot x\right) \cdot \left(a \cdot y2\right)} \]

   if 3.0999999999999999e143 < x

   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 x around inf 66.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 63.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 63.9%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 63.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 63.9%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 63.9%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 58.4%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 61.3%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot x\right) \cdot y2\right)} \]

   10. Simplified 61.3%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x\right) \cdot y2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-106}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(b \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-194}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(t \cdot \left(-y2\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;k \cdot \left(-y1 \cdot \left(z \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+143}:\\ \;\;\;\;\left(x \cdot y1\right) \cdot \left(-a \cdot y2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]

Alternative 30: 22.2% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y2 \leq -1.85 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y2 \leq -4.7 \cdot 10^{-74}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y1 \cdot \left(-z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* c (* y0 y2)))))
   (if (<= y2 -1.85e+46)
     t_1
     (if (<= y2 -4.7e-74)
       (* c (* y (* y3 y4)))
       (if (<= y2 9.5e+65) (* k (* i (* y1 (- z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (c * (y0 * y2));
	double tmp;
	if (y2 <= -1.85e+46) {
		tmp = t_1;
	} else if (y2 <= -4.7e-74) {
		tmp = c * (y * (y3 * y4));
	} else if (y2 <= 9.5e+65) {
		tmp = k * (i * (y1 * -z));
	} 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 = x * (c * (y0 * y2))
    if (y2 <= (-1.85d+46)) then
        tmp = t_1
    else if (y2 <= (-4.7d-74)) then
        tmp = c * (y * (y3 * y4))
    else if (y2 <= 9.5d+65) then
        tmp = k * (i * (y1 * -z))
    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 = x * (c * (y0 * y2));
	double tmp;
	if (y2 <= -1.85e+46) {
		tmp = t_1;
	} else if (y2 <= -4.7e-74) {
		tmp = c * (y * (y3 * y4));
	} else if (y2 <= 9.5e+65) {
		tmp = k * (i * (y1 * -z));
	} 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 = x * (c * (y0 * y2))
	tmp = 0
	if y2 <= -1.85e+46:
		tmp = t_1
	elif y2 <= -4.7e-74:
		tmp = c * (y * (y3 * y4))
	elif y2 <= 9.5e+65:
		tmp = k * (i * (y1 * -z))
	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(x * Float64(c * Float64(y0 * y2)))
	tmp = 0.0
	if (y2 <= -1.85e+46)
		tmp = t_1;
	elseif (y2 <= -4.7e-74)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	elseif (y2 <= 9.5e+65)
		tmp = Float64(k * Float64(i * Float64(y1 * Float64(-z))));
	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 = x * (c * (y0 * y2));
	tmp = 0.0;
	if (y2 <= -1.85e+46)
		tmp = t_1;
	elseif (y2 <= -4.7e-74)
		tmp = c * (y * (y3 * y4));
	elseif (y2 <= 9.5e+65)
		tmp = k * (i * (y1 * -z));
	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[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y2, -1.85e+46], t$95$1, If[LessEqual[y2, -4.7e-74], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 9.5e+65], N[(k * N[(i * N[(y1 * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -1.84999999999999995e46 or 9.5000000000000005e65 < y2

   1. Initial program 27.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 43.8%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 39.3%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.2%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 40.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 40.2%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 40.2%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 40.2%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 36.7%

      \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2\right)}\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   10. Simplified 36.7%

       \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   if -1.84999999999999995e46 < y2 < -4.7000000000000001e-74

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   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 c around inf 38.4%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 34.5%

      \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y4\right)} \]

      2. associate-*l* 38.3%

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   8. Simplified 38.3%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -4.7000000000000001e-74 < y2 < 9.5000000000000005e65

   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 31.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 40.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.4%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 40.4%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 40.4%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in k around inf 31.6%

      \[\leadsto -\color{blue}{k \cdot \left(\left(i \cdot y1 - y0 \cdot b\right) \cdot z\right)} \]

   8. Taylor expanded in y1 around inf 25.0%

      \[\leadsto -k \cdot \color{blue}{\left(i \cdot \left(y1 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y2 \leq -1.85 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y2 \leq -4.7 \cdot 10^{-74}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y1 \cdot \left(-z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 31: 21.6% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -5.3 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -3.2 \cdot 10^{-117}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 9.8 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -5.3e+71)
   (* c (* y0 (* x y2)))
   (if (<= y0 -3.2e-117)
     (* c (* y4 (* y y3)))
     (if (<= y0 9.8e-83) (* x (* b (* y a))) (* c (* y2 (* x y0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -5.3e+71) {
		tmp = c * (y0 * (x * y2));
	} else if (y0 <= -3.2e-117) {
		tmp = c * (y4 * (y * y3));
	} else if (y0 <= 9.8e-83) {
		tmp = x * (b * (y * a));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-5.3d+71)) then
        tmp = c * (y0 * (x * y2))
    else if (y0 <= (-3.2d-117)) then
        tmp = c * (y4 * (y * y3))
    else if (y0 <= 9.8d-83) then
        tmp = x * (b * (y * a))
    else
        tmp = c * (y2 * (x * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -5.3e+71) {
		tmp = c * (y0 * (x * y2));
	} else if (y0 <= -3.2e-117) {
		tmp = c * (y4 * (y * y3));
	} else if (y0 <= 9.8e-83) {
		tmp = x * (b * (y * a));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -5.3e+71:
		tmp = c * (y0 * (x * y2))
	elif y0 <= -3.2e-117:
		tmp = c * (y4 * (y * y3))
	elif y0 <= 9.8e-83:
		tmp = x * (b * (y * a))
	else:
		tmp = c * (y2 * (x * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -5.3e+71)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y0 <= -3.2e-117)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y0 <= 9.8e-83)
		tmp = Float64(x * Float64(b * Float64(y * a)));
	else
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -5.3e+71)
		tmp = c * (y0 * (x * y2));
	elseif (y0 <= -3.2e-117)
		tmp = c * (y4 * (y * y3));
	elseif (y0 <= 9.8e-83)
		tmp = x * (b * (y * a));
	else
		tmp = c * (y2 * (x * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -5.3e+71], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.2e-117], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9.8e-83], N[(x * N[(b * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -5.2999999999999999e71

   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 x around inf 37.4%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 47.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 47.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 47.4%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 47.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around -inf 41.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -5.2999999999999999e71 < y0 < -3.19999999999999995e-117

   1. Initial program 27.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 39.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 35.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 24.0%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -3.19999999999999995e-117 < y0 < 9.8e-83

   1. Initial program 32.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 50.0%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 45.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 45.2%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 45.2%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 22.0%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 22.0%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 22.0%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 24.4%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 24.4%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around inf 23.3%

       \[\leadsto x \cdot \left(b \cdot \color{blue}{\left(y \cdot a\right)}\right) \]

   if 9.8e-83 < y0

   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 x around inf 40.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 34.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 34.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 34.6%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 34.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 25.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.2%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot x\right) \cdot y2\right)} \]

   10. Simplified 28.2%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5.3 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -3.2 \cdot 10^{-117}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 9.8 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(b \cdot \left(y \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]

Alternative 32: 21.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.3 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.1 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.3e+71)
   (* c (* y0 (* x y2)))
   (if (<= y0 -2.1e-146)
     (* c (* y4 (* y y3)))
     (if (<= y0 5.2e-83) (* x (* y (* a b))) (* c (* y2 (* x y0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.3e+71) {
		tmp = c * (y0 * (x * y2));
	} else if (y0 <= -2.1e-146) {
		tmp = c * (y4 * (y * y3));
	} else if (y0 <= 5.2e-83) {
		tmp = x * (y * (a * b));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-4.3d+71)) then
        tmp = c * (y0 * (x * y2))
    else if (y0 <= (-2.1d-146)) then
        tmp = c * (y4 * (y * y3))
    else if (y0 <= 5.2d-83) then
        tmp = x * (y * (a * b))
    else
        tmp = c * (y2 * (x * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.3e+71) {
		tmp = c * (y0 * (x * y2));
	} else if (y0 <= -2.1e-146) {
		tmp = c * (y4 * (y * y3));
	} else if (y0 <= 5.2e-83) {
		tmp = x * (y * (a * b));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -4.3e+71:
		tmp = c * (y0 * (x * y2))
	elif y0 <= -2.1e-146:
		tmp = c * (y4 * (y * y3))
	elif y0 <= 5.2e-83:
		tmp = x * (y * (a * b))
	else:
		tmp = c * (y2 * (x * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.3e+71)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y0 <= -2.1e-146)
		tmp = Float64(c * Float64(y4 * Float64(y * y3)));
	elseif (y0 <= 5.2e-83)
		tmp = Float64(x * Float64(y * Float64(a * b)));
	else
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -4.3e+71)
		tmp = c * (y0 * (x * y2));
	elseif (y0 <= -2.1e-146)
		tmp = c * (y4 * (y * y3));
	elseif (y0 <= 5.2e-83)
		tmp = x * (y * (a * b));
	else
		tmp = c * (y2 * (x * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.3e+71], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.1e-146], N[(c * N[(y4 * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 5.2e-83], N[(x * N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -4.29999999999999984e71

   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 x around inf 37.4%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 47.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 47.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 47.4%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 47.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around -inf 41.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -4.29999999999999984e71 < y0 < -2.0999999999999999e-146

   1. Initial program 31.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 36.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 31.9%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 22.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]

   if -2.0999999999999999e-146 < y0 < 5.20000000000000018e-83

   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 30.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 51.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 46.1%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 46.1%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 46.1%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 23.7%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 23.7%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 23.7%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 24.9%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 24.9%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around inf 26.1%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b\right)\right)} \]

   if 5.20000000000000018e-83 < y0

   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 x around inf 40.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 34.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 34.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 34.6%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 34.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 25.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.2%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot x\right) \cdot y2\right)} \]

   10. Simplified 28.2%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.3 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.1 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]

Alternative 33: 21.4% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y0 \leq -4.8 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y0 -4.8e+71)
   (* c (* y0 (* x y2)))
   (if (<= y0 -5.4e-238)
     (* y4 (* c (* y y3)))
     (if (<= y0 2.2e-82) (* x (* y (* a b))) (* c (* y2 (* x y0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.8e+71) {
		tmp = c * (y0 * (x * y2));
	} else if (y0 <= -5.4e-238) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 2.2e-82) {
		tmp = x * (y * (a * b));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y0 <= (-4.8d+71)) then
        tmp = c * (y0 * (x * y2))
    else if (y0 <= (-5.4d-238)) then
        tmp = y4 * (c * (y * y3))
    else if (y0 <= 2.2d-82) then
        tmp = x * (y * (a * b))
    else
        tmp = c * (y2 * (x * y0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y0 <= -4.8e+71) {
		tmp = c * (y0 * (x * y2));
	} else if (y0 <= -5.4e-238) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 2.2e-82) {
		tmp = x * (y * (a * b));
	} else {
		tmp = c * (y2 * (x * y0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y0 <= -4.8e+71:
		tmp = c * (y0 * (x * y2))
	elif y0 <= -5.4e-238:
		tmp = y4 * (c * (y * y3))
	elif y0 <= 2.2e-82:
		tmp = x * (y * (a * b))
	else:
		tmp = c * (y2 * (x * y0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y0 <= -4.8e+71)
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	elseif (y0 <= -5.4e-238)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (y0 <= 2.2e-82)
		tmp = Float64(x * Float64(y * Float64(a * b)));
	else
		tmp = Float64(c * Float64(y2 * Float64(x * y0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y0 <= -4.8e+71)
		tmp = c * (y0 * (x * y2));
	elseif (y0 <= -5.4e-238)
		tmp = y4 * (c * (y * y3));
	elseif (y0 <= 2.2e-82)
		tmp = x * (y * (a * b));
	else
		tmp = c * (y2 * (x * y0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y0, -4.8e+71], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5.4e-238], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.2e-82], N[(x * N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -4.79999999999999961e71

   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 x around inf 37.4%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 47.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 47.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 47.4%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 47.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around -inf 41.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]

   if -4.79999999999999961e71 < y0 < -5.39999999999999981e-238

   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 38.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 28.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 20.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 20.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

      2. associate-*l* 24.5%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   8. Simplified 24.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   if -5.39999999999999981e-238 < y0 < 2.19999999999999986e-82

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 50.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 50.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 24.0%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 24.0%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 24.0%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 25.6%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 25.6%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around inf 28.8%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b\right)\right)} \]

   if 2.19999999999999986e-82 < y0

   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 x around inf 40.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 34.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 34.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 34.6%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 34.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 25.7%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.2%

         \[\leadsto c \cdot \color{blue}{\left(\left(y0 \cdot x\right) \cdot y2\right)} \]

   10. Simplified 28.2%

       \[\leadsto \color{blue}{c \cdot \left(\left(y0 \cdot x\right) \cdot y2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.8 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0\right)\right)\\ \end{array} \]

Alternative 34: 21.9% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{if}\;y0 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-239}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* c (* y0 y2)))))
   (if (<= y0 -5e+71)
     t_1
     (if (<= y0 -2.9e-239)
       (* y4 (* c (* y y3)))
       (if (<= y0 9e-83) (* x (* y (* a b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (c * (y0 * y2));
	double tmp;
	if (y0 <= -5e+71) {
		tmp = t_1;
	} else if (y0 <= -2.9e-239) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 9e-83) {
		tmp = x * (y * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (c * (y0 * y2))
    if (y0 <= (-5d+71)) then
        tmp = t_1
    else if (y0 <= (-2.9d-239)) then
        tmp = y4 * (c * (y * y3))
    else if (y0 <= 9d-83) then
        tmp = x * (y * (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (c * (y0 * y2));
	double tmp;
	if (y0 <= -5e+71) {
		tmp = t_1;
	} else if (y0 <= -2.9e-239) {
		tmp = y4 * (c * (y * y3));
	} else if (y0 <= 9e-83) {
		tmp = x * (y * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (c * (y0 * y2))
	tmp = 0
	if y0 <= -5e+71:
		tmp = t_1
	elif y0 <= -2.9e-239:
		tmp = y4 * (c * (y * y3))
	elif y0 <= 9e-83:
		tmp = x * (y * (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(c * Float64(y0 * y2)))
	tmp = 0.0
	if (y0 <= -5e+71)
		tmp = t_1;
	elseif (y0 <= -2.9e-239)
		tmp = Float64(y4 * Float64(c * Float64(y * y3)));
	elseif (y0 <= 9e-83)
		tmp = Float64(x * Float64(y * Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (c * (y0 * y2));
	tmp = 0.0;
	if (y0 <= -5e+71)
		tmp = t_1;
	elseif (y0 <= -2.9e-239)
		tmp = y4 * (c * (y * y3));
	elseif (y0 <= 9e-83)
		tmp = x * (y * (a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(c * N[(y0 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -5e+71], t$95$1, If[LessEqual[y0, -2.9e-239], N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 9e-83], N[(x * N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y0 < -4.99999999999999972e71 or 8.99999999999999995e-83 < y0

   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%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 39.1%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 39.6%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.6%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 39.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 39.6%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 39.6%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 39.6%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around inf 34.3%

      \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2\right)}\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   10. Simplified 34.3%

       \[\leadsto \left(c \cdot \color{blue}{\left(y2 \cdot y0\right)}\right) \cdot x \]

   if -4.99999999999999972e71 < y0 < -2.9000000000000002e-239

   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 38.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 28.1%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 20.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 20.8%

         \[\leadsto \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right) \cdot c} \]

      2. associate-*l* 24.5%

         \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   8. Simplified 24.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(y \cdot y3\right) \cdot c\right)} \]

   if -2.9000000000000002e-239 < y0 < 8.99999999999999995e-83

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.1%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 50.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 50.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 50.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 24.0%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 24.0%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 24.0%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 25.6%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 25.6%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around inf 28.8%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot \left(a \cdot b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \mathbf{elif}\;y0 \leq -2.9 \cdot 10^{-239}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 9 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(c \cdot \left(y0 \cdot y2\right)\right)\\ \end{array} \]

Alternative 35: 22.5% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -6.8 \cdot 10^{+124} \lor \neg \left(y3 \leq 0.3\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y3 -6.8e+124) (not (<= y3 0.3)))
   (* c (* y (* y3 y4)))
   (* a (* (* x y) b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -6.8e+124) || !(y3 <= 0.3)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y3 <= (-6.8d+124)) .or. (.not. (y3 <= 0.3d0))) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = a * ((x * y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y3 <= -6.8e+124) || !(y3 <= 0.3)) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = a * ((x * y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y3 <= -6.8e+124) or not (y3 <= 0.3):
		tmp = c * (y * (y3 * y4))
	else:
		tmp = a * ((x * y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y3 <= -6.8e+124) || !(y3 <= 0.3))
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(a * Float64(Float64(x * y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y3 <= -6.8e+124) || ~((y3 <= 0.3)))
		tmp = c * (y * (y3 * y4));
	else
		tmp = a * ((x * y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y3, -6.8e+124], N[Not[LessEqual[y3, 0.3]], $MachinePrecision]], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y3 < -6.8e124 or 0.299999999999999989 < y3

   1. Initial program 21.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.2%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 33.5%

      \[\leadsto \color{blue}{y4 \cdot \left(\left(\left(t \cdot j - k \cdot y\right) \cdot b + y1 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   5. Taylor expanded in c around inf 43.3%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 36.9%

      \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 36.9%

         \[\leadsto c \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y4\right)} \]

      2. associate-*l* 38.0%

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   8. Simplified 38.0%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if -6.8e124 < y3 < 0.299999999999999989

   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 x around inf 45.2%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 44.5%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 44.5%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 44.5%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 27.1%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 27.1%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 27.1%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 32.3%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 32.3%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around inf 18.9%

       \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 18.3%

          \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x\right)} \]

       2. *-commutative 18.3%

          \[\leadsto \color{blue}{\left(a \cdot y\right)} \cdot \left(b \cdot x\right) \]

       3. associate-*r* 20.7%

          \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

       4. *-commutative 20.7%

          \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(x \cdot b\right)}\right) \]

       5. associate-*r* 19.0%

          \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]

       6. *-commutative 19.0%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]

   14. Simplified 19.0%

       \[\leadsto \color{blue}{a \cdot \left(\left(x \cdot y\right) \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -6.8 \cdot 10^{+124} \lor \neg \left(y3 \leq 0.3\right):\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \end{array} \]

Alternative 36: 22.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -4.8e+52)
   (* a (* (* x y) b))
   (if (<= x 1.05e+69) (* c (* y (* y3 y4))) (* c (* y0 (* x y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -4.8e+52) {
		tmp = a * ((x * y) * b);
	} else if (x <= 1.05e+69) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-4.8d+52)) then
        tmp = a * ((x * y) * b)
    else if (x <= 1.05d+69) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -4.8e+52) {
		tmp = a * ((x * y) * b);
	} else if (x <= 1.05e+69) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -4.8e+52:
		tmp = a * ((x * y) * b)
	elif x <= 1.05e+69:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -4.8e+52)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (x <= 1.05e+69)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -4.8e+52)
		tmp = a * ((x * y) * b);
	elseif (x <= 1.05e+69)
		tmp = c * (y * (y3 * y4));
	else
		tmp = c * (y0 * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -4.8e+52], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+69], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e52

   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 x around inf 49.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 44.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 44.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 41.7%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 41.7%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 43.2%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 43.2%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around inf 31.7%

       \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 25.0%

          \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x\right)} \]

       2. *-commutative 25.0%

          \[\leadsto \color{blue}{\left(a \cdot y\right)} \cdot \left(b \cdot x\right) \]

       3. associate-*r* 33.3%

          \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

       4. *-commutative 33.3%

          \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(x \cdot b\right)}\right) \]

       5. associate-*r* 28.4%

          \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]

       6. *-commutative 28.4%

          \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]

   14. Simplified 28.4%

       \[\leadsto \color{blue}{a \cdot \left(\left(x \cdot y\right) \cdot b\right)} \]

   if -4.8e52 < x < 1.05000000000000008e69

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 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 c around inf 28.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 17.5%

      \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 17.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y4\right)} \]

      2. associate-*l* 18.1%

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   8. Simplified 18.1%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 1.05000000000000008e69 < x

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 65.9%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 50.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 50.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 50.4%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 50.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 50.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around -inf 50.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 37: 22.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= x -7.2e+52)
   (* y (* a (* x b)))
   (if (<= x 1.4e+68) (* c (* y (* y3 y4))) (* c (* y0 (* x y2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.2e+52) {
		tmp = y * (a * (x * b));
	} else if (x <= 1.4e+68) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (x <= (-7.2d+52)) then
        tmp = y * (a * (x * b))
    else if (x <= 1.4d+68) then
        tmp = c * (y * (y3 * y4))
    else
        tmp = c * (y0 * (x * y2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.2e+52) {
		tmp = y * (a * (x * b));
	} else if (x <= 1.4e+68) {
		tmp = c * (y * (y3 * y4));
	} else {
		tmp = c * (y0 * (x * y2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -7.2e+52:
		tmp = y * (a * (x * b))
	elif x <= 1.4e+68:
		tmp = c * (y * (y3 * y4))
	else:
		tmp = c * (y0 * (x * y2))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (x <= -7.2e+52)
		tmp = Float64(y * Float64(a * Float64(x * b)));
	elseif (x <= 1.4e+68)
		tmp = Float64(c * Float64(y * Float64(y3 * y4)));
	else
		tmp = Float64(c * Float64(y0 * Float64(x * y2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (x <= -7.2e+52)
		tmp = y * (a * (x * b));
	elseif (x <= 1.4e+68)
		tmp = c * (y * (y3 * y4));
	else
		tmp = c * (y0 * (x * y2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -7.2e+52], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+68], N[(c * N[(y * N[(y3 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2e52

   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 x around inf 49.5%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      3. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      4. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      5. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      6. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      7. *-commutative 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. Applied egg-rr 44.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
   7. Step-by-step derivation

      1. associate-*l* 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

      2. associate-*l* 44.4%

         \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   8. Simplified 44.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   9. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 41.7%

          \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

       2. *-commutative 41.7%

          \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

       3. associate-*l* 43.2%

          \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   11. Simplified 43.2%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

   12. Taylor expanded in a around inf 31.7%

       \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -7.2e52 < x < 1.4e68

   1. Initial program 31.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y4 around inf 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 c around inf 28.8%

      \[\leadsto \color{blue}{c \cdot \left(y4 \cdot \left(y \cdot y3 - t \cdot y2\right)\right)} \]

   6. Taylor expanded in y around inf 17.5%

      \[\leadsto c \cdot \color{blue}{\left(y4 \cdot \left(y \cdot y3\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 17.5%

         \[\leadsto c \cdot \color{blue}{\left(\left(y \cdot y3\right) \cdot y4\right)} \]

      2. associate-*l* 18.1%

         \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   8. Simplified 18.1%

      \[\leadsto c \cdot \color{blue}{\left(y \cdot \left(y3 \cdot y4\right)\right)} \]

   if 1.4e68 < x

   1. Initial program 28.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in x around inf 65.9%

      \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]

   5. Taylor expanded in c around inf 50.4%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right) \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-1 \cdot \left(i \cdot y\right) + y0 \cdot y2\right)\right) \cdot x} \]

      2. +-commutative 50.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(i \cdot y\right)\right)}\right) \cdot x \]

      3. mul-1-neg 50.4%

         \[\leadsto \left(c \cdot \left(y0 \cdot y2 + \color{blue}{\left(-i \cdot y\right)}\right)\right) \cdot x \]

      4. unsub-neg 50.4%

         \[\leadsto \left(c \cdot \color{blue}{\left(y0 \cdot y2 - i \cdot y\right)}\right) \cdot x \]

   7. Simplified 50.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(y0 \cdot y2 - i \cdot y\right)\right) \cdot x} \]

   8. Taylor expanded in y0 around -inf 50.8%

      \[\leadsto \color{blue}{c \cdot \left(y0 \cdot \left(y2 \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(y \cdot \left(y3 \cdot y4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2\right)\right)\\ \end{array} \]

Alternative 38: 17.2% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(\left(x \cdot y\right) \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* (* x y) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * ((x * y) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * ((x * y) * b);
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * ((x * y) * b)

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(Float64(x * y) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * ((x * y) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.0%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

3. Simplified 29.0%

   \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

4. Taylor expanded in x around inf 41.5%

   \[\leadsto \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x} \]
5. Step-by-step derivation

   1. add-cbrt-cube 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   2. *-commutative 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   3. *-commutative 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   4. *-commutative 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   5. *-commutative 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)\right) \cdot \left(\left(c \cdot y0 - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   6. *-commutative 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(\color{blue}{y0 \cdot c} - a \cdot y1\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   7. *-commutative 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - \color{blue}{y1 \cdot a}\right) \cdot y2\right)}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

6. Applied egg-rr 41.4%

   \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]
7. Step-by-step derivation

   1. associate-*l* 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

   2. associate-*l* 41.4%

      \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \color{blue}{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

8. Simplified 41.4%

   \[\leadsto \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + \color{blue}{\sqrt[3]{\left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right) \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot \left(y2 \cdot \left(\left(y0 \cdot c - y1 \cdot a\right) \cdot y2\right)\right)\right)}}\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot j\right) \cdot x \]

9. Taylor expanded in b around inf 25.5%

   \[\leadsto \color{blue}{\left(a \cdot y - y0 \cdot j\right) \cdot \left(b \cdot x\right)} \]
10. Step-by-step derivation

    1. *-commutative 25.5%

       \[\leadsto \color{blue}{\left(b \cdot x\right) \cdot \left(a \cdot y - y0 \cdot j\right)} \]

    2. *-commutative 25.5%

       \[\leadsto \color{blue}{\left(x \cdot b\right)} \cdot \left(a \cdot y - y0 \cdot j\right) \]

    3. associate-*l* 31.5%

       \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

11. Simplified 31.5%

    \[\leadsto \color{blue}{x \cdot \left(b \cdot \left(a \cdot y - y0 \cdot j\right)\right)} \]

12. Taylor expanded in a around inf 15.9%

    \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
13. Step-by-step derivation

    1. associate-*r* 14.8%

       \[\leadsto \color{blue}{\left(y \cdot a\right) \cdot \left(b \cdot x\right)} \]

    2. *-commutative 14.8%

       \[\leadsto \color{blue}{\left(a \cdot y\right)} \cdot \left(b \cdot x\right) \]

    3. associate-*r* 17.4%

       \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(b \cdot x\right)\right)} \]

    4. *-commutative 17.4%

       \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(x \cdot b\right)}\right) \]

    5. associate-*r* 16.0%

       \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]

    6. *-commutative 16.0%

       \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]

14. Simplified 16.0%

    \[\leadsto \color{blue}{a \cdot \left(\left(x \cdot y\right) \cdot b\right)} \]

15. Final simplification 16.0%

    \[\leadsto a \cdot \left(\left(x \cdot y\right) \cdot b\right) \]

Developer target: 28.2% 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 2023240 
(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)))))