Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.7% → 39.7%

Time: 1.6min

Alternatives: 36

Speedup: 3.5×

• 88.7% 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: 30.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 39.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot y1 - c \cdot y0\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y3 \leq -1.22 \cdot 10^{+237}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot t_1\right)\\ \mathbf{elif}\;y3 \leq -2.55 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq -4.6 \cdot 10^{-75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq -1.75 \cdot 10^{-154}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -4 \cdot 10^{-217}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq -4.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 6.9 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* a y1) (* c y0)))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_2))
           (* j (- (* i y1) (* b y0))))))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y3 -1.22e+237)
     (* z (+ (* k (- (* b y0) (* i y1))) (* y3 t_1)))
     (if (<= y3 -2.55e+126)
       t_3
       (if (<= y3 -4.6e-75)
         t_4
         (if (<= y3 -1.75e-154)
           (*
            y2
            (+
             (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y3 -4e-217)
             t_4
             (if (<= y3 -4.2e-236)
               (* x (* a (- (* y b) (* y1 y2))))
               (if (<= y3 6.9e-276)
                 (*
                  i
                  (+
                   (* y1 (- (* x j) (* z k)))
                   (- (* y5 (- (* y k) (* t j))) (* c (- (* x y) (* z t))))))
                 (if (<= y3 7.8e+99)
                   t_3
                   (*
                    y3
                    (+
                     (* y (- (* c y4) (* a y5)))
                     (+ (* j (- (* y0 y5) (* y1 y4))) (* 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 = (a * y1) - (c * y0);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -1.22e+237) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * t_1));
	} else if (y3 <= -2.55e+126) {
		tmp = t_3;
	} else if (y3 <= -4.6e-75) {
		tmp = t_4;
	} else if (y3 <= -1.75e-154) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= -4e-217) {
		tmp = t_4;
	} else if (y3 <= -4.2e-236) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y3 <= 6.9e-276) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y3 <= 7.8e+99) {
		tmp = t_3;
	} else {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (a * y1) - (c * y0)
    t_2 = (c * y0) - (a * y1)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (y3 <= (-1.22d+237)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * t_1))
    else if (y3 <= (-2.55d+126)) then
        tmp = t_3
    else if (y3 <= (-4.6d-75)) then
        tmp = t_4
    else if (y3 <= (-1.75d-154)) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y3 <= (-4d-217)) then
        tmp = t_4
    else if (y3 <= (-4.2d-236)) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (y3 <= 6.9d-276) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
    else if (y3 <= 7.8d+99) then
        tmp = t_3
    else
        tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (a * y1) - (c * y0);
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -1.22e+237) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * t_1));
	} else if (y3 <= -2.55e+126) {
		tmp = t_3;
	} else if (y3 <= -4.6e-75) {
		tmp = t_4;
	} else if (y3 <= -1.75e-154) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= -4e-217) {
		tmp = t_4;
	} else if (y3 <= -4.2e-236) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y3 <= 6.9e-276) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y3 <= 7.8e+99) {
		tmp = t_3;
	} else {
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (a * y1) - (c * y0)
	t_2 = (c * y0) - (a * y1)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y3 <= -1.22e+237:
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * t_1))
	elif y3 <= -2.55e+126:
		tmp = t_3
	elif y3 <= -4.6e-75:
		tmp = t_4
	elif y3 <= -1.75e-154:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y3 <= -4e-217:
		tmp = t_4
	elif y3 <= -4.2e-236:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif y3 <= 6.9e-276:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
	elif y3 <= 7.8e+99:
		tmp = t_3
	else:
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(a * y1) - Float64(c * y0))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y3 <= -1.22e+237)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y3 * t_1)));
	elseif (y3 <= -2.55e+126)
		tmp = t_3;
	elseif (y3 <= -4.6e-75)
		tmp = t_4;
	elseif (y3 <= -1.75e-154)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y3 <= -4e-217)
		tmp = t_4;
	elseif (y3 <= -4.2e-236)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y3 <= 6.9e-276)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * Float64(Float64(x * y) - Float64(z * t))))));
	elseif (y3 <= 7.8e+99)
		tmp = t_3;
	else
		tmp = Float64(y3 * Float64(Float64(y * Float64(Float64(c * y4) - Float64(a * y5))) + Float64(Float64(j * Float64(Float64(y0 * y5) - Float64(y1 * y4))) + Float64(z * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (a * y1) - (c * y0);
	t_2 = (c * y0) - (a * y1);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y3 <= -1.22e+237)
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * t_1));
	elseif (y3 <= -2.55e+126)
		tmp = t_3;
	elseif (y3 <= -4.6e-75)
		tmp = t_4;
	elseif (y3 <= -1.75e-154)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y3 <= -4e-217)
		tmp = t_4;
	elseif (y3 <= -4.2e-236)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (y3 <= 6.9e-276)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	elseif (y3 <= 7.8e+99)
		tmp = t_3;
	else
		tmp = y3 * ((y * ((c * y4) - (a * y5))) + ((j * ((y0 * y5) - (y1 * y4))) + (z * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.22e+237], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.55e+126], t$95$3, If[LessEqual[y3, -4.6e-75], t$95$4, If[LessEqual[y3, -1.75e-154], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -4e-217], t$95$4, If[LessEqual[y3, -4.2e-236], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 6.9e-276], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7.8e+99], t$95$3, N[(y3 * N[(N[(y * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(y0 * y5), $MachinePrecision] - N[(y1 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -1.2200000000000001e237

   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 z around -inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. associate--l+ 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in t around 0 76.5%

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

   if -1.2200000000000001e237 < y3 < -2.5500000000000001e126 or 6.89999999999999985e-276 < y3 < 7.79999999999999989e99

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   4. Taylor expanded in x around inf 57.8%

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

   if -2.5500000000000001e126 < y3 < -4.6e-75 or -1.75e-154 < y3 < -4.00000000000000033e-217

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in y4 around inf 57.2%

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

   if -4.6e-75 < y3 < -1.75e-154

   1. Initial program 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in y2 around inf 56.8%

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

   if -4.00000000000000033e-217 < y3 < -4.19999999999999958e-236

   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%

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

   4. Taylor expanded in a around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. mul-1-neg 50.1%

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

   6. Simplified 50.1%

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

   7. Taylor expanded in x around -inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-*r* 75.1%

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

      3. distribute-lft-out-- 75.1%

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

      4. *-commutative 75.1%

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

      5. *-commutative 75.1%

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

   9. Simplified 75.1%

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

   if -4.19999999999999958e-236 < y3 < 6.89999999999999985e-276

   1. Initial program 38.9%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in i around -inf 54.9%

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

   if 7.79999999999999989e99 < y3

   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 y3 around -inf 73.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.22 \cdot 10^{+237}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -2.55 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -4.6 \cdot 10^{-75}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -1.75 \cdot 10^{-154}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -4 \cdot 10^{-217}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -4.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 6.9 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y3 \cdot \left(y \cdot \left(c \cdot y4 - a \cdot y5\right) + \left(j \cdot \left(y0 \cdot y5 - y1 \cdot y4\right) + z \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\right)\\ \end{array} \]

Alternative 2: 50.4% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision] * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(y0 * N[(b * t$95$1), $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 95.7%

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

   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 8.4%

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

   4. Taylor expanded in y0 around inf 40.2%

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

      1. mul-1-neg 40.2%

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

   6. Simplified 40.2%

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

   7. Taylor expanded in b around inf 42.1%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.9%

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

Alternative 3: 38.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot y0 - a \cdot y1\\ t_2 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_1\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_3 := y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\\ t_4 := t \cdot j - y \cdot k\\ t_5 := y4 \cdot \left(\left(b \cdot t_4 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y3 \leq -5.2 \cdot 10^{+234}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t_3\right)\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq -1.15 \cdot 10^{-75}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y3 \leq -1.9 \cdot 10^{-154}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_1 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -5 \cdot 10^{-217}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y3 \leq -1.52 \cdot 10^{-245}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 1.72 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_4\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y3 \leq 6.5 \cdot 10^{+215}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* c y0) (* a y1)))
        (t_2
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_1))
           (* j (- (* i y1) (* b y0))))))
        (t_3 (* y3 (- (* a y1) (* c y0))))
        (t_4 (- (* t j) (* y k)))
        (t_5
         (*
          y4
          (+
           (+ (* b t_4) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y3 -5.2e+234)
     (* z (+ (* k (- (* b y0) (* i y1))) t_3))
     (if (<= y3 -1.3e+123)
       t_2
       (if (<= y3 -1.15e-75)
         t_5
         (if (<= y3 -1.9e-154)
           (*
            y2
            (+
             (+ (* x t_1) (* k (- (* y1 y4) (* y0 y5))))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y3 -5e-217)
             t_5
             (if (<= y3 -1.52e-245)
               t_2
               (if (<= y3 1.72e-279)
                 (*
                  b
                  (+
                   (+ (* a (- (* x y) (* z t))) (* y4 t_4))
                   (* y0 (- (* z k) (* x j)))))
                 (if (<= y3 3.8e+99)
                   t_2
                   (if (<= y3 6.5e+215)
                     (* y (* y4 (- (* c y3) (* b k))))
                     (* z t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double t_3 = y3 * ((a * y1) - (c * y0));
	double t_4 = (t * j) - (y * k);
	double t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -5.2e+234) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_3);
	} else if (y3 <= -1.3e+123) {
		tmp = t_2;
	} else if (y3 <= -1.15e-75) {
		tmp = t_5;
	} else if (y3 <= -1.9e-154) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= -5e-217) {
		tmp = t_5;
	} else if (y3 <= -1.52e-245) {
		tmp = t_2;
	} else if (y3 <= 1.72e-279) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 3.8e+99) {
		tmp = t_2;
	} else if (y3 <= 6.5e+215) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else {
		tmp = z * 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 = (c * y0) - (a * y1)
    t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
    t_3 = y3 * ((a * y1) - (c * y0))
    t_4 = (t * j) - (y * k)
    t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (y3 <= (-5.2d+234)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + t_3)
    else if (y3 <= (-1.3d+123)) then
        tmp = t_2
    else if (y3 <= (-1.15d-75)) then
        tmp = t_5
    else if (y3 <= (-1.9d-154)) then
        tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y3 <= (-5d-217)) then
        tmp = t_5
    else if (y3 <= (-1.52d-245)) then
        tmp = t_2
    else if (y3 <= 1.72d-279) then
        tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))))
    else if (y3 <= 3.8d+99) then
        tmp = t_2
    else if (y3 <= 6.5d+215) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else
        tmp = z * t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (c * y0) - (a * y1);
	double t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	double t_3 = y3 * ((a * y1) - (c * y0));
	double t_4 = (t * j) - (y * k);
	double t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -5.2e+234) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_3);
	} else if (y3 <= -1.3e+123) {
		tmp = t_2;
	} else if (y3 <= -1.15e-75) {
		tmp = t_5;
	} else if (y3 <= -1.9e-154) {
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= -5e-217) {
		tmp = t_5;
	} else if (y3 <= -1.52e-245) {
		tmp = t_2;
	} else if (y3 <= 1.72e-279) {
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))));
	} else if (y3 <= 3.8e+99) {
		tmp = t_2;
	} else if (y3 <= 6.5e+215) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else {
		tmp = z * t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (c * y0) - (a * y1)
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))))
	t_3 = y3 * ((a * y1) - (c * y0))
	t_4 = (t * j) - (y * k)
	t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y3 <= -5.2e+234:
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_3)
	elif y3 <= -1.3e+123:
		tmp = t_2
	elif y3 <= -1.15e-75:
		tmp = t_5
	elif y3 <= -1.9e-154:
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y3 <= -5e-217:
		tmp = t_5
	elif y3 <= -1.52e-245:
		tmp = t_2
	elif y3 <= 1.72e-279:
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))))
	elif y3 <= 3.8e+99:
		tmp = t_2
	elif y3 <= 6.5e+215:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	else:
		tmp = z * t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(c * y0) - Float64(a * y1))
	t_2 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_1)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_3 = Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0)))
	t_4 = Float64(Float64(t * j) - Float64(y * k))
	t_5 = Float64(y4 * Float64(Float64(Float64(b * t_4) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y3 <= -5.2e+234)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + t_3));
	elseif (y3 <= -1.3e+123)
		tmp = t_2;
	elseif (y3 <= -1.15e-75)
		tmp = t_5;
	elseif (y3 <= -1.9e-154)
		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 (y3 <= -5e-217)
		tmp = t_5;
	elseif (y3 <= -1.52e-245)
		tmp = t_2;
	elseif (y3 <= 1.72e-279)
		tmp = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_4)) + Float64(y0 * Float64(Float64(z * k) - Float64(x * j)))));
	elseif (y3 <= 3.8e+99)
		tmp = t_2;
	elseif (y3 <= 6.5e+215)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	else
		tmp = Float64(z * t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (c * y0) - (a * y1);
	t_2 = x * (((y * ((a * b) - (c * i))) + (y2 * t_1)) + (j * ((i * y1) - (b * y0))));
	t_3 = y3 * ((a * y1) - (c * y0));
	t_4 = (t * j) - (y * k);
	t_5 = y4 * (((b * t_4) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y3 <= -5.2e+234)
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_3);
	elseif (y3 <= -1.3e+123)
		tmp = t_2;
	elseif (y3 <= -1.15e-75)
		tmp = t_5;
	elseif (y3 <= -1.9e-154)
		tmp = y2 * (((x * t_1) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y3 <= -5e-217)
		tmp = t_5;
	elseif (y3 <= -1.52e-245)
		tmp = t_2;
	elseif (y3 <= 1.72e-279)
		tmp = b * (((a * ((x * y) - (z * t))) + (y4 * t_4)) + (y0 * ((z * k) - (x * j))));
	elseif (y3 <= 3.8e+99)
		tmp = t_2;
	elseif (y3 <= 6.5e+215)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	else
		tmp = z * t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y4 * N[(N[(N[(b * t$95$4), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -5.2e+234], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.3e+123], t$95$2, If[LessEqual[y3, -1.15e-75], t$95$5, If[LessEqual[y3, -1.9e-154], 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[y3, -5e-217], t$95$5, If[LessEqual[y3, -1.52e-245], t$95$2, If[LessEqual[y3, 1.72e-279], N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.8e+99], t$95$2, If[LessEqual[y3, 6.5e+215], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * t$95$3), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y3 < -5.2000000000000003e234

   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 z around -inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. associate--l+ 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in t around 0 76.5%

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

   if -5.2000000000000003e234 < y3 < -1.29999999999999993e123 or -5.0000000000000002e-217 < y3 < -1.5199999999999999e-245 or 1.7199999999999999e-279 < y3 < 3.8e99

   1. Initial program 35.7%

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

   3. Simplified 35.7%

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

   4. Taylor expanded in x around inf 58.5%

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

   if -1.29999999999999993e123 < y3 < -1.15e-75 or -1.90000000000000005e-154 < y3 < -5.0000000000000002e-217

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in y4 around inf 57.2%

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

   if -1.15e-75 < y3 < -1.90000000000000005e-154

   1. Initial program 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in y2 around inf 56.8%

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

   if -1.5199999999999999e-245 < y3 < 1.7199999999999999e-279

   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 b around inf 51.5%

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

   if 3.8e99 < y3 < 6.4999999999999997e215

   1. Initial program 39.3%

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

   3. Simplified 39.3%

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

   4. Taylor expanded in y around inf 43.5%

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

      1. associate--l+ 43.5%

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

      2. mul-1-neg 43.5%

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

      3. mul-1-neg 43.5%

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

   6. Simplified 43.5%

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

   7. Taylor expanded in y4 around inf 61.3%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 61.3%

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

      2. *-commutative 61.3%

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

   9. Simplified 61.3%

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

   if 6.4999999999999997e215 < y3

   1. Initial program 21.1%

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

   3. Simplified 21.1%

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

   4. Taylor expanded in z around -inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate--l+ 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in t around 0 68.5%

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

   8. Taylor expanded in y3 around inf 76.7%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - y1 \cdot a\right) \cdot y3\right)} \cdot z \]
3. Recombined 7 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -5.2 \cdot 10^{+234}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{+123}:\\ \;\;\;\;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}\;y3 \leq -1.15 \cdot 10^{-75}:\\ \;\;\;\;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}\;y3 \leq -1.9 \cdot 10^{-154}:\\ \;\;\;\;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}\;y3 \leq -5 \cdot 10^{-217}:\\ \;\;\;\;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}\;y3 \leq -1.52 \cdot 10^{-245}:\\ \;\;\;\;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}\;y3 \leq 1.72 \cdot 10^{-279}:\\ \;\;\;\;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}\;y3 \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;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}\;y3 \leq 6.5 \cdot 10^{+215}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \end{array} \]

Alternative 4: 37.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\\ t_2 := c \cdot y0 - a \cdot y1\\ t_3 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot t_2\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ t_4 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{if}\;y3 \leq -1.1 \cdot 10^{+229}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + t_1\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+126}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq -1.8 \cdot 10^{-154}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot t_2 + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -1.66 \cdot 10^{-214}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 3.35 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 4.4 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y3 (- (* a y1) (* c y0))))
        (t_2 (- (* c y0) (* a y1)))
        (t_3
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 t_2))
           (* j (- (* i y1) (* b y0))))))
        (t_4
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2)))))))
   (if (<= y3 -1.1e+229)
     (* z (+ (* k (- (* b y0) (* i y1))) t_1))
     (if (<= y3 -5.5e+126)
       t_3
       (if (<= y3 -4.8e-76)
         t_4
         (if (<= y3 -1.8e-154)
           (*
            y2
            (+
             (+ (* x t_2) (* k (- (* y1 y4) (* y0 y5))))
             (* t (- (* a y5) (* c y4)))))
           (if (<= y3 -1.66e-214)
             t_4
             (if (<= y3 -1.3e-237)
               (* x (* a (- (* y b) (* y1 y2))))
               (if (<= y3 3.35e-273)
                 (*
                  i
                  (+
                   (* y1 (- (* x j) (* z k)))
                   (- (* y5 (- (* y k) (* t j))) (* c (- (* x y) (* z t))))))
                 (if (<= y3 4.4e+98)
                   t_3
                   (if (<= y3 7e+217)
                     (* y (* y4 (- (* c y3) (* b k))))
                     (* 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 = y3 * ((a * y1) - (c * y0));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -1.1e+229) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_1);
	} else if (y3 <= -5.5e+126) {
		tmp = t_3;
	} else if (y3 <= -4.8e-76) {
		tmp = t_4;
	} else if (y3 <= -1.8e-154) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= -1.66e-214) {
		tmp = t_4;
	} else if (y3 <= -1.3e-237) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y3 <= 3.35e-273) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y3 <= 4.4e+98) {
		tmp = t_3;
	} else if (y3 <= 7e+217) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else {
		tmp = z * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y3 * ((a * y1) - (c * y0))
    t_2 = (c * y0) - (a * y1)
    t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
    t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    if (y3 <= (-1.1d+229)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + t_1)
    else if (y3 <= (-5.5d+126)) then
        tmp = t_3
    else if (y3 <= (-4.8d-76)) then
        tmp = t_4
    else if (y3 <= (-1.8d-154)) then
        tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
    else if (y3 <= (-1.66d-214)) then
        tmp = t_4
    else if (y3 <= (-1.3d-237)) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (y3 <= 3.35d-273) then
        tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
    else if (y3 <= 4.4d+98) then
        tmp = t_3
    else if (y3 <= 7d+217) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else
        tmp = z * 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 = y3 * ((a * y1) - (c * y0));
	double t_2 = (c * y0) - (a * y1);
	double t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	double t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double tmp;
	if (y3 <= -1.1e+229) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_1);
	} else if (y3 <= -5.5e+126) {
		tmp = t_3;
	} else if (y3 <= -4.8e-76) {
		tmp = t_4;
	} else if (y3 <= -1.8e-154) {
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	} else if (y3 <= -1.66e-214) {
		tmp = t_4;
	} else if (y3 <= -1.3e-237) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (y3 <= 3.35e-273) {
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	} else if (y3 <= 4.4e+98) {
		tmp = t_3;
	} else if (y3 <= 7e+217) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else {
		tmp = z * 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 = y3 * ((a * y1) - (c * y0))
	t_2 = (c * y0) - (a * y1)
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))))
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	tmp = 0
	if y3 <= -1.1e+229:
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_1)
	elif y3 <= -5.5e+126:
		tmp = t_3
	elif y3 <= -4.8e-76:
		tmp = t_4
	elif y3 <= -1.8e-154:
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))))
	elif y3 <= -1.66e-214:
		tmp = t_4
	elif y3 <= -1.3e-237:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif y3 <= 3.35e-273:
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))))
	elif y3 <= 4.4e+98:
		tmp = t_3
	elif y3 <= 7e+217:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	else:
		tmp = z * 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(y3 * Float64(Float64(a * y1) - Float64(c * y0)))
	t_2 = Float64(Float64(c * y0) - Float64(a * y1))
	t_3 = Float64(x * Float64(Float64(Float64(y * Float64(Float64(a * b) - Float64(c * i))) + Float64(y2 * t_2)) + Float64(j * Float64(Float64(i * y1) - Float64(b * y0)))))
	t_4 = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	tmp = 0.0
	if (y3 <= -1.1e+229)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + t_1));
	elseif (y3 <= -5.5e+126)
		tmp = t_3;
	elseif (y3 <= -4.8e-76)
		tmp = t_4;
	elseif (y3 <= -1.8e-154)
		tmp = Float64(y2 * Float64(Float64(Float64(x * t_2) + Float64(k * Float64(Float64(y1 * y4) - Float64(y0 * y5)))) + Float64(t * Float64(Float64(a * y5) - Float64(c * y4)))));
	elseif (y3 <= -1.66e-214)
		tmp = t_4;
	elseif (y3 <= -1.3e-237)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (y3 <= 3.35e-273)
		tmp = Float64(i * Float64(Float64(y1 * Float64(Float64(x * j) - Float64(z * k))) + Float64(Float64(y5 * Float64(Float64(y * k) - Float64(t * j))) - Float64(c * Float64(Float64(x * y) - Float64(z * t))))));
	elseif (y3 <= 4.4e+98)
		tmp = t_3;
	elseif (y3 <= 7e+217)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	else
		tmp = Float64(z * 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 = y3 * ((a * y1) - (c * y0));
	t_2 = (c * y0) - (a * y1);
	t_3 = x * (((y * ((a * b) - (c * i))) + (y2 * t_2)) + (j * ((i * y1) - (b * y0))));
	t_4 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	tmp = 0.0;
	if (y3 <= -1.1e+229)
		tmp = z * ((k * ((b * y0) - (i * y1))) + t_1);
	elseif (y3 <= -5.5e+126)
		tmp = t_3;
	elseif (y3 <= -4.8e-76)
		tmp = t_4;
	elseif (y3 <= -1.8e-154)
		tmp = y2 * (((x * t_2) + (k * ((y1 * y4) - (y0 * y5)))) + (t * ((a * y5) - (c * y4))));
	elseif (y3 <= -1.66e-214)
		tmp = t_4;
	elseif (y3 <= -1.3e-237)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (y3 <= 3.35e-273)
		tmp = i * ((y1 * ((x * j) - (z * k))) + ((y5 * ((y * k) - (t * j))) - (c * ((x * y) - (z * t)))));
	elseif (y3 <= 4.4e+98)
		tmp = t_3;
	elseif (y3 <= 7e+217)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	else
		tmp = z * 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[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y3, -1.1e+229], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -5.5e+126], t$95$3, If[LessEqual[y3, -4.8e-76], t$95$4, If[LessEqual[y3, -1.8e-154], N[(y2 * N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.66e-214], t$95$4, If[LessEqual[y3, -1.3e-237], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 3.35e-273], N[(i * N[(N[(y1 * N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.4e+98], t$95$3, If[LessEqual[y3, 7e+217], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * t$95$1), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y3 < -1.10000000000000002e229

   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 z around -inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. associate--l+ 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in t around 0 76.5%

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

   if -1.10000000000000002e229 < y3 < -5.5000000000000004e126 or 3.34999999999999991e-273 < y3 < 4.40000000000000017e98

   1. Initial program 35.6%

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

   3. Simplified 35.6%

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

   4. Taylor expanded in x around inf 57.8%

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

   if -5.5000000000000004e126 < y3 < -4.80000000000000026e-76 or -1.8000000000000001e-154 < y3 < -1.6600000000000001e-214

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in y4 around inf 57.2%

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

   if -4.80000000000000026e-76 < y3 < -1.8000000000000001e-154

   1. Initial program 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in y2 around inf 56.8%

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

   if -1.6600000000000001e-214 < y3 < -1.3000000000000001e-237

   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%

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

   4. Taylor expanded in a around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. mul-1-neg 50.1%

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

   6. Simplified 50.1%

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

   7. Taylor expanded in x around -inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-*r* 75.1%

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

      3. distribute-lft-out-- 75.1%

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

      4. *-commutative 75.1%

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

      5. *-commutative 75.1%

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

   9. Simplified 75.1%

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

   if -1.3000000000000001e-237 < y3 < 3.34999999999999991e-273

   1. Initial program 38.9%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in i around -inf 54.9%

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

   if 4.40000000000000017e98 < y3 < 6.9999999999999996e217

   1. Initial program 39.3%

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

   3. Simplified 39.3%

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

   4. Taylor expanded in y around inf 43.5%

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

      1. associate--l+ 43.5%

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

      2. mul-1-neg 43.5%

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

      3. mul-1-neg 43.5%

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

   6. Simplified 43.5%

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

   7. Taylor expanded in y4 around inf 61.3%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 61.3%

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

      2. *-commutative 61.3%

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

   9. Simplified 61.3%

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

   if 6.9999999999999996e217 < y3

   1. Initial program 21.1%

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

   3. Simplified 21.1%

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

   4. Taylor expanded in z around -inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate--l+ 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in t around 0 68.5%

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

   8. Taylor expanded in y3 around inf 76.7%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - y1 \cdot a\right) \cdot y3\right)} \cdot z \]
3. Recombined 8 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.1 \cdot 10^{+229}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -5.5 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq -4.8 \cdot 10^{-76}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -1.8 \cdot 10^{-154}:\\ \;\;\;\;y2 \cdot \left(\left(x \cdot \left(c \cdot y0 - a \cdot y1\right) + k \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq -1.66 \cdot 10^{-214}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq -1.3 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;y3 \leq 3.35 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(x \cdot j - z \cdot k\right) + \left(y5 \cdot \left(y \cdot k - t \cdot j\right) - c \cdot \left(x \cdot y - z \cdot t\right)\right)\right)\\ \mathbf{elif}\;y3 \leq 4.4 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;y3 \leq 7 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \end{array} \]

Alternative 5: 36.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot k - x \cdot j\\ t_2 := y0 \cdot \left(b \cdot t_1\right)\\ t_3 := t \cdot j - y \cdot k\\ t_4 := b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot t_3\right) + y0 \cdot t_1\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+238}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+187}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;\left(y1 \cdot y3 - t \cdot b\right) \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot t_3 + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+180}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* z k) (* x j)))
        (t_2 (* y0 (* b t_1)))
        (t_3 (- (* t j) (* y k)))
        (t_4 (* b (+ (+ (* a (- (* x y) (* z t))) (* y4 t_3)) (* y0 t_1)))))
   (if (<= x -2.5e+238)
     (* y0 (* c (- (* x y2) (* z y3))))
     (if (<= x -1.6e+187)
       t_4
       (if (<= x -1.5e+163)
         t_2
         (if (<= x -1.06e+77)
           (* y (* y4 (- (* c y3) (* b k))))
           (if (<= x -7.2e+56)
             (* (- (* y1 y3) (* t b)) (* z a))
             (if (<= x -6.4e+35)
               t_4
               (if (<= x 9.5e+110)
                 (*
                  y4
                  (+
                   (+ (* b t_3) (* y1 (- (* k y2) (* j y3))))
                   (* c (- (* y y3) (* t y2)))))
                 (if (<= x 1.2e+180)
                   (* (* y c) (- (* y3 y4) (* x i)))
                   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 = (z * k) - (x * j);
	double t_2 = y0 * (b * t_1);
	double t_3 = (t * j) - (y * k);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * t_1));
	double tmp;
	if (x <= -2.5e+238) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= -1.6e+187) {
		tmp = t_4;
	} else if (x <= -1.5e+163) {
		tmp = t_2;
	} else if (x <= -1.06e+77) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (x <= -7.2e+56) {
		tmp = ((y1 * y3) - (t * b)) * (z * a);
	} else if (x <= -6.4e+35) {
		tmp = t_4;
	} else if (x <= 9.5e+110) {
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 1.2e+180) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} 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 = (z * k) - (x * j)
    t_2 = y0 * (b * t_1)
    t_3 = (t * j) - (y * k)
    t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * t_1))
    if (x <= (-2.5d+238)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (x <= (-1.6d+187)) then
        tmp = t_4
    else if (x <= (-1.5d+163)) then
        tmp = t_2
    else if (x <= (-1.06d+77)) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (x <= (-7.2d+56)) then
        tmp = ((y1 * y3) - (t * b)) * (z * a)
    else if (x <= (-6.4d+35)) then
        tmp = t_4
    else if (x <= 9.5d+110) then
        tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (x <= 1.2d+180) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    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 = (z * k) - (x * j);
	double t_2 = y0 * (b * t_1);
	double t_3 = (t * j) - (y * k);
	double t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * t_1));
	double tmp;
	if (x <= -2.5e+238) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= -1.6e+187) {
		tmp = t_4;
	} else if (x <= -1.5e+163) {
		tmp = t_2;
	} else if (x <= -1.06e+77) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (x <= -7.2e+56) {
		tmp = ((y1 * y3) - (t * b)) * (z * a);
	} else if (x <= -6.4e+35) {
		tmp = t_4;
	} else if (x <= 9.5e+110) {
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 1.2e+180) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} 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 = (z * k) - (x * j)
	t_2 = y0 * (b * t_1)
	t_3 = (t * j) - (y * k)
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * t_1))
	tmp = 0
	if x <= -2.5e+238:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif x <= -1.6e+187:
		tmp = t_4
	elif x <= -1.5e+163:
		tmp = t_2
	elif x <= -1.06e+77:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif x <= -7.2e+56:
		tmp = ((y1 * y3) - (t * b)) * (z * a)
	elif x <= -6.4e+35:
		tmp = t_4
	elif x <= 9.5e+110:
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif x <= 1.2e+180:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	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(z * k) - Float64(x * j))
	t_2 = Float64(y0 * Float64(b * t_1))
	t_3 = Float64(Float64(t * j) - Float64(y * k))
	t_4 = Float64(b * Float64(Float64(Float64(a * Float64(Float64(x * y) - Float64(z * t))) + Float64(y4 * t_3)) + Float64(y0 * t_1)))
	tmp = 0.0
	if (x <= -2.5e+238)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= -1.6e+187)
		tmp = t_4;
	elseif (x <= -1.5e+163)
		tmp = t_2;
	elseif (x <= -1.06e+77)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (x <= -7.2e+56)
		tmp = Float64(Float64(Float64(y1 * y3) - Float64(t * b)) * Float64(z * a));
	elseif (x <= -6.4e+35)
		tmp = t_4;
	elseif (x <= 9.5e+110)
		tmp = Float64(y4 * Float64(Float64(Float64(b * t_3) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= 1.2e+180)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	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 = (z * k) - (x * j);
	t_2 = y0 * (b * t_1);
	t_3 = (t * j) - (y * k);
	t_4 = b * (((a * ((x * y) - (z * t))) + (y4 * t_3)) + (y0 * t_1));
	tmp = 0.0;
	if (x <= -2.5e+238)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (x <= -1.6e+187)
		tmp = t_4;
	elseif (x <= -1.5e+163)
		tmp = t_2;
	elseif (x <= -1.06e+77)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (x <= -7.2e+56)
		tmp = ((y1 * y3) - (t * b)) * (z * a);
	elseif (x <= -6.4e+35)
		tmp = t_4;
	elseif (x <= 9.5e+110)
		tmp = y4 * (((b * t_3) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (x <= 1.2e+180)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	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[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+238], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e+187], t$95$4, If[LessEqual[x, -1.5e+163], t$95$2, If[LessEqual[x, -1.06e+77], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e+56], N[(N[(N[(y1 * y3), $MachinePrecision] - N[(t * b), $MachinePrecision]), $MachinePrecision] * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.4e+35], t$95$4, If[LessEqual[x, 9.5e+110], N[(y4 * N[(N[(N[(b * t$95$3), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+180], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -2.49999999999999998e238

   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 4.5%

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

   4. Taylor expanded in y0 around inf 42.2%

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

      1. mul-1-neg 42.2%

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

   6. Simplified 42.2%

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

   7. Taylor expanded in c around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-*l* 55.9%

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

      4. *-commutative 55.9%

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

   9. Simplified 55.9%

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

   if -2.49999999999999998e238 < x < -1.59999999999999997e187 or -7.19999999999999996e56 < x < -6.39999999999999965e35

   1. Initial program 65.3%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in b around inf 75.5%

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

   if -1.59999999999999997e187 < x < -1.50000000000000007e163 or 1.1999999999999999e180 < x

   1. Initial program 16.6%

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

   3. Simplified 19.4%

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

   4. Taylor expanded in y0 around inf 50.3%

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

      1. mul-1-neg 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in b around inf 69.9%

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

   if -1.50000000000000007e163 < x < -1.06000000000000003e77

   1. Initial program 7.7%

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

   3. Simplified 7.7%

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

   4. Taylor expanded in y around inf 46.4%

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

      1. associate--l+ 46.4%

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

      2. mul-1-neg 46.4%

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

      3. mul-1-neg 46.4%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in y4 around inf 62.1%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 62.1%

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

      2. *-commutative 62.1%

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

   9. Simplified 62.1%

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

   if -1.06000000000000003e77 < x < -7.19999999999999996e56

   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 49.7%

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

   4. Taylor expanded in a around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. mul-1-neg 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in z around -inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. distribute-lft-out-- 67.8%

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

      3. cancel-sign-sub-inv 67.8%

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

      4. metadata-eval 67.8%

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

      5. *-lft-identity 67.8%

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

      6. +-commutative 67.8%

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

      7. mul-1-neg 67.8%

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

      8. unsub-neg 67.8%

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

      9. *-commutative 67.8%

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

      10. *-commutative 67.8%

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

   9. Simplified 67.8%

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

   if -6.39999999999999965e35 < x < 9.49999999999999939e110

   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 y4 around inf 49.1%

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

   if 9.49999999999999939e110 < x < 1.1999999999999999e180

   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 y around inf 50.4%

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

      1. associate--l+ 50.4%

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

      2. mul-1-neg 50.4%

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

      3. mul-1-neg 50.4%

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

   6. Simplified 50.4%

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

   7. Taylor expanded in c around inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. *-commutative 64.5%

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

      3. mul-1-neg 64.5%

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

      4. unsub-neg 64.5%

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

      5. *-commutative 64.5%

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

      6. *-commutative 64.5%

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

   9. Simplified 64.5%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+238}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+163}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.06 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;\left(y1 \cdot y3 - t \cdot b\right) \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(\left(a \cdot \left(x \cdot y - z \cdot t\right) + y4 \cdot \left(t \cdot j - y \cdot k\right)\right) + y0 \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+110}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+180}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 6: 36.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+237}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-88}:\\ \;\;\;\;\left(t \cdot a - k \cdot y0\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+180}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          y4
          (+
           (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
           (* c (- (* y y3) (* t y2))))))
        (t_2 (* y0 (* b (- (* z k) (* x j))))))
   (if (<= x -1.3e+237)
     (* y0 (* c (- (* x y2) (* z y3))))
     (if (<= x -2.35e+23)
       (* z (+ (* k (- (* b y0) (* i y1))) (* y3 (- (* a y1) (* c y0)))))
       (if (<= x -1.75e-31)
         t_1
         (if (<= x -2.3e-50)
           t_2
           (if (<= x -4.7e-88)
             (* (- (* t a) (* k y0)) (* y2 y5))
             (if (<= x 1.62e+111)
               t_1
               (if (<= x 1.25e+180)
                 (* (* y c) (- (* y3 y4) (* x i)))
                 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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (x <= -1.3e+237) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= -2.35e+23) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * ((a * y1) - (c * y0))));
	} else if (x <= -1.75e-31) {
		tmp = t_1;
	} else if (x <= -2.3e-50) {
		tmp = t_2;
	} else if (x <= -4.7e-88) {
		tmp = ((t * a) - (k * y0)) * (y2 * y5);
	} else if (x <= 1.62e+111) {
		tmp = t_1;
	} else if (x <= 1.25e+180) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    if (x <= (-1.3d+237)) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (x <= (-2.35d+23)) then
        tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * ((a * y1) - (c * y0))))
    else if (x <= (-1.75d-31)) then
        tmp = t_1
    else if (x <= (-2.3d-50)) then
        tmp = t_2
    else if (x <= (-4.7d-88)) then
        tmp = ((t * a) - (k * y0)) * (y2 * y5)
    else if (x <= 1.62d+111) then
        tmp = t_1
    else if (x <= 1.25d+180) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double tmp;
	if (x <= -1.3e+237) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (x <= -2.35e+23) {
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * ((a * y1) - (c * y0))));
	} else if (x <= -1.75e-31) {
		tmp = t_1;
	} else if (x <= -2.3e-50) {
		tmp = t_2;
	} else if (x <= -4.7e-88) {
		tmp = ((t * a) - (k * y0)) * (y2 * y5);
	} else if (x <= 1.62e+111) {
		tmp = t_1;
	} else if (x <= 1.25e+180) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} 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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	tmp = 0
	if x <= -1.3e+237:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif x <= -2.35e+23:
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * ((a * y1) - (c * y0))))
	elif x <= -1.75e-31:
		tmp = t_1
	elif x <= -2.3e-50:
		tmp = t_2
	elif x <= -4.7e-88:
		tmp = ((t * a) - (k * y0)) * (y2 * y5)
	elif x <= 1.62e+111:
		tmp = t_1
	elif x <= 1.25e+180:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	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(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	tmp = 0.0
	if (x <= -1.3e+237)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (x <= -2.35e+23)
		tmp = Float64(z * Float64(Float64(k * Float64(Float64(b * y0) - Float64(i * y1))) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0)))));
	elseif (x <= -1.75e-31)
		tmp = t_1;
	elseif (x <= -2.3e-50)
		tmp = t_2;
	elseif (x <= -4.7e-88)
		tmp = Float64(Float64(Float64(t * a) - Float64(k * y0)) * Float64(y2 * y5));
	elseif (x <= 1.62e+111)
		tmp = t_1;
	elseif (x <= 1.25e+180)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	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 = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	tmp = 0.0;
	if (x <= -1.3e+237)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (x <= -2.35e+23)
		tmp = z * ((k * ((b * y0) - (i * y1))) + (y3 * ((a * y1) - (c * y0))));
	elseif (x <= -1.75e-31)
		tmp = t_1;
	elseif (x <= -2.3e-50)
		tmp = t_2;
	elseif (x <= -4.7e-88)
		tmp = ((t * a) - (k * y0)) * (y2 * y5);
	elseif (x <= 1.62e+111)
		tmp = t_1;
	elseif (x <= 1.25e+180)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	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[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+237], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.35e+23], N[(z * N[(N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.75e-31], t$95$1, If[LessEqual[x, -2.3e-50], t$95$2, If[LessEqual[x, -4.7e-88], N[(N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision] * N[(y2 * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.62e+111], t$95$1, If[LessEqual[x, 1.25e+180], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.30000000000000001e237

   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 4.5%

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

   4. Taylor expanded in y0 around inf 42.2%

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

      1. mul-1-neg 42.2%

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

   6. Simplified 42.2%

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

   7. Taylor expanded in c around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-*l* 55.9%

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

      4. *-commutative 55.9%

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

   9. Simplified 55.9%

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

   if -1.30000000000000001e237 < x < -2.3499999999999999e23

   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 z around -inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. associate--l+ 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in t around 0 48.7%

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

   if -2.3499999999999999e23 < x < -1.74999999999999993e-31 or -4.7e-88 < x < 1.61999999999999999e111

   1. Initial program 41.5%

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

   3. Simplified 41.5%

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

   4. Taylor expanded in y4 around inf 53.6%

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

   if -1.74999999999999993e-31 < x < -2.3000000000000002e-50 or 1.2499999999999999e180 < x

   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 26.9%

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

   4. Taylor expanded in y0 around inf 43.7%

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

      1. mul-1-neg 43.7%

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

   6. Simplified 43.7%

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

   7. Taylor expanded in b around inf 65.3%

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

   if -2.3000000000000002e-50 < x < -4.7e-88

   1. Initial program 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in y5 around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. mul-1-neg 99.5%

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

      3. mul-1-neg 99.5%

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

      4. sub-neg 99.5%

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

      5. sub-neg 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in y2 around inf 52.1%

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

   if 1.61999999999999999e111 < x < 1.2499999999999999e180

   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 y around inf 50.4%

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

      1. associate--l+ 50.4%

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

      2. mul-1-neg 50.4%

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

      3. mul-1-neg 50.4%

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

   6. Simplified 50.4%

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

   7. Taylor expanded in c around inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. *-commutative 64.5%

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

      3. mul-1-neg 64.5%

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

      4. unsub-neg 64.5%

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

      5. *-commutative 64.5%

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

      6. *-commutative 64.5%

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

   9. Simplified 64.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+237}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-31}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-50}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-88}:\\ \;\;\;\;\left(t \cdot a - k \cdot y0\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{+111}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+180}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 7: 41.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+73}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+179}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          x
          (+
           (+ (* y (- (* a b) (* c i))) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* i y1) (* b y0)))))))
   (if (<= x -5.8e+24)
     t_1
     (if (<= x 2.1e+73)
       (*
        y4
        (+
         (+ (* b (- (* t j) (* y k))) (* y1 (- (* k y2) (* j y3))))
         (* c (- (* y y3) (* t y2)))))
       (if (<= x 1.02e+147)
         t_1
         (if (<= x 8e+179)
           (* (* y c) (- (* y3 y4) (* x i)))
           (* y0 (* b (- (* z k) (* x 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 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -5.8e+24) {
		tmp = t_1;
	} else if (x <= 2.1e+73) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 1.02e+147) {
		tmp = t_1;
	} else if (x <= 8e+179) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else {
		tmp = y0 * (b * ((z * k) - (x * 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) :: tmp
    t_1 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
    if (x <= (-5.8d+24)) then
        tmp = t_1
    else if (x <= 2.1d+73) then
        tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
    else if (x <= 1.02d+147) then
        tmp = t_1
    else if (x <= 8d+179) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    else
        tmp = y0 * (b * ((z * k) - (x * 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 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	double tmp;
	if (x <= -5.8e+24) {
		tmp = t_1;
	} else if (x <= 2.1e+73) {
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	} else if (x <= 1.02e+147) {
		tmp = t_1;
	} else if (x <= 8e+179) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else {
		tmp = y0 * (b * ((z * k) - (x * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))))
	tmp = 0
	if x <= -5.8e+24:
		tmp = t_1
	elif x <= 2.1e+73:
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))))
	elif x <= 1.02e+147:
		tmp = t_1
	elif x <= 8e+179:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	else:
		tmp = y0 * (b * ((z * k) - (x * 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(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 (x <= -5.8e+24)
		tmp = t_1;
	elseif (x <= 2.1e+73)
		tmp = Float64(y4 * Float64(Float64(Float64(b * Float64(Float64(t * j) - Float64(y * k))) + Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) + Float64(c * Float64(Float64(y * y3) - Float64(t * y2)))));
	elseif (x <= 1.02e+147)
		tmp = t_1;
	elseif (x <= 8e+179)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	else
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * 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 = x * (((y * ((a * b) - (c * i))) + (y2 * ((c * y0) - (a * y1)))) + (j * ((i * y1) - (b * y0))));
	tmp = 0.0;
	if (x <= -5.8e+24)
		tmp = t_1;
	elseif (x <= 2.1e+73)
		tmp = y4 * (((b * ((t * j) - (y * k))) + (y1 * ((k * y2) - (j * y3)))) + (c * ((y * y3) - (t * y2))));
	elseif (x <= 1.02e+147)
		tmp = t_1;
	elseif (x <= 8e+179)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	else
		tmp = y0 * (b * ((z * k) - (x * 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[(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[x, -5.8e+24], t$95$1, If[LessEqual[x, 2.1e+73], N[(y4 * N[(N[(N[(b * N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(y * y3), $MachinePrecision] - N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+147], t$95$1, If[LessEqual[x, 8e+179], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.79999999999999958e24 or 2.1000000000000001e73 < x < 1.0199999999999999e147

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   4. Taylor expanded in x around inf 57.1%

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

   if -5.79999999999999958e24 < x < 2.1000000000000001e73

   1. Initial program 43.4%

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

   3. Simplified 43.4%

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

   4. Taylor expanded in y4 around inf 52.1%

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

   if 1.0199999999999999e147 < x < 7.99999999999999984e179

   1. Initial program 30.8%

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

   3. Simplified 30.8%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. associate--l+ 61.7%

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

      2. mul-1-neg 61.7%

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

      3. mul-1-neg 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in c around inf 77.7%

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

      1. associate-*r* 77.7%

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

      2. *-commutative 77.7%

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

      3. mul-1-neg 77.7%

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

      4. unsub-neg 77.7%

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

      5. *-commutative 77.7%

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

      6. *-commutative 77.7%

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

   9. Simplified 77.7%

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

   if 7.99999999999999984e179 < x

   1. Initial program 19.3%

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

   3. Simplified 22.5%

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

   4. Taylor expanded in y0 around inf 45.5%

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

      1. mul-1-neg 45.5%

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

   6. Simplified 45.5%

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

   7. Taylor expanded in b around inf 68.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+73}:\\ \;\;\;\;y4 \cdot \left(\left(b \cdot \left(t \cdot j - y \cdot k\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(y \cdot y3 - t \cdot y2\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) + j \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+179}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 8: 30.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_2 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ t_3 := y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.95 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-275}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-266}:\\ \;\;\;\;\left(t \cdot a - k \cdot y0\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-187}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-106}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 0.102:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+220}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* z (- (* b y0) (* i y1)))))
        (t_2 (* a (* b (- (* x y) (* z t)))))
        (t_3 (* y0 (* x (- (* c y2) (* b j))))))
   (if (<= b -1.95e+96)
     t_2
     (if (<= b -3.5e+69)
       t_1
       (if (<= b -3.9e-54)
         t_3
         (if (<= b -9e-275)
           (* (* a y1) (- (* z y3) (* x y2)))
           (if (<= b 1.05e-266)
             (* (- (* t a) (* k y0)) (* y2 y5))
             (if (<= b 1.4e-187)
               (* (* y c) (- (* y3 y4) (* x i)))
               (if (<= b 1.85e-106)
                 (* i (* y5 (- (* y k) (* t j))))
                 (if (<= b 0.102)
                   (* y (* a (- (* x b) (* y3 y5))))
                   (if (<= b 9.2e+107)
                     (* z (* y3 (- (* a y1) (* c y0))))
                     (if (<= b 2.85e+200)
                       t_3
                       (if (<= b 1.5e+220) t_1 t_2)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (z * ((b * y0) - (i * y1)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double t_3 = y0 * (x * ((c * y2) - (b * j)));
	double tmp;
	if (b <= -1.95e+96) {
		tmp = t_2;
	} else if (b <= -3.5e+69) {
		tmp = t_1;
	} else if (b <= -3.9e-54) {
		tmp = t_3;
	} else if (b <= -9e-275) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 1.05e-266) {
		tmp = ((t * a) - (k * y0)) * (y2 * y5);
	} else if (b <= 1.4e-187) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (b <= 1.85e-106) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (b <= 0.102) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (b <= 9.2e+107) {
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	} else if (b <= 2.85e+200) {
		tmp = t_3;
	} else if (b <= 1.5e+220) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * (z * ((b * y0) - (i * y1)))
    t_2 = a * (b * ((x * y) - (z * t)))
    t_3 = y0 * (x * ((c * y2) - (b * j)))
    if (b <= (-1.95d+96)) then
        tmp = t_2
    else if (b <= (-3.5d+69)) then
        tmp = t_1
    else if (b <= (-3.9d-54)) then
        tmp = t_3
    else if (b <= (-9d-275)) then
        tmp = (a * y1) * ((z * y3) - (x * y2))
    else if (b <= 1.05d-266) then
        tmp = ((t * a) - (k * y0)) * (y2 * y5)
    else if (b <= 1.4d-187) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    else if (b <= 1.85d-106) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (b <= 0.102d0) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (b <= 9.2d+107) then
        tmp = z * (y3 * ((a * y1) - (c * y0)))
    else if (b <= 2.85d+200) then
        tmp = t_3
    else if (b <= 1.5d+220) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (z * ((b * y0) - (i * y1)));
	double t_2 = a * (b * ((x * y) - (z * t)));
	double t_3 = y0 * (x * ((c * y2) - (b * j)));
	double tmp;
	if (b <= -1.95e+96) {
		tmp = t_2;
	} else if (b <= -3.5e+69) {
		tmp = t_1;
	} else if (b <= -3.9e-54) {
		tmp = t_3;
	} else if (b <= -9e-275) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (b <= 1.05e-266) {
		tmp = ((t * a) - (k * y0)) * (y2 * y5);
	} else if (b <= 1.4e-187) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else if (b <= 1.85e-106) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (b <= 0.102) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (b <= 9.2e+107) {
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	} else if (b <= 2.85e+200) {
		tmp = t_3;
	} else if (b <= 1.5e+220) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (z * ((b * y0) - (i * y1)))
	t_2 = a * (b * ((x * y) - (z * t)))
	t_3 = y0 * (x * ((c * y2) - (b * j)))
	tmp = 0
	if b <= -1.95e+96:
		tmp = t_2
	elif b <= -3.5e+69:
		tmp = t_1
	elif b <= -3.9e-54:
		tmp = t_3
	elif b <= -9e-275:
		tmp = (a * y1) * ((z * y3) - (x * y2))
	elif b <= 1.05e-266:
		tmp = ((t * a) - (k * y0)) * (y2 * y5)
	elif b <= 1.4e-187:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	elif b <= 1.85e-106:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif b <= 0.102:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif b <= 9.2e+107:
		tmp = z * (y3 * ((a * y1) - (c * y0)))
	elif b <= 2.85e+200:
		tmp = t_3
	elif b <= 1.5e+220:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))))
	t_2 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	t_3 = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))))
	tmp = 0.0
	if (b <= -1.95e+96)
		tmp = t_2;
	elseif (b <= -3.5e+69)
		tmp = t_1;
	elseif (b <= -3.9e-54)
		tmp = t_3;
	elseif (b <= -9e-275)
		tmp = Float64(Float64(a * y1) * Float64(Float64(z * y3) - Float64(x * y2)));
	elseif (b <= 1.05e-266)
		tmp = Float64(Float64(Float64(t * a) - Float64(k * y0)) * Float64(y2 * y5));
	elseif (b <= 1.4e-187)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	elseif (b <= 1.85e-106)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (b <= 0.102)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (b <= 9.2e+107)
		tmp = Float64(z * Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))));
	elseif (b <= 2.85e+200)
		tmp = t_3;
	elseif (b <= 1.5e+220)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (z * ((b * y0) - (i * y1)));
	t_2 = a * (b * ((x * y) - (z * t)));
	t_3 = y0 * (x * ((c * y2) - (b * j)));
	tmp = 0.0;
	if (b <= -1.95e+96)
		tmp = t_2;
	elseif (b <= -3.5e+69)
		tmp = t_1;
	elseif (b <= -3.9e-54)
		tmp = t_3;
	elseif (b <= -9e-275)
		tmp = (a * y1) * ((z * y3) - (x * y2));
	elseif (b <= 1.05e-266)
		tmp = ((t * a) - (k * y0)) * (y2 * y5);
	elseif (b <= 1.4e-187)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	elseif (b <= 1.85e-106)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (b <= 0.102)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (b <= 9.2e+107)
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	elseif (b <= 2.85e+200)
		tmp = t_3;
	elseif (b <= 1.5e+220)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.95e+96], t$95$2, If[LessEqual[b, -3.5e+69], t$95$1, If[LessEqual[b, -3.9e-54], t$95$3, If[LessEqual[b, -9e-275], N[(N[(a * y1), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-266], N[(N[(N[(t * a), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision] * N[(y2 * y5), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-187], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e-106], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.102], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+107], N[(z * N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.85e+200], t$95$3, If[LessEqual[b, 1.5e+220], t$95$1, t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -1.95e96 or 1.50000000000000012e220 < b

   1. Initial program 19.0%

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

   3. Simplified 20.6%

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

   4. Taylor expanded in a around inf 43.4%

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

      1. mul-1-neg 43.4%

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

      2. mul-1-neg 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in b around inf 59.3%

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

   if -1.95e96 < b < -3.49999999999999987e69 or 2.85000000000000003e200 < b < 1.50000000000000012e220

   1. Initial program 28.5%

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

   3. Simplified 28.5%

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

   4. Taylor expanded in z around -inf 35.3%

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

      1. mul-1-neg 35.3%

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

      2. associate--l+ 35.3%

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

   6. Simplified 35.3%

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

   7. Taylor expanded in k around inf 78.4%

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

   if -3.49999999999999987e69 < b < -3.9e-54 or 9.2000000000000001e107 < b < 2.85000000000000003e200

   1. Initial program 40.5%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in y0 around inf 55.0%

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

      1. mul-1-neg 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in x around -inf 63.1%

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

      1. mul-1-neg 63.1%

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

      2. *-commutative 63.1%

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

      3. +-commutative 63.1%

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

      4. distribute-rgt-neg-in 63.1%

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

      5. +-commutative 63.1%

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

      6. *-commutative 63.1%

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

      7. distribute-rgt-neg-in 63.1%

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

      8. +-commutative 63.1%

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

      9. mul-1-neg 63.1%

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

      10. unsub-neg 63.1%

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

   9. Simplified 63.1%

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

   if -3.9e-54 < b < -8.99999999999999957e-275

   1. Initial program 34.5%

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

   3. Simplified 42.4%

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

   4. Taylor expanded in a around inf 37.9%

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

      1. mul-1-neg 37.9%

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

      2. mul-1-neg 37.9%

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

   6. Simplified 37.9%

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

   7. Taylor expanded in y1 around inf 41.0%

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

      1. associate-*r* 46.0%

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

      2. *-commutative 46.0%

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

      3. *-commutative 46.0%

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

   9. Simplified 46.0%

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

   if -8.99999999999999957e-275 < b < 1.04999999999999998e-266

   1. Initial program 22.5%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in y5 around inf 34.6%

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

      1. mul-1-neg 34.6%

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

      2. mul-1-neg 34.6%

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

      3. mul-1-neg 34.6%

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

      4. sub-neg 34.6%

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

      5. sub-neg 34.6%

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

   6. Simplified 34.6%

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

   7. Taylor expanded in y2 around inf 50.8%

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

   if 1.04999999999999998e-266 < b < 1.4e-187

   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 y around inf 22.8%

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

      1. associate--l+ 22.8%

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

      2. mul-1-neg 22.8%

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

      3. mul-1-neg 22.8%

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

   6. Simplified 22.8%

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

   7. Taylor expanded in c around inf 78.2%

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

      1. associate-*r* 78.2%

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

      2. *-commutative 78.2%

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

      3. mul-1-neg 78.2%

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

      4. unsub-neg 78.2%

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

      5. *-commutative 78.2%

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

      6. *-commutative 78.2%

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

   9. Simplified 78.2%

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

   if 1.4e-187 < b < 1.8499999999999999e-106

   1. Initial program 47.0%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in y5 around inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. mul-1-neg 47.0%

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

      3. mul-1-neg 47.0%

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

      4. sub-neg 47.0%

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

      5. sub-neg 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in i around inf 54.6%

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

   if 1.8499999999999999e-106 < b < 0.101999999999999993

   1. Initial program 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in a around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. mul-1-neg 50.4%

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

   6. Simplified 50.4%

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

   7. Taylor expanded in y around inf 42.7%

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

      1. associate-*r* 42.7%

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

      2. *-commutative 42.7%

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

      3. associate-*r* 50.7%

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

      4. +-commutative 50.7%

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

      5. mul-1-neg 50.7%

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

      6. unsub-neg 50.7%

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

   9. Simplified 50.7%

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

   if 0.101999999999999993 < b < 9.2000000000000001e107

   1. Initial program 39.1%

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

   3. Simplified 39.1%

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

   4. Taylor expanded in z around -inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate--l+ 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in t around 0 44.5%

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

   8. Taylor expanded in y3 around inf 45.4%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - y1 \cdot a\right) \cdot y3\right)} \cdot z \]
3. Recombined 9 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+69}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-275}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-266}:\\ \;\;\;\;\left(t \cdot a - k \cdot y0\right) \cdot \left(y2 \cdot y5\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-187}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-106}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 0.102:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+200}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+220}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 34.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y0 - i \cdot y1\\ t_2 := z \cdot \left(k \cdot t_1 + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-49}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-264}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+25}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+67}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(t \cdot b - y1 \cdot y3\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+192}:\\ \;\;\;\;k \cdot \left(z \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* b y0) (* i y1)))
        (t_2 (* z (+ (* k t_1) (* y3 (- (* a y1) (* c y0)))))))
   (if (<= z -2.15e-30)
     t_2
     (if (<= z -1.06e-49)
       (* k (* y (- (* i y5) (* b y4))))
       (if (<= z -2.35e-133)
         t_2
         (if (<= z 2.9e-264)
           (* y0 (* x (- (* c y2) (* b j))))
           (if (<= z 6e-180)
             (* y (* y4 (- (* c y3) (* b k))))
             (if (<= z 2.5e-43)
               (* x (* a (- (* y b) (* y1 y2))))
               (if (<= z 5.4e+25)
                 (* y0 (* y3 (- (* j y5) (* z c))))
                 (if (<= z 4.8e+67)
                   (* (* j y4) (- (* t b) (* y1 y3)))
                   (if (<= z 5.2e+116)
                     (* i (* y5 (- (* y k) (* t j))))
                     (if (<= z 1.55e+192)
                       (* k (* z t_1))
                       (* t (* z (- (* c i) (* a b))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y0) - (i * y1);
	double t_2 = z * ((k * t_1) + (y3 * ((a * y1) - (c * y0))));
	double tmp;
	if (z <= -2.15e-30) {
		tmp = t_2;
	} else if (z <= -1.06e-49) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (z <= -2.35e-133) {
		tmp = t_2;
	} else if (z <= 2.9e-264) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (z <= 6e-180) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 2.5e-43) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (z <= 5.4e+25) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (z <= 4.8e+67) {
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	} else if (z <= 5.2e+116) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (z <= 1.55e+192) {
		tmp = k * (z * t_1);
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * y0) - (i * y1)
    t_2 = z * ((k * t_1) + (y3 * ((a * y1) - (c * y0))))
    if (z <= (-2.15d-30)) then
        tmp = t_2
    else if (z <= (-1.06d-49)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (z <= (-2.35d-133)) then
        tmp = t_2
    else if (z <= 2.9d-264) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (z <= 6d-180) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (z <= 2.5d-43) then
        tmp = x * (a * ((y * b) - (y1 * y2)))
    else if (z <= 5.4d+25) then
        tmp = y0 * (y3 * ((j * y5) - (z * c)))
    else if (z <= 4.8d+67) then
        tmp = (j * y4) * ((t * b) - (y1 * y3))
    else if (z <= 5.2d+116) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (z <= 1.55d+192) then
        tmp = k * (z * t_1)
    else
        tmp = t * (z * ((c * i) - (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (b * y0) - (i * y1);
	double t_2 = z * ((k * t_1) + (y3 * ((a * y1) - (c * y0))));
	double tmp;
	if (z <= -2.15e-30) {
		tmp = t_2;
	} else if (z <= -1.06e-49) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (z <= -2.35e-133) {
		tmp = t_2;
	} else if (z <= 2.9e-264) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (z <= 6e-180) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 2.5e-43) {
		tmp = x * (a * ((y * b) - (y1 * y2)));
	} else if (z <= 5.4e+25) {
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	} else if (z <= 4.8e+67) {
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	} else if (z <= 5.2e+116) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (z <= 1.55e+192) {
		tmp = k * (z * t_1);
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = (b * y0) - (i * y1)
	t_2 = z * ((k * t_1) + (y3 * ((a * y1) - (c * y0))))
	tmp = 0
	if z <= -2.15e-30:
		tmp = t_2
	elif z <= -1.06e-49:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif z <= -2.35e-133:
		tmp = t_2
	elif z <= 2.9e-264:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif z <= 6e-180:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif z <= 2.5e-43:
		tmp = x * (a * ((y * b) - (y1 * y2)))
	elif z <= 5.4e+25:
		tmp = y0 * (y3 * ((j * y5) - (z * c)))
	elif z <= 4.8e+67:
		tmp = (j * y4) * ((t * b) - (y1 * y3))
	elif z <= 5.2e+116:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif z <= 1.55e+192:
		tmp = k * (z * t_1)
	else:
		tmp = t * (z * ((c * i) - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(b * y0) - Float64(i * y1))
	t_2 = Float64(z * Float64(Float64(k * t_1) + Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0)))))
	tmp = 0.0
	if (z <= -2.15e-30)
		tmp = t_2;
	elseif (z <= -1.06e-49)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (z <= -2.35e-133)
		tmp = t_2;
	elseif (z <= 2.9e-264)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (z <= 6e-180)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (z <= 2.5e-43)
		tmp = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))));
	elseif (z <= 5.4e+25)
		tmp = Float64(y0 * Float64(y3 * Float64(Float64(j * y5) - Float64(z * c))));
	elseif (z <= 4.8e+67)
		tmp = Float64(Float64(j * y4) * Float64(Float64(t * b) - Float64(y1 * y3)));
	elseif (z <= 5.2e+116)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (z <= 1.55e+192)
		tmp = Float64(k * Float64(z * t_1));
	else
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = (b * y0) - (i * y1);
	t_2 = z * ((k * t_1) + (y3 * ((a * y1) - (c * y0))));
	tmp = 0.0;
	if (z <= -2.15e-30)
		tmp = t_2;
	elseif (z <= -1.06e-49)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (z <= -2.35e-133)
		tmp = t_2;
	elseif (z <= 2.9e-264)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (z <= 6e-180)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (z <= 2.5e-43)
		tmp = x * (a * ((y * b) - (y1 * y2)));
	elseif (z <= 5.4e+25)
		tmp = y0 * (y3 * ((j * y5) - (z * c)));
	elseif (z <= 4.8e+67)
		tmp = (j * y4) * ((t * b) - (y1 * y3));
	elseif (z <= 5.2e+116)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (z <= 1.55e+192)
		tmp = k * (z * t_1);
	else
		tmp = t * (z * ((c * i) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(k * t$95$1), $MachinePrecision] + N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e-30], t$95$2, If[LessEqual[z, -1.06e-49], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-133], t$95$2, If[LessEqual[z, 2.9e-264], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-180], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-43], N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+25], N[(y0 * N[(y3 * N[(N[(j * y5), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+67], N[(N[(j * y4), $MachinePrecision] * N[(N[(t * b), $MachinePrecision] - N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+116], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+192], N[(k * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if z < -2.14999999999999983e-30 or -1.06000000000000002e-49 < z < -2.35000000000000001e-133

   1. Initial program 27.8%

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

   3. Simplified 27.8%

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

   4. Taylor expanded in z around -inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate--l+ 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in t around 0 57.2%

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

   if -2.14999999999999983e-30 < z < -1.06000000000000002e-49

   1. Initial program 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in y around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. mul-1-neg 63.0%

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

      3. mul-1-neg 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in k around inf 63.1%

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

   if -2.35000000000000001e-133 < z < 2.8999999999999999e-264

   1. Initial program 45.4%

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

   3. Simplified 49.1%

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

   4. Taylor expanded in y0 around inf 50.0%

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

      1. mul-1-neg 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in x around -inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. +-commutative 44.8%

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

      4. distribute-rgt-neg-in 44.8%

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

      5. +-commutative 44.8%

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

      6. *-commutative 44.8%

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

      7. distribute-rgt-neg-in 44.8%

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

      8. +-commutative 44.8%

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

      9. mul-1-neg 44.8%

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

      10. unsub-neg 44.8%

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

   9. Simplified 44.8%

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

   if 2.8999999999999999e-264 < z < 6.0000000000000001e-180

   1. Initial program 47.3%

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

   3. Simplified 47.3%

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

   4. Taylor expanded in y around inf 47.4%

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

      1. associate--l+ 47.4%

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

      2. mul-1-neg 47.4%

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

      3. mul-1-neg 47.4%

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

   6. Simplified 47.4%

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

   7. Taylor expanded in y4 around inf 53.8%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 53.8%

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

      2. *-commutative 53.8%

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

   9. Simplified 53.8%

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

   if 6.0000000000000001e-180 < z < 2.50000000000000009e-43

   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%

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

   4. Taylor expanded in a around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. mul-1-neg 50.4%

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

   6. Simplified 50.4%

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

   7. Taylor expanded in x around -inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. associate-*r* 56.4%

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

      3. distribute-lft-out-- 56.4%

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

      4. *-commutative 56.4%

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

      5. *-commutative 56.4%

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

   9. Simplified 56.4%

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

   if 2.50000000000000009e-43 < z < 5.4e25

   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 35.7%

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

   4. Taylor expanded in y0 around inf 36.5%

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

      1. mul-1-neg 36.5%

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

   6. Simplified 36.5%

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

   7. Taylor expanded in y3 around inf 58.1%

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

      1. distribute-lft-out-- 58.1%

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

      2. associate-*r* 58.1%

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

      3. mul-1-neg 58.1%

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

      4. *-commutative 58.1%

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

   9. Simplified 58.1%

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

   if 5.4e25 < z < 4.80000000000000004e67

   1. Initial program 26.6%

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

   3. Simplified 26.6%

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

   4. Taylor expanded in y4 around inf 75.9%

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

   5. Taylor expanded in j around inf 75.9%

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

      1. associate-*r* 75.9%

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

      2. mul-1-neg 75.9%

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

      3. sub-neg 75.9%

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

      4. *-commutative 75.9%

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

      5. *-commutative 75.9%

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

   7. Simplified 75.9%

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

   if 4.80000000000000004e67 < z < 5.19999999999999973e116

   1. Initial program 8.3%

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

   3. Simplified 8.3%

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

   4. Taylor expanded in y5 around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. mul-1-neg 59.8%

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

      3. mul-1-neg 59.8%

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

      4. sub-neg 59.8%

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

      5. sub-neg 59.8%

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

   6. Simplified 59.8%

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

   7. Taylor expanded in i around inf 60.2%

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

   if 5.19999999999999973e116 < z < 1.5499999999999999e192

   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 47.4%

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

      1. mul-1-neg 47.4%

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

      2. associate--l+ 47.4%

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

   6. Simplified 47.4%

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

   7. Taylor expanded in k around inf 73.8%

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

   if 1.5499999999999999e192 < z

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in z around -inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. associate--l+ 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in t around inf 63.1%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-49}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-133}:\\ \;\;\;\;z \cdot \left(k \cdot \left(b \cdot y0 - i \cdot y1\right) + y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-264}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+25}:\\ \;\;\;\;y0 \cdot \left(y3 \cdot \left(j \cdot y5 - z \cdot c\right)\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+67}:\\ \;\;\;\;\left(j \cdot y4\right) \cdot \left(t \cdot b - y1 \cdot y3\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+192}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]

Alternative 10: 30.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_2 := k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{if}\;y0 \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -0.1:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-16}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{-91}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 4.3 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{-105}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{+27}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y0 (* b (- (* z k) (* x j)))))
        (t_2 (* k (* y (- (* i y5) (* b y4))))))
   (if (<= y0 -6.8e+80)
     t_1
     (if (<= y0 -0.1)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y0 -5e-16)
         (* k (* i (* y y5)))
         (if (<= y0 -3.8e-91)
           (* (* a y1) (- (* z y3) (* x y2)))
           (if (<= y0 -1.65e-270)
             t_2
             (if (<= y0 5.8e-267)
               (* t (* z (- (* c i) (* a b))))
               (if (<= y0 4.3e-192)
                 t_2
                 (if (<= y0 1.8e-105)
                   (* (* y1 y4) (- (* k y2) (* j y3)))
                   (if (<= y0 2.05e+27)
                     (* (* y c) (- (* y3 y4) (* x i)))
                     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 * (b * ((z * k) - (x * j)));
	double t_2 = k * (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y0 <= -6.8e+80) {
		tmp = t_1;
	} else if (y0 <= -0.1) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y0 <= -5e-16) {
		tmp = k * (i * (y * y5));
	} else if (y0 <= -3.8e-91) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (y0 <= -1.65e-270) {
		tmp = t_2;
	} else if (y0 <= 5.8e-267) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y0 <= 4.3e-192) {
		tmp = t_2;
	} else if (y0 <= 1.8e-105) {
		tmp = (y1 * y4) * ((k * y2) - (j * y3));
	} else if (y0 <= 2.05e+27) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} 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 * (b * ((z * k) - (x * j)))
    t_2 = k * (y * ((i * y5) - (b * y4)))
    if (y0 <= (-6.8d+80)) then
        tmp = t_1
    else if (y0 <= (-0.1d0)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y0 <= (-5d-16)) then
        tmp = k * (i * (y * y5))
    else if (y0 <= (-3.8d-91)) then
        tmp = (a * y1) * ((z * y3) - (x * y2))
    else if (y0 <= (-1.65d-270)) then
        tmp = t_2
    else if (y0 <= 5.8d-267) then
        tmp = t * (z * ((c * i) - (a * b)))
    else if (y0 <= 4.3d-192) then
        tmp = t_2
    else if (y0 <= 1.8d-105) then
        tmp = (y1 * y4) * ((k * y2) - (j * y3))
    else if (y0 <= 2.05d+27) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    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 * (b * ((z * k) - (x * j)));
	double t_2 = k * (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y0 <= -6.8e+80) {
		tmp = t_1;
	} else if (y0 <= -0.1) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y0 <= -5e-16) {
		tmp = k * (i * (y * y5));
	} else if (y0 <= -3.8e-91) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (y0 <= -1.65e-270) {
		tmp = t_2;
	} else if (y0 <= 5.8e-267) {
		tmp = t * (z * ((c * i) - (a * b)));
	} else if (y0 <= 4.3e-192) {
		tmp = t_2;
	} else if (y0 <= 1.8e-105) {
		tmp = (y1 * y4) * ((k * y2) - (j * y3));
	} else if (y0 <= 2.05e+27) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} 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 * (b * ((z * k) - (x * j)))
	t_2 = k * (y * ((i * y5) - (b * y4)))
	tmp = 0
	if y0 <= -6.8e+80:
		tmp = t_1
	elif y0 <= -0.1:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y0 <= -5e-16:
		tmp = k * (i * (y * y5))
	elif y0 <= -3.8e-91:
		tmp = (a * y1) * ((z * y3) - (x * y2))
	elif y0 <= -1.65e-270:
		tmp = t_2
	elif y0 <= 5.8e-267:
		tmp = t * (z * ((c * i) - (a * b)))
	elif y0 <= 4.3e-192:
		tmp = t_2
	elif y0 <= 1.8e-105:
		tmp = (y1 * y4) * ((k * y2) - (j * y3))
	elif y0 <= 2.05e+27:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	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(b * Float64(Float64(z * k) - Float64(x * j))))
	t_2 = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))))
	tmp = 0.0
	if (y0 <= -6.8e+80)
		tmp = t_1;
	elseif (y0 <= -0.1)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y0 <= -5e-16)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	elseif (y0 <= -3.8e-91)
		tmp = Float64(Float64(a * y1) * Float64(Float64(z * y3) - Float64(x * y2)));
	elseif (y0 <= -1.65e-270)
		tmp = t_2;
	elseif (y0 <= 5.8e-267)
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	elseif (y0 <= 4.3e-192)
		tmp = t_2;
	elseif (y0 <= 1.8e-105)
		tmp = Float64(Float64(y1 * y4) * Float64(Float64(k * y2) - Float64(j * y3)));
	elseif (y0 <= 2.05e+27)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	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 * (b * ((z * k) - (x * j)));
	t_2 = k * (y * ((i * y5) - (b * y4)));
	tmp = 0.0;
	if (y0 <= -6.8e+80)
		tmp = t_1;
	elseif (y0 <= -0.1)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y0 <= -5e-16)
		tmp = k * (i * (y * y5));
	elseif (y0 <= -3.8e-91)
		tmp = (a * y1) * ((z * y3) - (x * y2));
	elseif (y0 <= -1.65e-270)
		tmp = t_2;
	elseif (y0 <= 5.8e-267)
		tmp = t * (z * ((c * i) - (a * b)));
	elseif (y0 <= 4.3e-192)
		tmp = t_2;
	elseif (y0 <= 1.8e-105)
		tmp = (y1 * y4) * ((k * y2) - (j * y3));
	elseif (y0 <= 2.05e+27)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	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[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -6.8e+80], t$95$1, If[LessEqual[y0, -0.1], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5e-16], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.8e-91], N[(N[(a * y1), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -1.65e-270], t$95$2, If[LessEqual[y0, 5.8e-267], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4.3e-192], t$95$2, If[LessEqual[y0, 1.8e-105], N[(N[(y1 * y4), $MachinePrecision] * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.05e+27], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y0 < -6.79999999999999984e80 or 2.0500000000000001e27 < y0

   1. Initial program 22.4%

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

   3. Simplified 26.7%

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

   4. Taylor expanded in y0 around inf 52.1%

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

      1. mul-1-neg 52.1%

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

   6. Simplified 52.1%

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

   7. Taylor expanded in b around inf 48.7%

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

   if -6.79999999999999984e80 < y0 < -0.10000000000000001

   1. Initial program 45.5%

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

   3. Simplified 45.5%

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

   4. Taylor expanded in a around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. mul-1-neg 50.9%

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

   6. Simplified 50.9%

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

   7. Taylor expanded in b around inf 55.4%

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

   if -0.10000000000000001 < y0 < -5.0000000000000004e-16

   1. Initial program 33.7%

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

   3. Simplified 33.7%

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

   4. Taylor expanded in y5 around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. mul-1-neg 51.1%

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

      3. mul-1-neg 51.1%

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

      4. sub-neg 51.1%

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

      5. sub-neg 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in k around inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. neg-mul-1 67.6%

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

      3. *-commutative 67.6%

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

      4. +-commutative 67.6%

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

      5. mul-1-neg 67.6%

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

      6. unsub-neg 67.6%

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

      7. *-commutative 67.6%

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

   9. Simplified 67.6%

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

   10. Taylor expanded in i around inf 83.4%

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

   if -5.0000000000000004e-16 < y0 < -3.79999999999999978e-91

   1. Initial program 49.9%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in a around inf 43.8%

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

      1. mul-1-neg 43.8%

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

      2. mul-1-neg 43.8%

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

   6. Simplified 43.8%

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

   7. Taylor expanded in y1 around inf 57.6%

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

      1. associate-*r* 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

   9. Simplified 57.7%

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

   if -3.79999999999999978e-91 < y0 < -1.65000000000000009e-270 or 5.80000000000000043e-267 < y0 < 4.29999999999999999e-192

   1. Initial program 36.8%

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

   3. Simplified 36.8%

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

   4. Taylor expanded in y around inf 46.0%

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

      1. associate--l+ 46.0%

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

      2. mul-1-neg 46.0%

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

      3. mul-1-neg 46.0%

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

   6. Simplified 46.0%

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

   7. Taylor expanded in k around inf 51.7%

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

   if -1.65000000000000009e-270 < y0 < 5.80000000000000043e-267

   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 z around -inf 45.2%

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

      1. mul-1-neg 45.2%

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

      2. associate--l+ 45.2%

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

   6. Simplified 45.2%

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

   7. Taylor expanded in t around inf 50.8%

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

   if 4.29999999999999999e-192 < y0 < 1.79999999999999982e-105

   1. Initial program 41.7%

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

   3. Simplified 41.7%

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

   4. Taylor expanded in y4 around inf 58.8%

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

   5. Taylor expanded in y1 around inf 67.4%

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

      1. associate-*r* 67.5%

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

      2. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   if 1.79999999999999982e-105 < y0 < 2.0500000000000001e27

   1. Initial program 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in y around inf 42.6%

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

      1. associate--l+ 42.6%

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

      2. mul-1-neg 42.6%

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

      3. mul-1-neg 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in c around inf 55.7%

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

      1. associate-*r* 46.4%

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

      2. *-commutative 46.4%

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

      3. mul-1-neg 46.4%

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

      4. unsub-neg 46.4%

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

      5. *-commutative 46.4%

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

      6. *-commutative 46.4%

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

   9. Simplified 46.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -0.1:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq -5 \cdot 10^{-16}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -3.8 \cdot 10^{-91}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;y0 \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 5.8 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \mathbf{elif}\;y0 \leq 4.3 \cdot 10^{-192}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.8 \cdot 10^{-105}:\\ \;\;\;\;\left(y1 \cdot y4\right) \cdot \left(k \cdot y2 - j \cdot y3\right)\\ \mathbf{elif}\;y0 \leq 2.05 \cdot 10^{+27}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 11: 33.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) - k \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-93}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-264}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+97}:\\ \;\;\;\;\left(b \cdot j - c \cdot y2\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+192}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* x (* a (- (* y b) (* y1 y2))))))
   (if (<= z -3.8e-30)
     (* z (- (* y3 (- (* a y1) (* c y0))) (* k (* i y1))))
     (if (<= z -1.62e-93)
       (* k (* y (- (* i y5) (* b y4))))
       (if (<= z -1.8e-132)
         (* y0 (* b (- (* z k) (* x j))))
         (if (<= z -2.4e-196)
           t_1
           (if (<= z 1.8e-264)
             (* y0 (* x (- (* c y2) (* b j))))
             (if (<= z 5.4e-181)
               (* y (* y4 (- (* c y3) (* b k))))
               (if (<= z 1.65e-26)
                 t_1
                 (if (<= z 1.6e+97)
                   (* (- (* b j) (* c y2)) (* t y4))
                   (if (<= z 3.9e+192)
                     (* k (* z (- (* b y0) (* i y1))))
                     (* t (* z (- (* c i) (* a b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (a * ((y * b) - (y1 * y2)));
	double tmp;
	if (z <= -3.8e-30) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (k * (i * y1)));
	} else if (z <= -1.62e-93) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (z <= -1.8e-132) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (z <= -2.4e-196) {
		tmp = t_1;
	} else if (z <= 1.8e-264) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (z <= 5.4e-181) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 1.65e-26) {
		tmp = t_1;
	} else if (z <= 1.6e+97) {
		tmp = ((b * j) - (c * y2)) * (t * y4);
	} else if (z <= 3.9e+192) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (a * ((y * b) - (y1 * y2)))
    if (z <= (-3.8d-30)) then
        tmp = z * ((y3 * ((a * y1) - (c * y0))) - (k * (i * y1)))
    else if (z <= (-1.62d-93)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (z <= (-1.8d-132)) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (z <= (-2.4d-196)) then
        tmp = t_1
    else if (z <= 1.8d-264) then
        tmp = y0 * (x * ((c * y2) - (b * j)))
    else if (z <= 5.4d-181) then
        tmp = y * (y4 * ((c * y3) - (b * k)))
    else if (z <= 1.65d-26) then
        tmp = t_1
    else if (z <= 1.6d+97) then
        tmp = ((b * j) - (c * y2)) * (t * y4)
    else if (z <= 3.9d+192) then
        tmp = k * (z * ((b * y0) - (i * y1)))
    else
        tmp = t * (z * ((c * i) - (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = x * (a * ((y * b) - (y1 * y2)));
	double tmp;
	if (z <= -3.8e-30) {
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (k * (i * y1)));
	} else if (z <= -1.62e-93) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (z <= -1.8e-132) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (z <= -2.4e-196) {
		tmp = t_1;
	} else if (z <= 1.8e-264) {
		tmp = y0 * (x * ((c * y2) - (b * j)));
	} else if (z <= 5.4e-181) {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	} else if (z <= 1.65e-26) {
		tmp = t_1;
	} else if (z <= 1.6e+97) {
		tmp = ((b * j) - (c * y2)) * (t * y4);
	} else if (z <= 3.9e+192) {
		tmp = k * (z * ((b * y0) - (i * y1)));
	} else {
		tmp = t * (z * ((c * i) - (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = x * (a * ((y * b) - (y1 * y2)))
	tmp = 0
	if z <= -3.8e-30:
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (k * (i * y1)))
	elif z <= -1.62e-93:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif z <= -1.8e-132:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif z <= -2.4e-196:
		tmp = t_1
	elif z <= 1.8e-264:
		tmp = y0 * (x * ((c * y2) - (b * j)))
	elif z <= 5.4e-181:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	elif z <= 1.65e-26:
		tmp = t_1
	elif z <= 1.6e+97:
		tmp = ((b * j) - (c * y2)) * (t * y4)
	elif z <= 3.9e+192:
		tmp = k * (z * ((b * y0) - (i * y1)))
	else:
		tmp = t * (z * ((c * i) - (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(x * Float64(a * Float64(Float64(y * b) - Float64(y1 * y2))))
	tmp = 0.0
	if (z <= -3.8e-30)
		tmp = Float64(z * Float64(Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))) - Float64(k * Float64(i * y1))));
	elseif (z <= -1.62e-93)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (z <= -1.8e-132)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (z <= -2.4e-196)
		tmp = t_1;
	elseif (z <= 1.8e-264)
		tmp = Float64(y0 * Float64(x * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (z <= 5.4e-181)
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	elseif (z <= 1.65e-26)
		tmp = t_1;
	elseif (z <= 1.6e+97)
		tmp = Float64(Float64(Float64(b * j) - Float64(c * y2)) * Float64(t * y4));
	elseif (z <= 3.9e+192)
		tmp = Float64(k * Float64(z * Float64(Float64(b * y0) - Float64(i * y1))));
	else
		tmp = Float64(t * Float64(z * Float64(Float64(c * i) - Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = x * (a * ((y * b) - (y1 * y2)));
	tmp = 0.0;
	if (z <= -3.8e-30)
		tmp = z * ((y3 * ((a * y1) - (c * y0))) - (k * (i * y1)));
	elseif (z <= -1.62e-93)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (z <= -1.8e-132)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (z <= -2.4e-196)
		tmp = t_1;
	elseif (z <= 1.8e-264)
		tmp = y0 * (x * ((c * y2) - (b * j)));
	elseif (z <= 5.4e-181)
		tmp = y * (y4 * ((c * y3) - (b * k)));
	elseif (z <= 1.65e-26)
		tmp = t_1;
	elseif (z <= 1.6e+97)
		tmp = ((b * j) - (c * y2)) * (t * y4);
	elseif (z <= 3.9e+192)
		tmp = k * (z * ((b * y0) - (i * y1)));
	else
		tmp = t * (z * ((c * i) - (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(x * N[(a * N[(N[(y * b), $MachinePrecision] - N[(y1 * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-30], N[(z * N[(N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.62e-93], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-132], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-196], t$95$1, If[LessEqual[z, 1.8e-264], N[(y0 * N[(x * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-181], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-26], t$95$1, If[LessEqual[z, 1.6e+97], N[(N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision] * N[(t * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+192], N[(k * N[(z * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * N[(N[(c * i), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -3.8000000000000003e-30

   1. Initial program 26.8%

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

   3. Simplified 26.8%

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

   4. Taylor expanded in z around -inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. associate--l+ 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in t around 0 58.3%

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

   8. Taylor expanded in y0 around 0 51.3%

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

      1. mul-1-neg 51.3%

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

   10. Simplified 51.3%

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

   if -3.8000000000000003e-30 < z < -1.6200000000000001e-93

   1. Initial program 46.5%

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

   3. Simplified 46.5%

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

   4. Taylor expanded in y around inf 46.9%

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

      1. associate--l+ 46.9%

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

      2. mul-1-neg 46.9%

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

      3. mul-1-neg 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in k around inf 54.0%

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

   if -1.6200000000000001e-93 < z < -1.80000000000000004e-132

   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%

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

   4. Taylor expanded in y0 around inf 70.0%

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

      1. mul-1-neg 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in b around inf 60.8%

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

   if -1.80000000000000004e-132 < z < -2.40000000000000021e-196 or 5.3999999999999999e-181 < z < 1.6499999999999999e-26

   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 48.9%

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

   4. Taylor expanded in a around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. mul-1-neg 59.6%

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

   6. Simplified 59.6%

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

   7. Taylor expanded in x around -inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. associate-*r* 57.4%

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

      3. distribute-lft-out-- 57.4%

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

      4. *-commutative 57.4%

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

      5. *-commutative 57.4%

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

   9. Simplified 57.4%

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

   if -2.40000000000000021e-196 < z < 1.8000000000000001e-264

   1. Initial program 46.0%

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

   3. Simplified 51.1%

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

   4. Taylor expanded in y0 around inf 57.0%

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

      1. mul-1-neg 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in x around -inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. *-commutative 47.6%

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

      3. +-commutative 47.6%

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

      4. distribute-rgt-neg-in 47.6%

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

      5. +-commutative 47.6%

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

      6. *-commutative 47.6%

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

      7. distribute-rgt-neg-in 47.6%

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

      8. +-commutative 47.6%

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

      9. mul-1-neg 47.6%

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

      10. unsub-neg 47.6%

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

   9. Simplified 47.6%

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

   if 1.8000000000000001e-264 < z < 5.3999999999999999e-181

   1. Initial program 47.3%

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

   3. Simplified 47.3%

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

   4. Taylor expanded in y around inf 47.4%

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

      1. associate--l+ 47.4%

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

      2. mul-1-neg 47.4%

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

      3. mul-1-neg 47.4%

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

   6. Simplified 47.4%

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

   7. Taylor expanded in y4 around inf 53.8%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 53.8%

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

      2. *-commutative 53.8%

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

   9. Simplified 53.8%

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

   if 1.6499999999999999e-26 < z < 1.60000000000000008e97

   1. Initial program 19.2%

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

   3. Simplified 19.2%

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

   4. Taylor expanded in y4 around inf 51.1%

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

   5. Taylor expanded in t around inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. *-commutative 57.1%

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

   7. Simplified 57.1%

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

   if 1.60000000000000008e97 < z < 3.8999999999999998e192

   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 42.9%

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

      1. mul-1-neg 42.9%

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

      2. associate--l+ 42.9%

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

   6. Simplified 42.9%

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

   7. Taylor expanded in k around inf 61.1%

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

   if 3.8999999999999998e192 < z

   1. Initial program 23.8%

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

   3. Simplified 23.8%

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

   4. Taylor expanded in z around -inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. associate--l+ 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in t around inf 63.1%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right) - k \cdot \left(i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-93}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-132}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-264}:\\ \;\;\;\;y0 \cdot \left(x \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot b - y1 \cdot y2\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+97}:\\ \;\;\;\;\left(b \cdot j - c \cdot y2\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+192}:\\ \;\;\;\;k \cdot \left(z \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(c \cdot i - a \cdot b\right)\right)\\ \end{array} \]

Alternative 12: 30.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ t_2 := y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ t_3 := \left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{if}\;y0 \leq -4.8 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y0 \leq -0.345:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y0 \leq -9 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-278}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y0 \leq 3 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y (- (* i y5) (* b y4)))))
        (t_2 (* y0 (* b (- (* z k) (* x j)))))
        (t_3 (* (* a y1) (- (* z y3) (* x y2)))))
   (if (<= y0 -4.8e+80)
     t_2
     (if (<= y0 -0.345)
       (* a (* b (- (* x y) (* z t))))
       (if (<= y0 -2.1e-16)
         (* k (* i (* y y5)))
         (if (<= y0 -3.3e-93)
           t_3
           (if (<= y0 -9e-270)
             t_1
             (if (<= y0 2.3e-278)
               t_3
               (if (<= y0 3e-180)
                 t_1
                 (if (<= y0 1.2e+26)
                   (* (* y c) (- (* y3 y4) (* x i)))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y * ((i * y5) - (b * y4)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = (a * y1) * ((z * y3) - (x * y2));
	double tmp;
	if (y0 <= -4.8e+80) {
		tmp = t_2;
	} else if (y0 <= -0.345) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y0 <= -2.1e-16) {
		tmp = k * (i * (y * y5));
	} else if (y0 <= -3.3e-93) {
		tmp = t_3;
	} else if (y0 <= -9e-270) {
		tmp = t_1;
	} else if (y0 <= 2.3e-278) {
		tmp = t_3;
	} else if (y0 <= 3e-180) {
		tmp = t_1;
	} else if (y0 <= 1.2e+26) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = k * (y * ((i * y5) - (b * y4)))
    t_2 = y0 * (b * ((z * k) - (x * j)))
    t_3 = (a * y1) * ((z * y3) - (x * y2))
    if (y0 <= (-4.8d+80)) then
        tmp = t_2
    else if (y0 <= (-0.345d0)) then
        tmp = a * (b * ((x * y) - (z * t)))
    else if (y0 <= (-2.1d-16)) then
        tmp = k * (i * (y * y5))
    else if (y0 <= (-3.3d-93)) then
        tmp = t_3
    else if (y0 <= (-9d-270)) then
        tmp = t_1
    else if (y0 <= 2.3d-278) then
        tmp = t_3
    else if (y0 <= 3d-180) then
        tmp = t_1
    else if (y0 <= 1.2d+26) then
        tmp = (y * c) * ((y3 * y4) - (x * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y * ((i * y5) - (b * y4)));
	double t_2 = y0 * (b * ((z * k) - (x * j)));
	double t_3 = (a * y1) * ((z * y3) - (x * y2));
	double tmp;
	if (y0 <= -4.8e+80) {
		tmp = t_2;
	} else if (y0 <= -0.345) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else if (y0 <= -2.1e-16) {
		tmp = k * (i * (y * y5));
	} else if (y0 <= -3.3e-93) {
		tmp = t_3;
	} else if (y0 <= -9e-270) {
		tmp = t_1;
	} else if (y0 <= 2.3e-278) {
		tmp = t_3;
	} else if (y0 <= 3e-180) {
		tmp = t_1;
	} else if (y0 <= 1.2e+26) {
		tmp = (y * c) * ((y3 * y4) - (x * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y * ((i * y5) - (b * y4)))
	t_2 = y0 * (b * ((z * k) - (x * j)))
	t_3 = (a * y1) * ((z * y3) - (x * y2))
	tmp = 0
	if y0 <= -4.8e+80:
		tmp = t_2
	elif y0 <= -0.345:
		tmp = a * (b * ((x * y) - (z * t)))
	elif y0 <= -2.1e-16:
		tmp = k * (i * (y * y5))
	elif y0 <= -3.3e-93:
		tmp = t_3
	elif y0 <= -9e-270:
		tmp = t_1
	elif y0 <= 2.3e-278:
		tmp = t_3
	elif y0 <= 3e-180:
		tmp = t_1
	elif y0 <= 1.2e+26:
		tmp = (y * c) * ((y3 * y4) - (x * i))
	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(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))))
	t_2 = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))))
	t_3 = Float64(Float64(a * y1) * Float64(Float64(z * y3) - Float64(x * y2)))
	tmp = 0.0
	if (y0 <= -4.8e+80)
		tmp = t_2;
	elseif (y0 <= -0.345)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	elseif (y0 <= -2.1e-16)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	elseif (y0 <= -3.3e-93)
		tmp = t_3;
	elseif (y0 <= -9e-270)
		tmp = t_1;
	elseif (y0 <= 2.3e-278)
		tmp = t_3;
	elseif (y0 <= 3e-180)
		tmp = t_1;
	elseif (y0 <= 1.2e+26)
		tmp = Float64(Float64(y * c) * Float64(Float64(y3 * y4) - Float64(x * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y * ((i * y5) - (b * y4)));
	t_2 = y0 * (b * ((z * k) - (x * j)));
	t_3 = (a * y1) * ((z * y3) - (x * y2));
	tmp = 0.0;
	if (y0 <= -4.8e+80)
		tmp = t_2;
	elseif (y0 <= -0.345)
		tmp = a * (b * ((x * y) - (z * t)));
	elseif (y0 <= -2.1e-16)
		tmp = k * (i * (y * y5));
	elseif (y0 <= -3.3e-93)
		tmp = t_3;
	elseif (y0 <= -9e-270)
		tmp = t_1;
	elseif (y0 <= 2.3e-278)
		tmp = t_3;
	elseif (y0 <= 3e-180)
		tmp = t_1;
	elseif (y0 <= 1.2e+26)
		tmp = (y * c) * ((y3 * y4) - (x * i));
	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[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * y1), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.8e+80], t$95$2, If[LessEqual[y0, -0.345], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -2.1e-16], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.3e-93], t$95$3, If[LessEqual[y0, -9e-270], t$95$1, If[LessEqual[y0, 2.3e-278], t$95$3, If[LessEqual[y0, 3e-180], t$95$1, If[LessEqual[y0, 1.2e+26], N[(N[(y * c), $MachinePrecision] * N[(N[(y3 * y4), $MachinePrecision] - N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -4.79999999999999958e80 or 1.20000000000000002e26 < y0

   1. Initial program 22.4%

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

   3. Simplified 26.7%

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

   4. Taylor expanded in y0 around inf 52.1%

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

      1. mul-1-neg 52.1%

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

   6. Simplified 52.1%

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

   7. Taylor expanded in b around inf 48.7%

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

   if -4.79999999999999958e80 < y0 < -0.34499999999999997

   1. Initial program 45.5%

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

   3. Simplified 45.5%

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

   4. Taylor expanded in a around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. mul-1-neg 50.9%

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

   6. Simplified 50.9%

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

   7. Taylor expanded in b around inf 55.4%

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

   if -0.34499999999999997 < y0 < -2.1000000000000001e-16

   1. Initial program 33.7%

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

   3. Simplified 33.7%

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

   4. Taylor expanded in y5 around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. mul-1-neg 51.1%

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

      3. mul-1-neg 51.1%

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

      4. sub-neg 51.1%

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

      5. sub-neg 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in k around inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. neg-mul-1 67.6%

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

      3. *-commutative 67.6%

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

      4. +-commutative 67.6%

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

      5. mul-1-neg 67.6%

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

      6. unsub-neg 67.6%

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

      7. *-commutative 67.6%

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

   9. Simplified 67.6%

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

   10. Taylor expanded in i around inf 83.4%

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

   if -2.1000000000000001e-16 < y0 < -3.3000000000000001e-93 or -8.99999999999999996e-270 < y0 < 2.30000000000000003e-278

   1. Initial program 43.3%

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

   3. Simplified 53.3%

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

   4. Taylor expanded in a around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. mul-1-neg 44.3%

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

   6. Simplified 44.3%

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

   7. Taylor expanded in y1 around inf 51.0%

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

      1. associate-*r* 54.2%

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

      2. *-commutative 54.2%

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

      3. *-commutative 54.2%

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

   9. Simplified 54.2%

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

   if -3.3000000000000001e-93 < y0 < -8.99999999999999996e-270 or 2.30000000000000003e-278 < y0 < 3.0000000000000001e-180

   1. Initial program 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in y around inf 41.6%

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

      1. associate--l+ 41.6%

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

      2. mul-1-neg 41.6%

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

      3. mul-1-neg 41.6%

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

   6. Simplified 41.6%

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

   7. Taylor expanded in k around inf 50.1%

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

   if 3.0000000000000001e-180 < y0 < 1.20000000000000002e26

   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 y around inf 35.5%

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

      1. associate--l+ 35.5%

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

      2. mul-1-neg 35.5%

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

      3. mul-1-neg 35.5%

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

   6. Simplified 35.5%

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

   7. Taylor expanded in c around inf 52.7%

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

      1. associate-*r* 43.3%

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

      2. *-commutative 43.3%

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

      3. mul-1-neg 43.3%

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

      4. unsub-neg 43.3%

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

      5. *-commutative 43.3%

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

      6. *-commutative 43.3%

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

   9. Simplified 43.3%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.8 \cdot 10^{+80}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y0 \leq -0.345:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq -3.3 \cdot 10^{-93}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;y0 \leq -9 \cdot 10^{-270}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 2.3 \cdot 10^{-278}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;y0 \leq 3 \cdot 10^{-180}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y0 \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;\left(y \cdot c\right) \cdot \left(y3 \cdot y4 - x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \end{array} \]

Alternative 13: 28.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{if}\;y5 \leq -3.8 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq -1.1 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -1.52 \cdot 10^{-260}:\\ \;\;\;\;\left(b \cdot j - c \cdot y2\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 2.45 \cdot 10^{-247}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-173}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y5 \leq 14.2:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* k (* y (- (* i y5) (* b y4))))))
   (if (<= y5 -3.8e+183)
     t_1
     (if (<= y5 -1.1e+105)
       (* i (* y5 (- (* y k) (* t j))))
       (if (<= y5 -7.2e+21)
         (* z (* y3 (- (* a y1) (* c y0))))
         (if (<= y5 -1.52e-260)
           (* (- (* b j) (* c y2)) (* t y4))
           (if (<= y5 2.45e-247)
             (* y0 (* c (- (* x y2) (* z y3))))
             (if (<= y5 5.6e-173)
               (* (* a y1) (- (* z y3) (* x y2)))
               (if (<= y5 2.3e-106)
                 t_1
                 (if (<= y5 14.2)
                   (* y4 (* y1 (- (* k y2) (* j y3))))
                   (* a (* y (- (* x b) (* y3 y5))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y5 <= -3.8e+183) {
		tmp = t_1;
	} else if (y5 <= -1.1e+105) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -7.2e+21) {
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	} else if (y5 <= -1.52e-260) {
		tmp = ((b * j) - (c * y2)) * (t * y4);
	} else if (y5 <= 2.45e-247) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y5 <= 5.6e-173) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (y5 <= 2.3e-106) {
		tmp = t_1;
	} else if (y5 <= 14.2) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = k * (y * ((i * y5) - (b * y4)))
    if (y5 <= (-3.8d+183)) then
        tmp = t_1
    else if (y5 <= (-1.1d+105)) then
        tmp = i * (y5 * ((y * k) - (t * j)))
    else if (y5 <= (-7.2d+21)) then
        tmp = z * (y3 * ((a * y1) - (c * y0)))
    else if (y5 <= (-1.52d-260)) then
        tmp = ((b * j) - (c * y2)) * (t * y4)
    else if (y5 <= 2.45d-247) then
        tmp = y0 * (c * ((x * y2) - (z * y3)))
    else if (y5 <= 5.6d-173) then
        tmp = (a * y1) * ((z * y3) - (x * y2))
    else if (y5 <= 2.3d-106) then
        tmp = t_1
    else if (y5 <= 14.2d0) then
        tmp = y4 * (y1 * ((k * y2) - (j * y3)))
    else
        tmp = a * (y * ((x * b) - (y3 * y5)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = k * (y * ((i * y5) - (b * y4)));
	double tmp;
	if (y5 <= -3.8e+183) {
		tmp = t_1;
	} else if (y5 <= -1.1e+105) {
		tmp = i * (y5 * ((y * k) - (t * j)));
	} else if (y5 <= -7.2e+21) {
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	} else if (y5 <= -1.52e-260) {
		tmp = ((b * j) - (c * y2)) * (t * y4);
	} else if (y5 <= 2.45e-247) {
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	} else if (y5 <= 5.6e-173) {
		tmp = (a * y1) * ((z * y3) - (x * y2));
	} else if (y5 <= 2.3e-106) {
		tmp = t_1;
	} else if (y5 <= 14.2) {
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	} else {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = k * (y * ((i * y5) - (b * y4)))
	tmp = 0
	if y5 <= -3.8e+183:
		tmp = t_1
	elif y5 <= -1.1e+105:
		tmp = i * (y5 * ((y * k) - (t * j)))
	elif y5 <= -7.2e+21:
		tmp = z * (y3 * ((a * y1) - (c * y0)))
	elif y5 <= -1.52e-260:
		tmp = ((b * j) - (c * y2)) * (t * y4)
	elif y5 <= 2.45e-247:
		tmp = y0 * (c * ((x * y2) - (z * y3)))
	elif y5 <= 5.6e-173:
		tmp = (a * y1) * ((z * y3) - (x * y2))
	elif y5 <= 2.3e-106:
		tmp = t_1
	elif y5 <= 14.2:
		tmp = y4 * (y1 * ((k * y2) - (j * y3)))
	else:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))))
	tmp = 0.0
	if (y5 <= -3.8e+183)
		tmp = t_1;
	elseif (y5 <= -1.1e+105)
		tmp = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))));
	elseif (y5 <= -7.2e+21)
		tmp = Float64(z * Float64(y3 * Float64(Float64(a * y1) - Float64(c * y0))));
	elseif (y5 <= -1.52e-260)
		tmp = Float64(Float64(Float64(b * j) - Float64(c * y2)) * Float64(t * y4));
	elseif (y5 <= 2.45e-247)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(z * y3))));
	elseif (y5 <= 5.6e-173)
		tmp = Float64(Float64(a * y1) * Float64(Float64(z * y3) - Float64(x * y2)));
	elseif (y5 <= 2.3e-106)
		tmp = t_1;
	elseif (y5 <= 14.2)
		tmp = Float64(y4 * Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3))));
	else
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = k * (y * ((i * y5) - (b * y4)));
	tmp = 0.0;
	if (y5 <= -3.8e+183)
		tmp = t_1;
	elseif (y5 <= -1.1e+105)
		tmp = i * (y5 * ((y * k) - (t * j)));
	elseif (y5 <= -7.2e+21)
		tmp = z * (y3 * ((a * y1) - (c * y0)));
	elseif (y5 <= -1.52e-260)
		tmp = ((b * j) - (c * y2)) * (t * y4);
	elseif (y5 <= 2.45e-247)
		tmp = y0 * (c * ((x * y2) - (z * y3)));
	elseif (y5 <= 5.6e-173)
		tmp = (a * y1) * ((z * y3) - (x * y2));
	elseif (y5 <= 2.3e-106)
		tmp = t_1;
	elseif (y5 <= 14.2)
		tmp = y4 * (y1 * ((k * y2) - (j * y3)));
	else
		tmp = a * (y * ((x * b) - (y3 * y5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y5, -3.8e+183], t$95$1, If[LessEqual[y5, -1.1e+105], N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -7.2e+21], N[(z * N[(y3 * N[(N[(a * y1), $MachinePrecision] - N[(c * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, -1.52e-260], N[(N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision] * N[(t * y4), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.45e-247], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 5.6e-173], N[(N[(a * y1), $MachinePrecision] * N[(N[(z * y3), $MachinePrecision] - N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.3e-106], t$95$1, If[LessEqual[y5, 14.2], N[(y4 * N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y5 < -3.80000000000000001e183 or 5.5999999999999998e-173 < y5 < 2.3000000000000001e-106

   1. Initial program 16.6%

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

   3. Simplified 16.6%

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

   4. Taylor expanded in y around inf 45.4%

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

      1. associate--l+ 45.4%

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

      2. mul-1-neg 45.4%

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

      3. mul-1-neg 45.4%

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

   6. Simplified 45.4%

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

   7. Taylor expanded in k around inf 64.3%

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

   if -3.80000000000000001e183 < y5 < -1.10000000000000003e105

   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 24.9%

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

   4. Taylor expanded in y5 around inf 47.4%

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

      1. mul-1-neg 47.4%

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

      2. mul-1-neg 47.4%

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

      3. mul-1-neg 47.4%

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

      4. sub-neg 47.4%

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

      5. sub-neg 47.4%

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

   6. Simplified 47.4%

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

   7. Taylor expanded in i around inf 51.4%

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

   if -1.10000000000000003e105 < y5 < -7.2e21

   1. Initial program 47.0%

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

   3. Simplified 47.0%

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

   4. Taylor expanded in z around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. associate--l+ 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in t around 0 70.4%

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

   8. Taylor expanded in y3 around inf 59.7%

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

   if -7.2e21 < y5 < -1.52e-260

   1. Initial program 38.8%

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

   3. Simplified 38.8%

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

   4. Taylor expanded in y4 around inf 47.2%

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

   5. Taylor expanded in t around inf 41.7%

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

      1. associate-*r* 41.6%

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

      2. *-commutative 41.6%

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

      3. *-commutative 41.6%

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

   7. Simplified 41.6%

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

   if -1.52e-260 < y5 < 2.45e-247

   1. Initial program 51.8%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in y0 around inf 41.6%

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

      1. mul-1-neg 41.6%

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

   6. Simplified 41.6%

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

   7. Taylor expanded in c around inf 42.1%

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

      1. *-commutative 42.1%

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

      2. *-commutative 42.1%

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

      3. associate-*l* 45.8%

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

      4. *-commutative 45.8%

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

   9. Simplified 45.8%

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

   if 2.45e-247 < y5 < 5.5999999999999998e-173

   1. Initial program 66.5%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in a around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. mul-1-neg 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in y1 around inf 57.0%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. *-commutative 67.3%

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

   9. Simplified 67.3%

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

   if 2.3000000000000001e-106 < y5 < 14.199999999999999

   1. Initial program 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in y4 around inf 42.3%

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

   5. Taylor expanded in y1 around inf 50.8%

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

   if 14.199999999999999 < y5

   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 29.4%

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

   4. Taylor expanded in a around inf 39.2%

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

      1. mul-1-neg 39.2%

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

      2. mul-1-neg 39.2%

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

   6. Simplified 39.2%

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

   7. Taylor expanded in y around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   9. Simplified 48.4%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y5 \leq -3.8 \cdot 10^{+183}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq -1.1 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;y5 \leq -7.2 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(y3 \cdot \left(a \cdot y1 - c \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq -1.52 \cdot 10^{-260}:\\ \;\;\;\;\left(b \cdot j - c \cdot y2\right) \cdot \left(t \cdot y4\right)\\ \mathbf{elif}\;y5 \leq 2.45 \cdot 10^{-247}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - z \cdot y3\right)\right)\\ \mathbf{elif}\;y5 \leq 5.6 \cdot 10^{-173}:\\ \;\;\;\;\left(a \cdot y1\right) \cdot \left(z \cdot y3 - x \cdot y2\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{-106}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y5 \leq 14.2:\\ \;\;\;\;y4 \cdot \left(y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \end{array} \]

Alternative 14: 28.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ t_2 := i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (- (* x b) (* y3 y5)))))
        (t_2 (* i (* y5 (- (* y k) (* t j))))))
   (if (<= z -3.2e-15)
     (* a (* t (- (* y2 y5) (* z b))))
     (if (<= z 6.8e-304)
       t_1
       (if (<= z 1.02e-139)
         t_2
         (if (<= z 5200.0)
           t_1
           (if (<= z 6.8e+125) t_2 (* k (* y0 (* z b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * ((x * b) - (y3 * y5)));
	double t_2 = i * (y5 * ((y * k) - (t * j)));
	double tmp;
	if (z <= -3.2e-15) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (z <= 6.8e-304) {
		tmp = t_1;
	} else if (z <= 1.02e-139) {
		tmp = t_2;
	} else if (z <= 5200.0) {
		tmp = t_1;
	} else if (z <= 6.8e+125) {
		tmp = t_2;
	} else {
		tmp = k * (y0 * (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y * ((x * b) - (y3 * y5)))
    t_2 = i * (y5 * ((y * k) - (t * j)))
    if (z <= (-3.2d-15)) then
        tmp = a * (t * ((y2 * y5) - (z * b)))
    else if (z <= 6.8d-304) then
        tmp = t_1
    else if (z <= 1.02d-139) then
        tmp = t_2
    else if (z <= 5200.0d0) then
        tmp = t_1
    else if (z <= 6.8d+125) then
        tmp = t_2
    else
        tmp = k * (y0 * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * ((x * b) - (y3 * y5)));
	double t_2 = i * (y5 * ((y * k) - (t * j)));
	double tmp;
	if (z <= -3.2e-15) {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	} else if (z <= 6.8e-304) {
		tmp = t_1;
	} else if (z <= 1.02e-139) {
		tmp = t_2;
	} else if (z <= 5200.0) {
		tmp = t_1;
	} else if (z <= 6.8e+125) {
		tmp = t_2;
	} else {
		tmp = k * (y0 * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * ((x * b) - (y3 * y5)))
	t_2 = i * (y5 * ((y * k) - (t * j)))
	tmp = 0
	if z <= -3.2e-15:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	elif z <= 6.8e-304:
		tmp = t_1
	elif z <= 1.02e-139:
		tmp = t_2
	elif z <= 5200.0:
		tmp = t_1
	elif z <= 6.8e+125:
		tmp = t_2
	else:
		tmp = k * (y0 * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))))
	t_2 = Float64(i * Float64(y5 * Float64(Float64(y * k) - Float64(t * j))))
	tmp = 0.0
	if (z <= -3.2e-15)
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	elseif (z <= 6.8e-304)
		tmp = t_1;
	elseif (z <= 1.02e-139)
		tmp = t_2;
	elseif (z <= 5200.0)
		tmp = t_1;
	elseif (z <= 6.8e+125)
		tmp = t_2;
	else
		tmp = Float64(k * Float64(y0 * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * ((x * b) - (y3 * y5)));
	t_2 = i * (y5 * ((y * k) - (t * j)));
	tmp = 0.0;
	if (z <= -3.2e-15)
		tmp = a * (t * ((y2 * y5) - (z * b)));
	elseif (z <= 6.8e-304)
		tmp = t_1;
	elseif (z <= 1.02e-139)
		tmp = t_2;
	elseif (z <= 5200.0)
		tmp = t_1;
	elseif (z <= 6.8e+125)
		tmp = t_2;
	else
		tmp = k * (y0 * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y5 * N[(N[(y * k), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-15], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-304], t$95$1, If[LessEqual[z, 1.02e-139], t$95$2, If[LessEqual[z, 5200.0], t$95$1, If[LessEqual[z, 6.8e+125], t$95$2, N[(k * N[(y0 * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999999e-15

   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 39.8%

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

   4. Taylor expanded in a around inf 46.1%

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

      1. mul-1-neg 46.1%

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

      2. mul-1-neg 46.1%

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

   6. Simplified 46.1%

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

   7. Taylor expanded in t around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. mul-1-neg 42.3%

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

      3. unsub-neg 42.3%

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

      4. *-commutative 42.3%

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

      5. *-commutative 42.3%

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

   9. Simplified 42.3%

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

   if -3.1999999999999999e-15 < z < 6.7999999999999997e-304 or 1.0200000000000001e-139 < z < 5200

   1. Initial program 38.7%

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

   3. Simplified 43.0%

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

   4. Taylor expanded in a around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. mul-1-neg 47.8%

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

   6. Simplified 47.8%

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

   7. Taylor expanded in y around inf 42.8%

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

      1. +-commutative 42.8%

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

      2. mul-1-neg 42.8%

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

      3. unsub-neg 42.8%

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

   9. Simplified 42.8%

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

   if 6.7999999999999997e-304 < z < 1.0200000000000001e-139 or 5200 < z < 6.7999999999999998e125

   1. Initial program 38.0%

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

   3. Simplified 39.7%

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

   4. Taylor expanded in y5 around inf 38.8%

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

      1. mul-1-neg 38.8%

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

      2. mul-1-neg 38.8%

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

      3. mul-1-neg 38.8%

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

      4. sub-neg 38.8%

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

      5. sub-neg 38.8%

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

   6. Simplified 38.8%

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

   7. Taylor expanded in i around inf 37.6%

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

   if 6.7999999999999998e125 < z

   1. Initial program 24.3%

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

   3. Simplified 24.3%

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

   4. Taylor expanded in z around -inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate--l+ 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in t around 0 46.4%

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

   8. Taylor expanded in b around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-rgt-neg-in 49.6%

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

      3. distribute-rgt-neg-in 49.6%

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

      4. *-commutative 49.6%

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

      5. distribute-rgt-neg-in 49.6%

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

   10. Simplified 49.6%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-139}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 5200:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(y5 \cdot \left(y \cdot k - t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \end{array} \]

Alternative 15: 22.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+185}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(z \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -6.2e+146)
   (* a (* t (* z (- b))))
   (if (<= z -2.6e+47)
     (* c (* y3 (* z (- y0))))
     (if (<= z -1.85e-29)
       (* a (* z (* y1 y3)))
       (if (<= z -1.8e-294)
         (* a (* (* x y) b))
         (if (<= z 1.55e+122)
           (* i (* j (* t (- y5))))
           (if (<= z 5.2e+185)
             (* k (* y1 (* z (- i))))
             (* c (* y0 (* z (- y3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -6.2e+146) {
		tmp = a * (t * (z * -b));
	} else if (z <= -2.6e+47) {
		tmp = c * (y3 * (z * -y0));
	} else if (z <= -1.85e-29) {
		tmp = a * (z * (y1 * y3));
	} else if (z <= -1.8e-294) {
		tmp = a * ((x * y) * b);
	} else if (z <= 1.55e+122) {
		tmp = i * (j * (t * -y5));
	} else if (z <= 5.2e+185) {
		tmp = k * (y1 * (z * -i));
	} else {
		tmp = c * (y0 * (z * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-6.2d+146)) then
        tmp = a * (t * (z * -b))
    else if (z <= (-2.6d+47)) then
        tmp = c * (y3 * (z * -y0))
    else if (z <= (-1.85d-29)) then
        tmp = a * (z * (y1 * y3))
    else if (z <= (-1.8d-294)) then
        tmp = a * ((x * y) * b)
    else if (z <= 1.55d+122) then
        tmp = i * (j * (t * -y5))
    else if (z <= 5.2d+185) then
        tmp = k * (y1 * (z * -i))
    else
        tmp = c * (y0 * (z * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -6.2e+146) {
		tmp = a * (t * (z * -b));
	} else if (z <= -2.6e+47) {
		tmp = c * (y3 * (z * -y0));
	} else if (z <= -1.85e-29) {
		tmp = a * (z * (y1 * y3));
	} else if (z <= -1.8e-294) {
		tmp = a * ((x * y) * b);
	} else if (z <= 1.55e+122) {
		tmp = i * (j * (t * -y5));
	} else if (z <= 5.2e+185) {
		tmp = k * (y1 * (z * -i));
	} else {
		tmp = c * (y0 * (z * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -6.2e+146:
		tmp = a * (t * (z * -b))
	elif z <= -2.6e+47:
		tmp = c * (y3 * (z * -y0))
	elif z <= -1.85e-29:
		tmp = a * (z * (y1 * y3))
	elif z <= -1.8e-294:
		tmp = a * ((x * y) * b)
	elif z <= 1.55e+122:
		tmp = i * (j * (t * -y5))
	elif z <= 5.2e+185:
		tmp = k * (y1 * (z * -i))
	else:
		tmp = c * (y0 * (z * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -6.2e+146)
		tmp = Float64(a * Float64(t * Float64(z * Float64(-b))));
	elseif (z <= -2.6e+47)
		tmp = Float64(c * Float64(y3 * Float64(z * Float64(-y0))));
	elseif (z <= -1.85e-29)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	elseif (z <= -1.8e-294)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (z <= 1.55e+122)
		tmp = Float64(i * Float64(j * Float64(t * Float64(-y5))));
	elseif (z <= 5.2e+185)
		tmp = Float64(k * Float64(y1 * Float64(z * Float64(-i))));
	else
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -6.2e+146)
		tmp = a * (t * (z * -b));
	elseif (z <= -2.6e+47)
		tmp = c * (y3 * (z * -y0));
	elseif (z <= -1.85e-29)
		tmp = a * (z * (y1 * y3));
	elseif (z <= -1.8e-294)
		tmp = a * ((x * y) * b);
	elseif (z <= 1.55e+122)
		tmp = i * (j * (t * -y5));
	elseif (z <= 5.2e+185)
		tmp = k * (y1 * (z * -i));
	else
		tmp = c * (y0 * (z * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -6.2e+146], N[(a * N[(t * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e+47], N[(c * N[(y3 * N[(z * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-29], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-294], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+122], N[(i * N[(j * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+185], N[(k * N[(y1 * N[(z * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -6.2000000000000004e146

   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 29.6%

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

   4. Taylor expanded in a around inf 41.3%

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

      1. mul-1-neg 41.3%

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

      2. mul-1-neg 41.3%

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

   6. Simplified 41.3%

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

   7. Taylor expanded in b around inf 44.0%

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

   8. Taylor expanded in y around 0 44.4%

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

      1. associate-*r* 44.4%

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

      2. neg-mul-1 44.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot \left(z \cdot b\right)\right) \]

      3. *-commutative 44.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]

   10. Simplified 44.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]

   if -6.2000000000000004e146 < z < -2.60000000000000003e47

   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 z around -inf 64.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 64.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 64.8%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 37.5%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.3%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 37.3%

         \[\leadsto -c \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot z\right) \]

      3. associate-*l* 43.1%

         \[\leadsto -c \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   10. Simplified 43.1%

       \[\leadsto -\color{blue}{c \cdot \left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   if -2.60000000000000003e47 < z < -1.8499999999999999e-29

   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 z around -inf 60.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.5%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 60.5%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 60.4%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in a around inf 60.7%

      \[\leadsto -\color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 60.7%

         \[\leadsto -\color{blue}{\left(-a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]

      2. associate-*r* 60.7%

         \[\leadsto -\left(-a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)}\right) \]

   10. Simplified 60.7%

       \[\leadsto -\color{blue}{\left(-a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)\right)} \]

   if -1.8499999999999999e-29 < z < -1.8000000000000001e-294

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 30.1%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 30.1%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(x \cdot b\right)}\right) \]

      2. associate-*r* 31.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]

      3. *-commutative 31.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]

   10. Simplified 31.7%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if -1.8000000000000001e-294 < z < 1.54999999999999999e122

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 40.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 40.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 40.5%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in j around -inf 27.9%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot j\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 27.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot y5 \]

      2. mul-1-neg 27.9%

         \[\leadsto \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot y5 \]

      3. unsub-neg 27.9%

         \[\leadsto \left(j \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot y5 \]

      4. *-commutative 27.9%

         \[\leadsto \left(j \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \cdot y5 \]

      5. *-commutative 27.9%

         \[\leadsto \left(j \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \cdot y5 \]

   9. Simplified 27.9%

      \[\leadsto \color{blue}{\left(j \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \cdot y5 \]

   10. Taylor expanded in y3 around 0 29.9%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 29.9%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. distribute-rgt-neg-in 29.9%

          \[\leadsto \color{blue}{i \cdot \left(-t \cdot \left(j \cdot y5\right)\right)} \]

       3. associate-*r* 28.8%

          \[\leadsto i \cdot \left(-\color{blue}{\left(t \cdot j\right) \cdot y5}\right) \]

       4. *-commutative 28.8%

          \[\leadsto i \cdot \left(-\color{blue}{\left(j \cdot t\right)} \cdot y5\right) \]

       5. associate-*l* 28.8%

          \[\leadsto i \cdot \left(-\color{blue}{j \cdot \left(t \cdot y5\right)}\right) \]

   12. Simplified 28.8%

       \[\leadsto \color{blue}{i \cdot \left(-j \cdot \left(t \cdot y5\right)\right)} \]

   if 1.54999999999999999e122 < z < 5.20000000000000001e185

   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 z around -inf 46.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 46.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 46.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 47.0%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in i around inf 54.2%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 54.2%

         \[\leadsto -k \cdot \color{blue}{\left(\left(i \cdot y1\right) \cdot z\right)} \]

      2. *-commutative 54.2%

         \[\leadsto -k \cdot \left(\color{blue}{\left(y1 \cdot i\right)} \cdot z\right) \]

      3. associate-*l* 60.5%

         \[\leadsto -k \cdot \color{blue}{\left(y1 \cdot \left(i \cdot z\right)\right)} \]

   10. Simplified 60.5%

       \[\leadsto -\color{blue}{k \cdot \left(y1 \cdot \left(i \cdot z\right)\right)} \]

   if 5.20000000000000001e185 < z

   1. Initial program 21.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 61.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 61.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 61.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 61.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 48.4%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 44.2%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+185}:\\ \;\;\;\;k \cdot \left(y1 \cdot \left(z \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 16: 30.2% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-190} \lor \neg \left(y \leq 3.2 \cdot 10^{+62}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y (- (* x b) (* y3 y5))))))
   (if (<= y -1.2e+83)
     t_1
     (if (<= y -1.22e+35)
       (* c (* y0 (* z (- y3))))
       (if (or (<= y -1.5e-190) (not (<= y 3.2e+62)))
         t_1
         (* a (* t (- (* y2 y5) (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y <= -1.2e+83) {
		tmp = t_1;
	} else if (y <= -1.22e+35) {
		tmp = c * (y0 * (z * -y3));
	} else if ((y <= -1.5e-190) || !(y <= 3.2e+62)) {
		tmp = t_1;
	} else {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y * ((x * b) - (y3 * y5)))
    if (y <= (-1.2d+83)) then
        tmp = t_1
    else if (y <= (-1.22d+35)) then
        tmp = c * (y0 * (z * -y3))
    else if ((y <= (-1.5d-190)) .or. (.not. (y <= 3.2d+62))) then
        tmp = t_1
    else
        tmp = a * (t * ((y2 * y5) - (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y * ((x * b) - (y3 * y5)));
	double tmp;
	if (y <= -1.2e+83) {
		tmp = t_1;
	} else if (y <= -1.22e+35) {
		tmp = c * (y0 * (z * -y3));
	} else if ((y <= -1.5e-190) || !(y <= 3.2e+62)) {
		tmp = t_1;
	} else {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y * ((x * b) - (y3 * y5)))
	tmp = 0
	if y <= -1.2e+83:
		tmp = t_1
	elif y <= -1.22e+35:
		tmp = c * (y0 * (z * -y3))
	elif (y <= -1.5e-190) or not (y <= 3.2e+62):
		tmp = t_1
	else:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))))
	tmp = 0.0
	if (y <= -1.2e+83)
		tmp = t_1;
	elseif (y <= -1.22e+35)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	elseif ((y <= -1.5e-190) || !(y <= 3.2e+62))
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y * ((x * b) - (y3 * y5)));
	tmp = 0.0;
	if (y <= -1.2e+83)
		tmp = t_1;
	elseif (y <= -1.22e+35)
		tmp = c * (y0 * (z * -y3));
	elseif ((y <= -1.5e-190) || ~((y <= 3.2e+62)))
		tmp = t_1;
	else
		tmp = a * (t * ((y2 * y5) - (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+83], t$95$1, If[LessEqual[y, -1.22e+35], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.5e-190], N[Not[LessEqual[y, 3.2e+62]], $MachinePrecision]], t$95$1, N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999996e83 or -1.21999999999999999e35 < y < -1.4999999999999999e-190 or 3.19999999999999984e62 < y

   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 35.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 38.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 38.5%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 38.5%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y around inf 46.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 46.0%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 46.0%

         \[\leadsto a \cdot \left(y \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 46.0%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 46.0%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -1.19999999999999996e83 < y < -1.21999999999999999e35

   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 z around -inf 41.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.4%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 41.4%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 41.4%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 36.5%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 36.8%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if -1.4999999999999999e-190 < y < 3.19999999999999984e62

   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 42.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 48.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 48.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in t around inf 35.8%

      \[\leadsto a \cdot \color{blue}{\left(\left(y5 \cdot y2 + -1 \cdot \left(z \cdot b\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2 + -1 \cdot \left(z \cdot b\right)\right)\right)} \]

      2. mul-1-neg 35.8%

         \[\leadsto a \cdot \left(t \cdot \left(y5 \cdot y2 + \color{blue}{\left(-z \cdot b\right)}\right)\right) \]

      3. unsub-neg 35.8%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2 - z \cdot b\right)}\right) \]

      4. *-commutative 35.8%

         \[\leadsto a \cdot \left(t \cdot \left(\color{blue}{y2 \cdot y5} - z \cdot b\right)\right) \]

      5. *-commutative 35.8%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 - \color{blue}{b \cdot z}\right)\right) \]

   9. Simplified 35.8%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-190} \lor \neg \left(y \leq 3.2 \cdot 10^{+62}\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]

Alternative 17: 28.1% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{if}\;y0 \leq -4.5 \cdot 10^{+94}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -400:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.45 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* b (- (* x y) (* z t))))))
   (if (<= y0 -4.5e+94)
     (* k (* y2 (* y0 (- y5))))
     (if (<= y0 -400.0)
       t_1
       (if (<= y0 -2.4e-21)
         (* k (* i (* y y5)))
         (if (<= y0 1.45e+124) t_1 (* k (* y0 (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -4.5e+94) {
		tmp = k * (y2 * (y0 * -y5));
	} else if (y0 <= -400.0) {
		tmp = t_1;
	} else if (y0 <= -2.4e-21) {
		tmp = k * (i * (y * y5));
	} else if (y0 <= 1.45e+124) {
		tmp = t_1;
	} else {
		tmp = k * (y0 * (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * ((x * y) - (z * t)))
    if (y0 <= (-4.5d+94)) then
        tmp = k * (y2 * (y0 * -y5))
    else if (y0 <= (-400.0d0)) then
        tmp = t_1
    else if (y0 <= (-2.4d-21)) then
        tmp = k * (i * (y * y5))
    else if (y0 <= 1.45d+124) then
        tmp = t_1
    else
        tmp = k * (y0 * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (b * ((x * y) - (z * t)));
	double tmp;
	if (y0 <= -4.5e+94) {
		tmp = k * (y2 * (y0 * -y5));
	} else if (y0 <= -400.0) {
		tmp = t_1;
	} else if (y0 <= -2.4e-21) {
		tmp = k * (i * (y * y5));
	} else if (y0 <= 1.45e+124) {
		tmp = t_1;
	} else {
		tmp = k * (y0 * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (b * ((x * y) - (z * t)))
	tmp = 0
	if y0 <= -4.5e+94:
		tmp = k * (y2 * (y0 * -y5))
	elif y0 <= -400.0:
		tmp = t_1
	elif y0 <= -2.4e-21:
		tmp = k * (i * (y * y5))
	elif y0 <= 1.45e+124:
		tmp = t_1
	else:
		tmp = k * (y0 * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))))
	tmp = 0.0
	if (y0 <= -4.5e+94)
		tmp = Float64(k * Float64(y2 * Float64(y0 * Float64(-y5))));
	elseif (y0 <= -400.0)
		tmp = t_1;
	elseif (y0 <= -2.4e-21)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	elseif (y0 <= 1.45e+124)
		tmp = t_1;
	else
		tmp = Float64(k * Float64(y0 * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (b * ((x * y) - (z * t)));
	tmp = 0.0;
	if (y0 <= -4.5e+94)
		tmp = k * (y2 * (y0 * -y5));
	elseif (y0 <= -400.0)
		tmp = t_1;
	elseif (y0 <= -2.4e-21)
		tmp = k * (i * (y * y5));
	elseif (y0 <= 1.45e+124)
		tmp = t_1;
	else
		tmp = k * (y0 * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.5e+94], N[(k * N[(y2 * N[(y0 * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -400.0], t$95$1, If[LessEqual[y0, -2.4e-21], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.45e+124], t$95$1, N[(k * N[(y0 * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y0 < -4.49999999999999972e94

   1. Initial program 19.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 24.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 37.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 37.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 37.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 37.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 37.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 37.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 42.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 42.4%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 42.4%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 42.4%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 42.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 42.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 42.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 42.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 42.4%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around inf 32.9%

       \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y0 \cdot \left(y5 \cdot y2\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 39.9%

          \[\leadsto \left(-k\right) \cdot \color{blue}{\left(\left(y0 \cdot y5\right) \cdot y2\right)} \]

   12. Simplified 39.9%

       \[\leadsto \left(-k\right) \cdot \color{blue}{\left(\left(y0 \cdot y5\right) \cdot y2\right)} \]

   if -4.49999999999999972e94 < y0 < -400 or -2.3999999999999999e-21 < y0 < 1.45000000000000011e124

   1. Initial program 40.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.2%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -400 < y0 < -2.3999999999999999e-21

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 33.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 51.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 51.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 51.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 51.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 51.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 67.6%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 67.6%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 67.6%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 67.6%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 67.6%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 67.6%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 67.6%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 67.6%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 67.6%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in i around inf 83.4%

       \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5\right)\right)} \]

   if 1.45000000000000011e124 < y0

   1. Initial program 12.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 12.3%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 52.2%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 52.2%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 52.2%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 52.2%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 58.0%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in b around inf 55.6%

      \[\leadsto -\color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 55.6%

         \[\leadsto -\color{blue}{\left(-k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]

      2. distribute-rgt-neg-in 55.6%

         \[\leadsto -\color{blue}{k \cdot \left(-y0 \cdot \left(b \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 55.6%

         \[\leadsto -k \cdot \color{blue}{\left(y0 \cdot \left(-b \cdot z\right)\right)} \]

      4. *-commutative 55.6%

         \[\leadsto -k \cdot \left(y0 \cdot \left(-\color{blue}{z \cdot b}\right)\right) \]

      5. distribute-rgt-neg-in 55.6%

         \[\leadsto -k \cdot \left(y0 \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)}\right) \]

   10. Simplified 55.6%

       \[\leadsto -\color{blue}{k \cdot \left(y0 \cdot \left(z \cdot \left(-b\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y0 \leq -4.5 \cdot 10^{+94}:\\ \;\;\;\;k \cdot \left(y2 \cdot \left(y0 \cdot \left(-y5\right)\right)\right)\\ \mathbf{elif}\;y0 \leq -400:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{elif}\;y0 \leq -2.4 \cdot 10^{-21}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 1.45 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \end{array} \]

Alternative 18: 30.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.85 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{-216}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{-198}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.85e+55)
   (* y (* a (- (* x b) (* y3 y5))))
   (if (<= y3 -9.5e-216)
     (* k (* y (- (* i y5) (* b y4))))
     (if (<= y3 1.7e-198)
       (* y0 (* b (- (* z k) (* x j))))
       (if (<= y3 1.4e+65)
         (* a (* b (- (* x y) (* z t))))
         (* y (* y4 (- (* c y3) (* b k)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.85e+55) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= -9.5e-216) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 1.7e-198) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (y3 <= 1.4e+65) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-1.85d+55)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y3 <= (-9.5d-216)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y3 <= 1.7d-198) then
        tmp = y0 * (b * ((z * k) - (x * j)))
    else if (y3 <= 1.4d+65) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = y * (y4 * ((c * y3) - (b * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.85e+55) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= -9.5e-216) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 1.7e-198) {
		tmp = y0 * (b * ((z * k) - (x * j)));
	} else if (y3 <= 1.4e+65) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -1.85e+55:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y3 <= -9.5e-216:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y3 <= 1.7e-198:
		tmp = y0 * (b * ((z * k) - (x * j)))
	elif y3 <= 1.4e+65:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -1.85e+55)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y3 <= -9.5e-216)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y3 <= 1.7e-198)
		tmp = Float64(y0 * Float64(b * Float64(Float64(z * k) - Float64(x * j))));
	elseif (y3 <= 1.4e+65)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -1.85e+55)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y3 <= -9.5e-216)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y3 <= 1.7e-198)
		tmp = y0 * (b * ((z * k) - (x * j)));
	elseif (y3 <= 1.4e+65)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = y * (y4 * ((c * y3) - (b * k)));
	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[y3, -1.85e+55], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -9.5e-216], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.7e-198], N[(y0 * N[(b * N[(N[(z * k), $MachinePrecision] - N[(x * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.4e+65], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y3 < -1.8500000000000001e55

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 45.5%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. associate-*r* 47.4%

         \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      4. +-commutative 47.4%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      5. mul-1-neg 47.4%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      6. unsub-neg 47.4%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -1.8500000000000001e55 < y3 < -9.49999999999999943e-216

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      3. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

   7. Taylor expanded in k around inf 41.1%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - y4 \cdot b\right)\right)} \]

   if -9.49999999999999943e-216 < y3 < 1.6999999999999999e-198

   1. Initial program 41.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 41.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(k \cdot y2 - j \cdot y3, y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(c \cdot y4 - a \cdot y5, y \cdot y3 - t \cdot y2, \mathsf{fma}\left(x \cdot y - z \cdot t, a \cdot b - c \cdot i, \mathsf{fma}\left(b \cdot y0 - i \cdot y1, z \cdot k - x \cdot j, \mathsf{fma}\left(t \cdot j - y \cdot k, b \cdot y4 - i \cdot y5, \left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y0 around inf 48.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 48.1%

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\color{blue}{\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)} + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right) \]

   6. Simplified 48.1%

      \[\leadsto \color{blue}{y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right) + \left(\left(-y5 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right) + \left(k \cdot z - j \cdot x\right) \cdot b\right)\right)} \]

   7. Taylor expanded in b around inf 45.7%

      \[\leadsto y0 \cdot \color{blue}{\left(\left(k \cdot z - j \cdot x\right) \cdot b\right)} \]

   if 1.6999999999999999e-198 < y3 < 1.3999999999999999e65

   1. Initial program 39.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.8%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 40.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 1.3999999999999999e65 < y3

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 38.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.5%

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. mul-1-neg 38.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      3. mul-1-neg 38.5%

         \[\leadsto y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   6. Simplified 38.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 56.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot c} - k \cdot b\right)\right) \]

      2. *-commutative 56.9%

         \[\leadsto y \cdot \left(y4 \cdot \left(y3 \cdot c - \color{blue}{b \cdot k}\right)\right) \]

   9. Simplified 56.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(y3 \cdot c - b \cdot k\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.85 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -9.5 \cdot 10^{-216}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 1.7 \cdot 10^{-198}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(z \cdot k - x \cdot j\right)\right)\\ \mathbf{elif}\;y3 \leq 1.4 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 19: 22.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-240}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-183}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 245000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (* x b)))))
   (if (<= b -4.4e+54)
     t_1
     (if (<= b -7.4e-240)
       (* (* x y2) (* a (- y1)))
       (if (<= b 6.2e-183)
         (* c (* y3 (* z (- y0))))
         (if (<= b 245000.0)
           (* k (* y (* i y5)))
           (if (<= b 6.5e+146) (* c (* y0 (* z (- y3)))) 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 = y * (a * (x * b));
	double tmp;
	if (b <= -4.4e+54) {
		tmp = t_1;
	} else if (b <= -7.4e-240) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 6.2e-183) {
		tmp = c * (y3 * (z * -y0));
	} else if (b <= 245000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 6.5e+146) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
    if (b <= (-4.4d+54)) then
        tmp = t_1
    else if (b <= (-7.4d-240)) then
        tmp = (x * y2) * (a * -y1)
    else if (b <= 6.2d-183) then
        tmp = c * (y3 * (z * -y0))
    else if (b <= 245000.0d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 6.5d+146) then
        tmp = c * (y0 * (z * -y3))
    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 = y * (a * (x * b));
	double tmp;
	if (b <= -4.4e+54) {
		tmp = t_1;
	} else if (b <= -7.4e-240) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 6.2e-183) {
		tmp = c * (y3 * (z * -y0));
	} else if (b <= 245000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 6.5e+146) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
	tmp = 0
	if b <= -4.4e+54:
		tmp = t_1
	elif b <= -7.4e-240:
		tmp = (x * y2) * (a * -y1)
	elif b <= 6.2e-183:
		tmp = c * (y3 * (z * -y0))
	elif b <= 245000.0:
		tmp = k * (y * (i * y5))
	elif b <= 6.5e+146:
		tmp = c * (y0 * (z * -y3))
	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(y * Float64(a * Float64(x * b)))
	tmp = 0.0
	if (b <= -4.4e+54)
		tmp = t_1;
	elseif (b <= -7.4e-240)
		tmp = Float64(Float64(x * y2) * Float64(a * Float64(-y1)));
	elseif (b <= 6.2e-183)
		tmp = Float64(c * Float64(y3 * Float64(z * Float64(-y0))));
	elseif (b <= 245000.0)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 6.5e+146)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	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 = y * (a * (x * b));
	tmp = 0.0;
	if (b <= -4.4e+54)
		tmp = t_1;
	elseif (b <= -7.4e-240)
		tmp = (x * y2) * (a * -y1);
	elseif (b <= 6.2e-183)
		tmp = c * (y3 * (z * -y0));
	elseif (b <= 245000.0)
		tmp = k * (y * (i * y5));
	elseif (b <= 6.5e+146)
		tmp = c * (y0 * (z * -y3));
	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[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+54], t$95$1, If[LessEqual[b, -7.4e-240], N[(N[(x * y2), $MachinePrecision] * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-183], N[(c * N[(y3 * N[(z * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 245000.0], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+146], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.3999999999999998e54 or 6.4999999999999997e146 < b

   1. Initial program 23.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.2%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 42.2%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -4.3999999999999998e54 < b < -7.4000000000000003e-240

   1. Initial program 41.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 27.5%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 22.9%

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(y \cdot b - y1 \cdot y2\right)} \]

      2. *-commutative 22.9%

         \[\leadsto \left(a \cdot x\right) \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right) \]

      3. *-commutative 22.9%

         \[\leadsto \left(a \cdot x\right) \cdot \left(b \cdot y - \color{blue}{y2 \cdot y1}\right) \]

   9. Simplified 22.9%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(b \cdot y - y2 \cdot y1\right)} \]

   10. Taylor expanded in b around 0 27.4%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 27.4%

          \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)} \]

       2. associate-*r* 25.9%

          \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]

       3. *-commutative 25.9%

          \[\leadsto -\left(a \cdot y1\right) \cdot \color{blue}{\left(x \cdot y2\right)} \]

   12. Simplified 25.9%

       \[\leadsto \color{blue}{-\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if -7.4000000000000003e-240 < b < 6.19999999999999999e-183

   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 z around -inf 35.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.8%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 35.8%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 35.8%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 41.5%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 30.0%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.6%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 27.6%

         \[\leadsto -c \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot z\right) \]

      3. associate-*l* 30.3%

         \[\leadsto -c \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   10. Simplified 30.3%

       \[\leadsto -\color{blue}{c \cdot \left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   if 6.19999999999999999e-183 < b < 245000

   1. Initial program 52.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 39.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 39.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 34.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.4%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 34.4%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 34.4%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 37.2%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 37.2%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 37.2%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 245000 < b < 6.4999999999999997e146

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 44.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 44.1%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 44.2%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 24.9%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-240}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-183}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 245000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 20: 22.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-289}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 13500000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+149}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (* x b)))))
   (if (<= b -4.8e+54)
     t_1
     (if (<= b -2.3e-289)
       (* (* x y2) (* a (- y1)))
       (if (<= b 4.4e-169)
         (* (* i k) (* z (- y1)))
         (if (<= b 13500000.0)
           (* k (* y (* i y5)))
           (if (<= b 4e+149) (* c (* y0 (* z (- y3)))) 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 = y * (a * (x * b));
	double tmp;
	if (b <= -4.8e+54) {
		tmp = t_1;
	} else if (b <= -2.3e-289) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 4.4e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 13500000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 4e+149) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
    if (b <= (-4.8d+54)) then
        tmp = t_1
    else if (b <= (-2.3d-289)) then
        tmp = (x * y2) * (a * -y1)
    else if (b <= 4.4d-169) then
        tmp = (i * k) * (z * -y1)
    else if (b <= 13500000.0d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 4d+149) then
        tmp = c * (y0 * (z * -y3))
    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 = y * (a * (x * b));
	double tmp;
	if (b <= -4.8e+54) {
		tmp = t_1;
	} else if (b <= -2.3e-289) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 4.4e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 13500000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 4e+149) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
	tmp = 0
	if b <= -4.8e+54:
		tmp = t_1
	elif b <= -2.3e-289:
		tmp = (x * y2) * (a * -y1)
	elif b <= 4.4e-169:
		tmp = (i * k) * (z * -y1)
	elif b <= 13500000.0:
		tmp = k * (y * (i * y5))
	elif b <= 4e+149:
		tmp = c * (y0 * (z * -y3))
	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(y * Float64(a * Float64(x * b)))
	tmp = 0.0
	if (b <= -4.8e+54)
		tmp = t_1;
	elseif (b <= -2.3e-289)
		tmp = Float64(Float64(x * y2) * Float64(a * Float64(-y1)));
	elseif (b <= 4.4e-169)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(-y1)));
	elseif (b <= 13500000.0)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 4e+149)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	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 = y * (a * (x * b));
	tmp = 0.0;
	if (b <= -4.8e+54)
		tmp = t_1;
	elseif (b <= -2.3e-289)
		tmp = (x * y2) * (a * -y1);
	elseif (b <= 4.4e-169)
		tmp = (i * k) * (z * -y1);
	elseif (b <= 13500000.0)
		tmp = k * (y * (i * y5));
	elseif (b <= 4e+149)
		tmp = c * (y0 * (z * -y3));
	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[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+54], t$95$1, If[LessEqual[b, -2.3e-289], N[(N[(x * y2), $MachinePrecision] * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e-169], N[(N[(i * k), $MachinePrecision] * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 13500000.0], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+149], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.79999999999999997e54 or 4.0000000000000002e149 < b

   1. Initial program 23.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.2%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 42.2%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -4.79999999999999997e54 < b < -2.3000000000000002e-289

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.3%

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(y \cdot b - y1 \cdot y2\right)} \]

      2. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right) \]

      3. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(b \cdot y - \color{blue}{y2 \cdot y1}\right) \]

   9. Simplified 23.3%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(b \cdot y - y2 \cdot y1\right)} \]

   10. Taylor expanded in b around 0 28.7%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 28.7%

          \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)} \]

       2. associate-*r* 27.3%

          \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]

       3. *-commutative 27.3%

          \[\leadsto -\left(a \cdot y1\right) \cdot \color{blue}{\left(x \cdot y2\right)} \]

   12. Simplified 27.3%

       \[\leadsto \color{blue}{-\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if -2.3000000000000002e-289 < b < 4.40000000000000015e-169

   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 z around -inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 34.0%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 37.3%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in i around inf 24.0%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.0%

         \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   10. Simplified 27.0%

       \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   if 4.40000000000000015e-169 < b < 1.35e7

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 38.5%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 41.6%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 1.35e7 < b < 4.0000000000000002e149

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 44.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 44.1%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 44.2%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 24.9%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-289}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 13500000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+149}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 21: 22.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{-290}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 250000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (* x b)))))
   (if (<= b -4.4e+54)
     t_1
     (if (<= b -9.4e-290)
       (* (* x y2) (* a (- y1)))
       (if (<= b 3.5e-169)
         (* (* i k) (* z (- y1)))
         (if (<= b 250000.0)
           (* k (* y (* i y5)))
           (if (<= b 5.4e+144) (* z (* y0 (* c (- y3)))) 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 = y * (a * (x * b));
	double tmp;
	if (b <= -4.4e+54) {
		tmp = t_1;
	} else if (b <= -9.4e-290) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 3.5e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 250000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 5.4e+144) {
		tmp = z * (y0 * (c * -y3));
	} 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 = y * (a * (x * b))
    if (b <= (-4.4d+54)) then
        tmp = t_1
    else if (b <= (-9.4d-290)) then
        tmp = (x * y2) * (a * -y1)
    else if (b <= 3.5d-169) then
        tmp = (i * k) * (z * -y1)
    else if (b <= 250000.0d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 5.4d+144) then
        tmp = z * (y0 * (c * -y3))
    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 = y * (a * (x * b));
	double tmp;
	if (b <= -4.4e+54) {
		tmp = t_1;
	} else if (b <= -9.4e-290) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 3.5e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 250000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 5.4e+144) {
		tmp = z * (y0 * (c * -y3));
	} 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 = y * (a * (x * b))
	tmp = 0
	if b <= -4.4e+54:
		tmp = t_1
	elif b <= -9.4e-290:
		tmp = (x * y2) * (a * -y1)
	elif b <= 3.5e-169:
		tmp = (i * k) * (z * -y1)
	elif b <= 250000.0:
		tmp = k * (y * (i * y5))
	elif b <= 5.4e+144:
		tmp = z * (y0 * (c * -y3))
	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(y * Float64(a * Float64(x * b)))
	tmp = 0.0
	if (b <= -4.4e+54)
		tmp = t_1;
	elseif (b <= -9.4e-290)
		tmp = Float64(Float64(x * y2) * Float64(a * Float64(-y1)));
	elseif (b <= 3.5e-169)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(-y1)));
	elseif (b <= 250000.0)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 5.4e+144)
		tmp = Float64(z * Float64(y0 * Float64(c * Float64(-y3))));
	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 = y * (a * (x * b));
	tmp = 0.0;
	if (b <= -4.4e+54)
		tmp = t_1;
	elseif (b <= -9.4e-290)
		tmp = (x * y2) * (a * -y1);
	elseif (b <= 3.5e-169)
		tmp = (i * k) * (z * -y1);
	elseif (b <= 250000.0)
		tmp = k * (y * (i * y5));
	elseif (b <= 5.4e+144)
		tmp = z * (y0 * (c * -y3));
	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[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+54], t$95$1, If[LessEqual[b, -9.4e-290], N[(N[(x * y2), $MachinePrecision] * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e-169], N[(N[(i * k), $MachinePrecision] * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 250000.0], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.4e+144], N[(z * N[(y0 * N[(c * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.3999999999999998e54 or 5.4000000000000003e144 < b

   1. Initial program 23.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 26.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 44.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 44.7%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 52.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 41.8%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -4.3999999999999998e54 < b < -9.4000000000000003e-290

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.3%

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(y \cdot b - y1 \cdot y2\right)} \]

      2. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right) \]

      3. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(b \cdot y - \color{blue}{y2 \cdot y1}\right) \]

   9. Simplified 23.3%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(b \cdot y - y2 \cdot y1\right)} \]

   10. Taylor expanded in b around 0 28.7%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 28.7%

          \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)} \]

       2. associate-*r* 27.3%

          \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]

       3. *-commutative 27.3%

          \[\leadsto -\left(a \cdot y1\right) \cdot \color{blue}{\left(x \cdot y2\right)} \]

   12. Simplified 27.3%

       \[\leadsto \color{blue}{-\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if -9.4000000000000003e-290 < b < 3.5000000000000003e-169

   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 z around -inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 34.0%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 37.3%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in i around inf 24.0%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.0%

         \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   10. Simplified 27.0%

       \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   if 3.5000000000000003e-169 < b < 2.5e5

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 38.5%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 41.6%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 2.5e5 < b < 5.4000000000000003e144

   1. Initial program 37.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 37.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 45.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 45.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 45.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 45.8%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 25.8%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 22.5%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. associate-*r* 19.3%

         \[\leadsto -\color{blue}{\left(c \cdot \left(y0 \cdot y3\right)\right) \cdot z} \]

      3. *-commutative 19.3%

         \[\leadsto -\color{blue}{\left(\left(y0 \cdot y3\right) \cdot c\right)} \cdot z \]

      4. associate-*l* 25.9%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right)} \cdot z \]

   10. Simplified 25.9%

       \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{-290}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 250000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 22: 22.7% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-289}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 700:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.7e+54)
   (* y (* a (* x b)))
   (if (<= b -1.3e-289)
     (* (* x y2) (* a (- y1)))
     (if (<= b 6.2e-169)
       (* (* i k) (* z (- y1)))
       (if (<= b 700.0)
         (* k (* y (* i y5)))
         (if (<= b 1.5e+66)
           (* z (* y0 (* c (- y3))))
           (* a (* b (* z (- t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.7e+54) {
		tmp = y * (a * (x * b));
	} else if (b <= -1.3e-289) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 6.2e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 700.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 1.5e+66) {
		tmp = z * (y0 * (c * -y3));
	} else {
		tmp = a * (b * (z * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-4.7d+54)) then
        tmp = y * (a * (x * b))
    else if (b <= (-1.3d-289)) then
        tmp = (x * y2) * (a * -y1)
    else if (b <= 6.2d-169) then
        tmp = (i * k) * (z * -y1)
    else if (b <= 700.0d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 1.5d+66) then
        tmp = z * (y0 * (c * -y3))
    else
        tmp = a * (b * (z * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.7e+54) {
		tmp = y * (a * (x * b));
	} else if (b <= -1.3e-289) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 6.2e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 700.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 1.5e+66) {
		tmp = z * (y0 * (c * -y3));
	} else {
		tmp = a * (b * (z * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -4.7e+54:
		tmp = y * (a * (x * b))
	elif b <= -1.3e-289:
		tmp = (x * y2) * (a * -y1)
	elif b <= 6.2e-169:
		tmp = (i * k) * (z * -y1)
	elif b <= 700.0:
		tmp = k * (y * (i * y5))
	elif b <= 1.5e+66:
		tmp = z * (y0 * (c * -y3))
	else:
		tmp = a * (b * (z * -t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -4.7e+54)
		tmp = Float64(y * Float64(a * Float64(x * b)));
	elseif (b <= -1.3e-289)
		tmp = Float64(Float64(x * y2) * Float64(a * Float64(-y1)));
	elseif (b <= 6.2e-169)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(-y1)));
	elseif (b <= 700.0)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 1.5e+66)
		tmp = Float64(z * Float64(y0 * Float64(c * Float64(-y3))));
	else
		tmp = Float64(a * Float64(b * Float64(z * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (b <= -4.7e+54)
		tmp = y * (a * (x * b));
	elseif (b <= -1.3e-289)
		tmp = (x * y2) * (a * -y1);
	elseif (b <= 6.2e-169)
		tmp = (i * k) * (z * -y1);
	elseif (b <= 700.0)
		tmp = k * (y * (i * y5));
	elseif (b <= 1.5e+66)
		tmp = z * (y0 * (c * -y3));
	else
		tmp = a * (b * (z * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -4.7e+54], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e-289], N[(N[(x * y2), $MachinePrecision] * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-169], N[(N[(i * k), $MachinePrecision] * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 700.0], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+66], N[(z * N[(y0 * N[(c * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.69999999999999993e54

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 43.9%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -4.69999999999999993e54 < b < -1.2999999999999999e-289

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.3%

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(y \cdot b - y1 \cdot y2\right)} \]

      2. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right) \]

      3. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(b \cdot y - \color{blue}{y2 \cdot y1}\right) \]

   9. Simplified 23.3%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(b \cdot y - y2 \cdot y1\right)} \]

   10. Taylor expanded in b around 0 28.7%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 28.7%

          \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)} \]

       2. associate-*r* 27.3%

          \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]

       3. *-commutative 27.3%

          \[\leadsto -\left(a \cdot y1\right) \cdot \color{blue}{\left(x \cdot y2\right)} \]

   12. Simplified 27.3%

       \[\leadsto \color{blue}{-\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if -1.2999999999999999e-289 < b < 6.2000000000000004e-169

   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 z around -inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 34.0%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 37.3%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in i around inf 24.0%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.0%

         \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   10. Simplified 27.0%

       \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   if 6.2000000000000004e-169 < b < 700

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 38.5%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 41.6%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 700 < b < 1.50000000000000001e66

   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 50.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.5%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 50.5%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 50.5%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 42.4%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 35.1%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.1%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. associate-*r* 27.1%

         \[\leadsto -\color{blue}{\left(c \cdot \left(y0 \cdot y3\right)\right) \cdot z} \]

      3. *-commutative 27.1%

         \[\leadsto -\color{blue}{\left(\left(y0 \cdot y3\right) \cdot c\right)} \cdot z \]

      4. associate-*l* 43.1%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right)} \cdot z \]

   10. Simplified 43.1%

       \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right) \cdot z} \]

   if 1.50000000000000001e66 < b

   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 30.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 43.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 34.0%

      \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}\right) \]
   9. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(-t \cdot z\right)}\right) \]

      2. distribute-lft-neg-out 34.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(\left(-t\right) \cdot z\right)}\right) \]

      3. *-commutative 34.0%

         \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(z \cdot \left(-t\right)\right)}\right) \]

   10. Simplified 34.0%

       \[\leadsto a \cdot \left(b \cdot \color{blue}{\left(z \cdot \left(-t\right)\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-289}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 700:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot \left(z \cdot \left(-t\right)\right)\right)\\ \end{array} \]

Alternative 23: 23.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-289}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-168}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 0.052:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.7e+54)
   (* y (* a (* x b)))
   (if (<= b -2.1e-289)
     (* (* x y2) (* a (- y1)))
     (if (<= b 1.25e-168)
       (* (* i k) (* z (- y1)))
       (if (<= b 0.052)
         (* k (* y (* i y5)))
         (if (<= b 1.6e+64)
           (* z (* y0 (* c (- y3))))
           (* a (* t (* z (- b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.7e+54) {
		tmp = y * (a * (x * b));
	} else if (b <= -2.1e-289) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 1.25e-168) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 0.052) {
		tmp = k * (y * (i * y5));
	} else if (b <= 1.6e+64) {
		tmp = z * (y0 * (c * -y3));
	} else {
		tmp = a * (t * (z * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-4.7d+54)) then
        tmp = y * (a * (x * b))
    else if (b <= (-2.1d-289)) then
        tmp = (x * y2) * (a * -y1)
    else if (b <= 1.25d-168) then
        tmp = (i * k) * (z * -y1)
    else if (b <= 0.052d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 1.6d+64) then
        tmp = z * (y0 * (c * -y3))
    else
        tmp = a * (t * (z * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.7e+54) {
		tmp = y * (a * (x * b));
	} else if (b <= -2.1e-289) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 1.25e-168) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 0.052) {
		tmp = k * (y * (i * y5));
	} else if (b <= 1.6e+64) {
		tmp = z * (y0 * (c * -y3));
	} else {
		tmp = a * (t * (z * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -4.7e+54:
		tmp = y * (a * (x * b))
	elif b <= -2.1e-289:
		tmp = (x * y2) * (a * -y1)
	elif b <= 1.25e-168:
		tmp = (i * k) * (z * -y1)
	elif b <= 0.052:
		tmp = k * (y * (i * y5))
	elif b <= 1.6e+64:
		tmp = z * (y0 * (c * -y3))
	else:
		tmp = a * (t * (z * -b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -4.7e+54)
		tmp = Float64(y * Float64(a * Float64(x * b)));
	elseif (b <= -2.1e-289)
		tmp = Float64(Float64(x * y2) * Float64(a * Float64(-y1)));
	elseif (b <= 1.25e-168)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(-y1)));
	elseif (b <= 0.052)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 1.6e+64)
		tmp = Float64(z * Float64(y0 * Float64(c * Float64(-y3))));
	else
		tmp = Float64(a * Float64(t * Float64(z * Float64(-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 (b <= -4.7e+54)
		tmp = y * (a * (x * b));
	elseif (b <= -2.1e-289)
		tmp = (x * y2) * (a * -y1);
	elseif (b <= 1.25e-168)
		tmp = (i * k) * (z * -y1);
	elseif (b <= 0.052)
		tmp = k * (y * (i * y5));
	elseif (b <= 1.6e+64)
		tmp = z * (y0 * (c * -y3));
	else
		tmp = a * (t * (z * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -4.7e+54], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-289], N[(N[(x * y2), $MachinePrecision] * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e-168], N[(N[(i * k), $MachinePrecision] * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.052], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+64], N[(z * N[(y0 * N[(c * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.69999999999999993e54

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 43.9%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -4.69999999999999993e54 < b < -2.0999999999999998e-289

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.3%

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(y \cdot b - y1 \cdot y2\right)} \]

      2. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right) \]

      3. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(b \cdot y - \color{blue}{y2 \cdot y1}\right) \]

   9. Simplified 23.3%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(b \cdot y - y2 \cdot y1\right)} \]

   10. Taylor expanded in b around 0 28.7%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 28.7%

          \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)} \]

       2. associate-*r* 27.3%

          \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]

       3. *-commutative 27.3%

          \[\leadsto -\left(a \cdot y1\right) \cdot \color{blue}{\left(x \cdot y2\right)} \]

   12. Simplified 27.3%

       \[\leadsto \color{blue}{-\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if -2.0999999999999998e-289 < b < 1.25e-168

   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 z around -inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 34.0%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 37.3%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in i around inf 24.0%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.0%

         \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   10. Simplified 27.0%

       \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   if 1.25e-168 < b < 0.0519999999999999976

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 38.5%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 41.6%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 0.0519999999999999976 < b < 1.60000000000000009e64

   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 50.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.5%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 50.5%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 50.5%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 42.4%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 35.1%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.1%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. associate-*r* 27.1%

         \[\leadsto -\color{blue}{\left(c \cdot \left(y0 \cdot y3\right)\right) \cdot z} \]

      3. *-commutative 27.1%

         \[\leadsto -\color{blue}{\left(\left(y0 \cdot y3\right) \cdot c\right)} \cdot z \]

      4. associate-*l* 43.1%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right)} \cdot z \]

   10. Simplified 43.1%

       \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right) \cdot z} \]

   if 1.60000000000000009e64 < b

   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 30.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 41.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 41.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 43.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 37.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot \left(z \cdot b\right)\right)} \]

      2. neg-mul-1 37.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot \left(z \cdot b\right)\right) \]

      3. *-commutative 37.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]

   10. Simplified 37.6%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-289}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-168}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 0.052:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \end{array} \]

Alternative 24: 23.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-290}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 1650000000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+76}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y0 \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= b -4.4e+54)
   (* y (* a (* x b)))
   (if (<= b -7.8e-290)
     (* (* x y2) (* a (- y1)))
     (if (<= b 3.1e-169)
       (* (* i k) (* z (- y1)))
       (if (<= b 1650000000.0)
         (* k (* y (* i y5)))
         (if (<= b 2.05e+76)
           (* y5 (* k (* y0 (- y2))))
           (* a (* t (* z (- b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.4e+54) {
		tmp = y * (a * (x * b));
	} else if (b <= -7.8e-290) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 3.1e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 1650000000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 2.05e+76) {
		tmp = y5 * (k * (y0 * -y2));
	} else {
		tmp = a * (t * (z * -b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (b <= (-4.4d+54)) then
        tmp = y * (a * (x * b))
    else if (b <= (-7.8d-290)) then
        tmp = (x * y2) * (a * -y1)
    else if (b <= 3.1d-169) then
        tmp = (i * k) * (z * -y1)
    else if (b <= 1650000000.0d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 2.05d+76) then
        tmp = y5 * (k * (y0 * -y2))
    else
        tmp = a * (t * (z * -b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (b <= -4.4e+54) {
		tmp = y * (a * (x * b));
	} else if (b <= -7.8e-290) {
		tmp = (x * y2) * (a * -y1);
	} else if (b <= 3.1e-169) {
		tmp = (i * k) * (z * -y1);
	} else if (b <= 1650000000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 2.05e+76) {
		tmp = y5 * (k * (y0 * -y2));
	} else {
		tmp = a * (t * (z * -b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -4.4e+54:
		tmp = y * (a * (x * b))
	elif b <= -7.8e-290:
		tmp = (x * y2) * (a * -y1)
	elif b <= 3.1e-169:
		tmp = (i * k) * (z * -y1)
	elif b <= 1650000000.0:
		tmp = k * (y * (i * y5))
	elif b <= 2.05e+76:
		tmp = y5 * (k * (y0 * -y2))
	else:
		tmp = a * (t * (z * -b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (b <= -4.4e+54)
		tmp = Float64(y * Float64(a * Float64(x * b)));
	elseif (b <= -7.8e-290)
		tmp = Float64(Float64(x * y2) * Float64(a * Float64(-y1)));
	elseif (b <= 3.1e-169)
		tmp = Float64(Float64(i * k) * Float64(z * Float64(-y1)));
	elseif (b <= 1650000000.0)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 2.05e+76)
		tmp = Float64(y5 * Float64(k * Float64(y0 * Float64(-y2))));
	else
		tmp = Float64(a * Float64(t * Float64(z * Float64(-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 (b <= -4.4e+54)
		tmp = y * (a * (x * b));
	elseif (b <= -7.8e-290)
		tmp = (x * y2) * (a * -y1);
	elseif (b <= 3.1e-169)
		tmp = (i * k) * (z * -y1);
	elseif (b <= 1650000000.0)
		tmp = k * (y * (i * y5));
	elseif (b <= 2.05e+76)
		tmp = y5 * (k * (y0 * -y2));
	else
		tmp = a * (t * (z * -b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -4.4e+54], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.8e-290], N[(N[(x * y2), $MachinePrecision] * N[(a * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-169], N[(N[(i * k), $MachinePrecision] * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1650000000.0], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+76], N[(y5 * N[(k * N[(y0 * (-y2)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.3999999999999998e54

   1. Initial program 24.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 28.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.6%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 43.9%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -4.3999999999999998e54 < b < -7.79999999999999946e-290

   1. Initial program 39.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in x around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(x \cdot \left(y \cdot b - y1 \cdot y2\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.3%

         \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(y \cdot b - y1 \cdot y2\right)} \]

      2. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(\color{blue}{b \cdot y} - y1 \cdot y2\right) \]

      3. *-commutative 23.3%

         \[\leadsto \left(a \cdot x\right) \cdot \left(b \cdot y - \color{blue}{y2 \cdot y1}\right) \]

   9. Simplified 23.3%

      \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \left(b \cdot y - y2 \cdot y1\right)} \]

   10. Taylor expanded in b around 0 28.7%

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 28.7%

          \[\leadsto \color{blue}{-a \cdot \left(y1 \cdot \left(y2 \cdot x\right)\right)} \]

       2. associate-*r* 27.3%

          \[\leadsto -\color{blue}{\left(a \cdot y1\right) \cdot \left(y2 \cdot x\right)} \]

       3. *-commutative 27.3%

          \[\leadsto -\left(a \cdot y1\right) \cdot \color{blue}{\left(x \cdot y2\right)} \]

   12. Simplified 27.3%

       \[\leadsto \color{blue}{-\left(a \cdot y1\right) \cdot \left(x \cdot y2\right)} \]

   if -7.79999999999999946e-290 < b < 3.1000000000000002e-169

   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 z around -inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 34.0%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 34.0%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 37.3%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in i around inf 24.0%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 27.0%

         \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   10. Simplified 27.0%

       \[\leadsto -\color{blue}{\left(k \cdot i\right) \cdot \left(y1 \cdot z\right)} \]

   if 3.1000000000000002e-169 < b < 1.65e9

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 38.5%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 41.6%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 1.65e9 < b < 2.0499999999999999e76

   1. Initial program 37.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 56.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.5%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 56.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 56.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 56.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 56.5%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 56.5%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in y0 around inf 32.1%

      \[\leadsto \color{blue}{\left(\left(y3 \cdot j - k \cdot y2\right) \cdot y0\right)} \cdot y5 \]

   8. Taylor expanded in y3 around 0 38.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(k \cdot \left(y0 \cdot y2\right)\right)\right)} \cdot y5 \]
   9. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot k\right) \cdot \left(y0 \cdot y2\right)\right)} \cdot y5 \]

      2. neg-mul-1 38.6%

         \[\leadsto \left(\color{blue}{\left(-k\right)} \cdot \left(y0 \cdot y2\right)\right) \cdot y5 \]

   10. Simplified 38.6%

       \[\leadsto \color{blue}{\left(\left(-k\right) \cdot \left(y0 \cdot y2\right)\right)} \cdot y5 \]

   if 2.0499999999999999e76 < b

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 27.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 46.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 40.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 40.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot \left(z \cdot b\right)\right)} \]

      2. neg-mul-1 40.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot \left(z \cdot b\right)\right) \]

      3. *-commutative 40.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]

   10. Simplified 40.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-290}:\\ \;\;\;\;\left(x \cdot y2\right) \cdot \left(a \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-169}:\\ \;\;\;\;\left(i \cdot k\right) \cdot \left(z \cdot \left(-y1\right)\right)\\ \mathbf{elif}\;b \leq 1650000000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+76}:\\ \;\;\;\;y5 \cdot \left(k \cdot \left(y0 \cdot \left(-y2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \end{array} \]

Alternative 25: 21.8% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -8.5e+140)
   (* a (* t (* z (- b))))
   (if (<= z -5.3e+42)
     (* c (* y3 (* z (- y0))))
     (if (<= z -1.95e-29)
       (* a (* z (* y1 y3)))
       (if (<= z -1.25e-299)
         (* a (* (* x y) b))
         (if (<= z 2e+120) (* i (* j (* t (- y5)))) (* k (* y0 (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -8.5e+140) {
		tmp = a * (t * (z * -b));
	} else if (z <= -5.3e+42) {
		tmp = c * (y3 * (z * -y0));
	} else if (z <= -1.95e-29) {
		tmp = a * (z * (y1 * y3));
	} else if (z <= -1.25e-299) {
		tmp = a * ((x * y) * b);
	} else if (z <= 2e+120) {
		tmp = i * (j * (t * -y5));
	} else {
		tmp = k * (y0 * (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (z <= (-8.5d+140)) then
        tmp = a * (t * (z * -b))
    else if (z <= (-5.3d+42)) then
        tmp = c * (y3 * (z * -y0))
    else if (z <= (-1.95d-29)) then
        tmp = a * (z * (y1 * y3))
    else if (z <= (-1.25d-299)) then
        tmp = a * ((x * y) * b)
    else if (z <= 2d+120) then
        tmp = i * (j * (t * -y5))
    else
        tmp = k * (y0 * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -8.5e+140) {
		tmp = a * (t * (z * -b));
	} else if (z <= -5.3e+42) {
		tmp = c * (y3 * (z * -y0));
	} else if (z <= -1.95e-29) {
		tmp = a * (z * (y1 * y3));
	} else if (z <= -1.25e-299) {
		tmp = a * ((x * y) * b);
	} else if (z <= 2e+120) {
		tmp = i * (j * (t * -y5));
	} else {
		tmp = k * (y0 * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if z <= -8.5e+140:
		tmp = a * (t * (z * -b))
	elif z <= -5.3e+42:
		tmp = c * (y3 * (z * -y0))
	elif z <= -1.95e-29:
		tmp = a * (z * (y1 * y3))
	elif z <= -1.25e-299:
		tmp = a * ((x * y) * b)
	elif z <= 2e+120:
		tmp = i * (j * (t * -y5))
	else:
		tmp = k * (y0 * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -8.5e+140)
		tmp = Float64(a * Float64(t * Float64(z * Float64(-b))));
	elseif (z <= -5.3e+42)
		tmp = Float64(c * Float64(y3 * Float64(z * Float64(-y0))));
	elseif (z <= -1.95e-29)
		tmp = Float64(a * Float64(z * Float64(y1 * y3)));
	elseif (z <= -1.25e-299)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	elseif (z <= 2e+120)
		tmp = Float64(i * Float64(j * Float64(t * Float64(-y5))));
	else
		tmp = Float64(k * Float64(y0 * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (z <= -8.5e+140)
		tmp = a * (t * (z * -b));
	elseif (z <= -5.3e+42)
		tmp = c * (y3 * (z * -y0));
	elseif (z <= -1.95e-29)
		tmp = a * (z * (y1 * y3));
	elseif (z <= -1.25e-299)
		tmp = a * ((x * y) * b);
	elseif (z <= 2e+120)
		tmp = i * (j * (t * -y5));
	else
		tmp = k * (y0 * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -8.5e+140], N[(a * N[(t * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e+42], N[(c * N[(y3 * N[(z * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-29], N[(a * N[(z * N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-299], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+120], N[(i * N[(j * N[(t * (-y5)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y0 * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.4999999999999996e140

   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 29.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 41.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 41.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 41.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 41.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 44.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around 0 44.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot \left(z \cdot b\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot \left(z \cdot b\right)\right)} \]

      2. neg-mul-1 44.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot \left(z \cdot b\right)\right) \]

      3. *-commutative 44.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]

   10. Simplified 44.4%

       \[\leadsto a \cdot \color{blue}{\left(\left(z \cdot b\right) \cdot \left(-t\right)\right)} \]

   if -8.4999999999999996e140 < z < -5.30000000000000028e42

   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 z around -inf 64.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 64.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 64.8%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 37.5%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 37.3%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 37.3%

         \[\leadsto -c \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot z\right) \]

      3. associate-*l* 43.1%

         \[\leadsto -c \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   10. Simplified 43.1%

       \[\leadsto -\color{blue}{c \cdot \left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   if -5.30000000000000028e42 < z < -1.9499999999999999e-29

   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 z around -inf 60.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 60.5%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 60.5%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 60.5%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 60.4%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in a around inf 60.7%

      \[\leadsto -\color{blue}{-1 \cdot \left(a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 60.7%

         \[\leadsto -\color{blue}{\left(-a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\right)} \]

      2. associate-*r* 60.7%

         \[\leadsto -\left(-a \cdot \color{blue}{\left(\left(y1 \cdot y3\right) \cdot z\right)}\right) \]

   10. Simplified 60.7%

       \[\leadsto -\color{blue}{\left(-a \cdot \left(\left(y1 \cdot y3\right) \cdot z\right)\right)} \]

   if -1.9499999999999999e-29 < z < -1.24999999999999989e-299

   1. Initial program 37.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 39.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 46.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 30.1%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 30.1%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(x \cdot b\right)}\right) \]

      2. associate-*r* 31.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]

      3. *-commutative 31.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]

   10. Simplified 31.7%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if -1.24999999999999989e-299 < z < 2e120

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 44.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 40.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.9%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 40.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 40.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 40.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 40.9%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 40.9%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in j around -inf 28.2%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot j\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 28.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot y5 \]

      2. mul-1-neg 28.2%

         \[\leadsto \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot y5 \]

      3. unsub-neg 28.2%

         \[\leadsto \left(j \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot y5 \]

      4. *-commutative 28.2%

         \[\leadsto \left(j \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \cdot y5 \]

      5. *-commutative 28.2%

         \[\leadsto \left(j \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \cdot y5 \]

   9. Simplified 28.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \cdot y5 \]

   10. Taylor expanded in y3 around 0 30.2%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(t \cdot \left(j \cdot y5\right)\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 30.2%

          \[\leadsto \color{blue}{-i \cdot \left(t \cdot \left(j \cdot y5\right)\right)} \]

       2. distribute-rgt-neg-in 30.2%

          \[\leadsto \color{blue}{i \cdot \left(-t \cdot \left(j \cdot y5\right)\right)} \]

       3. associate-*r* 29.1%

          \[\leadsto i \cdot \left(-\color{blue}{\left(t \cdot j\right) \cdot y5}\right) \]

       4. *-commutative 29.1%

          \[\leadsto i \cdot \left(-\color{blue}{\left(j \cdot t\right)} \cdot y5\right) \]

       5. associate-*l* 29.1%

          \[\leadsto i \cdot \left(-\color{blue}{j \cdot \left(t \cdot y5\right)}\right) \]

   12. Simplified 29.1%

       \[\leadsto \color{blue}{i \cdot \left(-j \cdot \left(t \cdot y5\right)\right)} \]

   if 2e120 < z

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.6%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 54.4%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 54.4%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 54.4%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 46.7%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in b around inf 47.1%

      \[\leadsto -\color{blue}{-1 \cdot \left(k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 47.1%

         \[\leadsto -\color{blue}{\left(-k \cdot \left(y0 \cdot \left(b \cdot z\right)\right)\right)} \]

      2. distribute-rgt-neg-in 47.1%

         \[\leadsto -\color{blue}{k \cdot \left(-y0 \cdot \left(b \cdot z\right)\right)} \]

      3. distribute-rgt-neg-in 47.1%

         \[\leadsto -k \cdot \color{blue}{\left(y0 \cdot \left(-b \cdot z\right)\right)} \]

      4. *-commutative 47.1%

         \[\leadsto -k \cdot \left(y0 \cdot \left(-\color{blue}{z \cdot b}\right)\right) \]

      5. distribute-rgt-neg-in 47.1%

         \[\leadsto -k \cdot \left(y0 \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)}\right) \]

   10. Simplified 47.1%

       \[\leadsto -\color{blue}{k \cdot \left(y0 \cdot \left(z \cdot \left(-b\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+140}:\\ \;\;\;\;a \cdot \left(t \cdot \left(z \cdot \left(-b\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(z \cdot \left(y1 \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(j \cdot \left(t \cdot \left(-y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y0 \cdot \left(z \cdot b\right)\right)\\ \end{array} \]

Alternative 26: 28.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -1.7 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -7.5 \cdot 10^{-215}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -1.7e+59)
   (* a (* y (- (* x b) (* y3 y5))))
   (if (<= y3 -7.5e-215)
     (* k (* y (- (* i y5) (* b y4))))
     (if (<= y3 2.5e+56)
       (* a (* b (- (* x y) (* z t))))
       (* z (* y0 (* c (- y3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.7e+59) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y3 <= -7.5e-215) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 2.5e+56) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = z * (y0 * (c * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-1.7d+59)) then
        tmp = a * (y * ((x * b) - (y3 * y5)))
    else if (y3 <= (-7.5d-215)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y3 <= 2.5d+56) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = z * (y0 * (c * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -1.7e+59) {
		tmp = a * (y * ((x * b) - (y3 * y5)));
	} else if (y3 <= -7.5e-215) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 2.5e+56) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = z * (y0 * (c * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -1.7e+59:
		tmp = a * (y * ((x * b) - (y3 * y5)))
	elif y3 <= -7.5e-215:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y3 <= 2.5e+56:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = z * (y0 * (c * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -1.7e+59)
		tmp = Float64(a * Float64(y * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y3 <= -7.5e-215)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y3 <= 2.5e+56)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(z * Float64(y0 * Float64(c * Float64(-y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -1.7e+59)
		tmp = a * (y * ((x * b) - (y3 * y5)));
	elseif (y3 <= -7.5e-215)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y3 <= 2.5e+56)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = z * (y0 * (c * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -1.7e+59], N[(a * N[(y * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -7.5e-215], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.5e+56], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y0 * N[(c * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -1.70000000000000003e59

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y around inf 45.5%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      2. mul-1-neg 45.5%

         \[\leadsto a \cdot \left(y \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      3. unsub-neg 45.5%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 45.5%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -1.70000000000000003e59 < y3 < -7.49999999999999986e-215

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      3. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

   7. Taylor expanded in k around inf 41.1%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - y4 \cdot b\right)\right)} \]

   if -7.49999999999999986e-215 < y3 < 2.50000000000000012e56

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 2.50000000000000012e56 < y3

   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 z around -inf 46.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 46.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 46.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 52.5%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 36.2%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.0%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. associate-*r* 36.0%

         \[\leadsto -\color{blue}{\left(c \cdot \left(y0 \cdot y3\right)\right) \cdot z} \]

      3. *-commutative 36.0%

         \[\leadsto -\color{blue}{\left(\left(y0 \cdot y3\right) \cdot c\right)} \cdot z \]

      4. associate-*l* 41.6%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right)} \cdot z \]

   10. Simplified 41.6%

       \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -1.7 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -7.5 \cdot 10^{-215}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.5 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 27: 28.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -3.55 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -5.8 \cdot 10^{-215}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -3.55e+59)
   (* y (* a (- (* x b) (* y3 y5))))
   (if (<= y3 -5.8e-215)
     (* k (* y (- (* i y5) (* b y4))))
     (if (<= y3 2.6e+56)
       (* a (* b (- (* x y) (* z t))))
       (* z (* y0 (* c (- y3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -3.55e+59) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= -5.8e-215) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 2.6e+56) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = z * (y0 * (c * -y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-3.55d+59)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y3 <= (-5.8d-215)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y3 <= 2.6d+56) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = z * (y0 * (c * -y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -3.55e+59) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= -5.8e-215) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 2.6e+56) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = z * (y0 * (c * -y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -3.55e+59:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y3 <= -5.8e-215:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y3 <= 2.6e+56:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = z * (y0 * (c * -y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -3.55e+59)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y3 <= -5.8e-215)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y3 <= 2.6e+56)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(z * Float64(y0 * Float64(c * Float64(-y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -3.55e+59)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y3 <= -5.8e-215)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y3 <= 2.6e+56)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = z * (y0 * (c * -y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -3.55e+59], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -5.8e-215], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 2.6e+56], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y0 * N[(c * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -3.55000000000000002e59

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 45.5%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. associate-*r* 47.4%

         \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      4. +-commutative 47.4%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      5. mul-1-neg 47.4%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      6. unsub-neg 47.4%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -3.55000000000000002e59 < y3 < -5.8000000000000001e-215

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      3. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

   7. Taylor expanded in k around inf 41.1%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - y4 \cdot b\right)\right)} \]

   if -5.8000000000000001e-215 < y3 < 2.60000000000000011e56

   1. Initial program 40.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.0%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.0%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 2.60000000000000011e56 < y3

   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 z around -inf 46.7%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 46.7%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 46.7%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 52.5%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 36.2%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.0%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. associate-*r* 36.0%

         \[\leadsto -\color{blue}{\left(c \cdot \left(y0 \cdot y3\right)\right) \cdot z} \]

      3. *-commutative 36.0%

         \[\leadsto -\color{blue}{\left(\left(y0 \cdot y3\right) \cdot c\right)} \cdot z \]

      4. associate-*l* 41.6%

         \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right)} \cdot z \]

   10. Simplified 41.6%

       \[\leadsto -\color{blue}{\left(y0 \cdot \left(y3 \cdot c\right)\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -3.55 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -5.8 \cdot 10^{-215}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 2.6 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y0 \cdot \left(c \cdot \left(-y3\right)\right)\right)\\ \end{array} \]

Alternative 28: 30.1% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -4.5 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -4.5e+59)
   (* y (* a (- (* x b) (* y3 y5))))
   (if (<= y3 -2.6e-215)
     (* k (* y (- (* i y5) (* b y4))))
     (if (<= y3 9.5e+62)
       (* a (* b (- (* x y) (* z t))))
       (* y (* y4 (- (* c y3) (* b k))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -4.5e+59) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= -2.6e-215) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 9.5e+62) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-4.5d+59)) then
        tmp = y * (a * ((x * b) - (y3 * y5)))
    else if (y3 <= (-2.6d-215)) then
        tmp = k * (y * ((i * y5) - (b * y4)))
    else if (y3 <= 9.5d+62) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = y * (y4 * ((c * y3) - (b * k)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -4.5e+59) {
		tmp = y * (a * ((x * b) - (y3 * y5)));
	} else if (y3 <= -2.6e-215) {
		tmp = k * (y * ((i * y5) - (b * y4)));
	} else if (y3 <= 9.5e+62) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = y * (y4 * ((c * y3) - (b * k)));
	}
	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 <= -4.5e+59:
		tmp = y * (a * ((x * b) - (y3 * y5)))
	elif y3 <= -2.6e-215:
		tmp = k * (y * ((i * y5) - (b * y4)))
	elif y3 <= 9.5e+62:
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = y * (y4 * ((c * y3) - (b * k)))
	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 <= -4.5e+59)
		tmp = Float64(y * Float64(a * Float64(Float64(x * b) - Float64(y3 * y5))));
	elseif (y3 <= -2.6e-215)
		tmp = Float64(k * Float64(y * Float64(Float64(i * y5) - Float64(b * y4))));
	elseif (y3 <= 9.5e+62)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(y * Float64(y4 * Float64(Float64(c * y3) - Float64(b * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -4.5e+59)
		tmp = y * (a * ((x * b) - (y3 * y5)));
	elseif (y3 <= -2.6e-215)
		tmp = k * (y * ((i * y5) - (b * y4)));
	elseif (y3 <= 9.5e+62)
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = y * (y4 * ((c * y3) - (b * k)));
	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[y3, -4.5e+59], N[(y * N[(a * N[(N[(x * b), $MachinePrecision] - N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -2.6e-215], N[(k * N[(y * N[(N[(i * y5), $MachinePrecision] - N[(b * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 9.5e+62], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(y4 * N[(N[(c * y3), $MachinePrecision] - N[(b * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -4.49999999999999959e59

   1. Initial program 19.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 21.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 38.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 38.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in y around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(y \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto \color{blue}{\left(a \cdot y\right) \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)} \]

      2. *-commutative 45.5%

         \[\leadsto \color{blue}{\left(y \cdot a\right)} \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right) \]

      3. associate-*r* 47.4%

         \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(-1 \cdot \left(y3 \cdot y5\right) + b \cdot x\right)\right)} \]

      4. +-commutative 47.4%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x + -1 \cdot \left(y3 \cdot y5\right)\right)}\right) \]

      5. mul-1-neg 47.4%

         \[\leadsto y \cdot \left(a \cdot \left(b \cdot x + \color{blue}{\left(-y3 \cdot y5\right)}\right)\right) \]

      6. unsub-neg 47.4%

         \[\leadsto y \cdot \left(a \cdot \color{blue}{\left(b \cdot x - y3 \cdot y5\right)}\right) \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x - y3 \cdot y5\right)\right)} \]

   if -4.49999999999999959e59 < y3 < -2.6e-215

   1. Initial program 35.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 35.8%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 42.1%

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      3. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   6. Simplified 42.1%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

   7. Taylor expanded in k around inf 41.1%

      \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5 - y4 \cdot b\right)\right)} \]

   if -2.6e-215 < y3 < 9.5000000000000003e62

   1. Initial program 40.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.3%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.3%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if 9.5000000000000003e62 < y3

   1. Initial program 32.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 32.0%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in y around inf 38.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(a \cdot b - c \cdot i\right) \cdot x\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 38.5%

         \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

      2. mul-1-neg 38.5%

         \[\leadsto y \cdot \left(\color{blue}{\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right)} + \left(\left(a \cdot b - c \cdot i\right) \cdot x - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right) \]

      3. mul-1-neg 38.5%

         \[\leadsto y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \color{blue}{\left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right)\right) \]

   6. Simplified 38.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(-k \cdot \left(y4 \cdot b - i \cdot y5\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot x - \left(-y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)\right)} \]

   7. Taylor expanded in y4 around inf 56.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(c \cdot y3 - k \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 56.9%

         \[\leadsto y \cdot \left(y4 \cdot \left(\color{blue}{y3 \cdot c} - k \cdot b\right)\right) \]

      2. *-commutative 56.9%

         \[\leadsto y \cdot \left(y4 \cdot \left(y3 \cdot c - \color{blue}{b \cdot k}\right)\right) \]

   9. Simplified 56.9%

      \[\leadsto y \cdot \color{blue}{\left(y4 \cdot \left(y3 \cdot c - b \cdot k\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -4.5 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b - y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq -2.6 \cdot 10^{-215}:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5 - b \cdot y4\right)\right)\\ \mathbf{elif}\;y3 \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y4 \cdot \left(c \cdot y3 - b \cdot k\right)\right)\\ \end{array} \]

Alternative 29: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ t_2 := c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4700000000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (* x b)))) (t_2 (* c (* y0 (* z (- y3))))))
   (if (<= b -2.3e-7)
     t_1
     (if (<= b 1e-182)
       t_2
       (if (<= b 4700000000.0)
         (* k (* y (* i y5)))
         (if (<= b 2.25e+145) 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 = y * (a * (x * b));
	double t_2 = c * (y0 * (z * -y3));
	double tmp;
	if (b <= -2.3e-7) {
		tmp = t_1;
	} else if (b <= 1e-182) {
		tmp = t_2;
	} else if (b <= 4700000000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 2.25e+145) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (a * (x * b))
    t_2 = c * (y0 * (z * -y3))
    if (b <= (-2.3d-7)) then
        tmp = t_1
    else if (b <= 1d-182) then
        tmp = t_2
    else if (b <= 4700000000.0d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 2.25d+145) 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 = y * (a * (x * b));
	double t_2 = c * (y0 * (z * -y3));
	double tmp;
	if (b <= -2.3e-7) {
		tmp = t_1;
	} else if (b <= 1e-182) {
		tmp = t_2;
	} else if (b <= 4700000000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 2.25e+145) {
		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 = y * (a * (x * b))
	t_2 = c * (y0 * (z * -y3))
	tmp = 0
	if b <= -2.3e-7:
		tmp = t_1
	elif b <= 1e-182:
		tmp = t_2
	elif b <= 4700000000.0:
		tmp = k * (y * (i * y5))
	elif b <= 2.25e+145:
		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(y * Float64(a * Float64(x * b)))
	t_2 = Float64(c * Float64(y0 * Float64(z * Float64(-y3))))
	tmp = 0.0
	if (b <= -2.3e-7)
		tmp = t_1;
	elseif (b <= 1e-182)
		tmp = t_2;
	elseif (b <= 4700000000.0)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 2.25e+145)
		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 = y * (a * (x * b));
	t_2 = c * (y0 * (z * -y3));
	tmp = 0.0;
	if (b <= -2.3e-7)
		tmp = t_1;
	elseif (b <= 1e-182)
		tmp = t_2;
	elseif (b <= 4700000000.0)
		tmp = k * (y * (i * y5));
	elseif (b <= 2.25e+145)
		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[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e-7], t$95$1, If[LessEqual[b, 1e-182], t$95$2, If[LessEqual[b, 4700000000.0], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+145], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.29999999999999995e-7 or 2.2499999999999999e145 < b

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.9%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 37.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -2.29999999999999995e-7 < b < 1e-182 or 4.7e9 < b < 2.2499999999999999e145

   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 z around -inf 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 37.8%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 37.8%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 37.8%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 37.6%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 23.2%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]

   if 1e-182 < b < 4.7e9

   1. Initial program 52.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 39.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 39.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 34.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.4%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 34.4%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 34.4%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 37.2%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 37.2%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 37.2%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 10^{-182}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{elif}\;b \leq 4700000000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 30: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-182}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 0.3:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (* x b)))))
   (if (<= b -2e-7)
     t_1
     (if (<= b 1.02e-182)
       (* c (* y3 (* z (- y0))))
       (if (<= b 0.3)
         (* k (* y (* i y5)))
         (if (<= b 2.15e+148) (* c (* y0 (* z (- y3)))) 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 = y * (a * (x * b));
	double tmp;
	if (b <= -2e-7) {
		tmp = t_1;
	} else if (b <= 1.02e-182) {
		tmp = c * (y3 * (z * -y0));
	} else if (b <= 0.3) {
		tmp = k * (y * (i * y5));
	} else if (b <= 2.15e+148) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
    if (b <= (-2d-7)) then
        tmp = t_1
    else if (b <= 1.02d-182) then
        tmp = c * (y3 * (z * -y0))
    else if (b <= 0.3d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 2.15d+148) then
        tmp = c * (y0 * (z * -y3))
    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 = y * (a * (x * b));
	double tmp;
	if (b <= -2e-7) {
		tmp = t_1;
	} else if (b <= 1.02e-182) {
		tmp = c * (y3 * (z * -y0));
	} else if (b <= 0.3) {
		tmp = k * (y * (i * y5));
	} else if (b <= 2.15e+148) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
	tmp = 0
	if b <= -2e-7:
		tmp = t_1
	elif b <= 1.02e-182:
		tmp = c * (y3 * (z * -y0))
	elif b <= 0.3:
		tmp = k * (y * (i * y5))
	elif b <= 2.15e+148:
		tmp = c * (y0 * (z * -y3))
	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(y * Float64(a * Float64(x * b)))
	tmp = 0.0
	if (b <= -2e-7)
		tmp = t_1;
	elseif (b <= 1.02e-182)
		tmp = Float64(c * Float64(y3 * Float64(z * Float64(-y0))));
	elseif (b <= 0.3)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 2.15e+148)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	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 = y * (a * (x * b));
	tmp = 0.0;
	if (b <= -2e-7)
		tmp = t_1;
	elseif (b <= 1.02e-182)
		tmp = c * (y3 * (z * -y0));
	elseif (b <= 0.3)
		tmp = k * (y * (i * y5));
	elseif (b <= 2.15e+148)
		tmp = c * (y0 * (z * -y3));
	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[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e-7], t$95$1, If[LessEqual[b, 1.02e-182], N[(c * N[(y3 * N[(z * (-y0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.3], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+148], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9999999999999999e-7 or 2.1500000000000001e148 < b

   1. Initial program 28.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 31.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.9%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.9%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 47.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 37.1%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -1.9999999999999999e-7 < b < 1.02e-182

   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 z around -inf 35.3%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.3%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 35.3%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 35.3%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 35.0%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 22.5%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 22.6%

         \[\leadsto -c \cdot \color{blue}{\left(\left(y0 \cdot y3\right) \cdot z\right)} \]

      2. *-commutative 22.6%

         \[\leadsto -c \cdot \left(\color{blue}{\left(y3 \cdot y0\right)} \cdot z\right) \]

      3. associate-*l* 22.6%

         \[\leadsto -c \cdot \color{blue}{\left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   10. Simplified 22.6%

       \[\leadsto -\color{blue}{c \cdot \left(y3 \cdot \left(y0 \cdot z\right)\right)} \]

   if 1.02e-182 < b < 0.299999999999999989

   1. Initial program 52.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 39.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 39.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 39.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 34.4%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 34.4%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 34.4%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 34.4%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 34.4%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 37.2%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 37.2%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 37.2%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 0.299999999999999989 < b < 2.1500000000000001e148

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 44.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 44.1%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 44.2%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 24.9%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-182}:\\ \;\;\;\;c \cdot \left(y3 \cdot \left(z \cdot \left(-y0\right)\right)\right)\\ \mathbf{elif}\;b \leq 0.3:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+148}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 31: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-169}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;b \leq 2700000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* y (* a (* x b)))))
   (if (<= b -3.7e-66)
     t_1
     (if (<= b 9e-169)
       (* k (* i (* z (- y1))))
       (if (<= b 2700000.0)
         (* k (* y (* i y5)))
         (if (<= b 1.15e+146) (* c (* y0 (* z (- y3)))) 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 = y * (a * (x * b));
	double tmp;
	if (b <= -3.7e-66) {
		tmp = t_1;
	} else if (b <= 9e-169) {
		tmp = k * (i * (z * -y1));
	} else if (b <= 2700000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 1.15e+146) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
    if (b <= (-3.7d-66)) then
        tmp = t_1
    else if (b <= 9d-169) then
        tmp = k * (i * (z * -y1))
    else if (b <= 2700000.0d0) then
        tmp = k * (y * (i * y5))
    else if (b <= 1.15d+146) then
        tmp = c * (y0 * (z * -y3))
    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 = y * (a * (x * b));
	double tmp;
	if (b <= -3.7e-66) {
		tmp = t_1;
	} else if (b <= 9e-169) {
		tmp = k * (i * (z * -y1));
	} else if (b <= 2700000.0) {
		tmp = k * (y * (i * y5));
	} else if (b <= 1.15e+146) {
		tmp = c * (y0 * (z * -y3));
	} 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 = y * (a * (x * b))
	tmp = 0
	if b <= -3.7e-66:
		tmp = t_1
	elif b <= 9e-169:
		tmp = k * (i * (z * -y1))
	elif b <= 2700000.0:
		tmp = k * (y * (i * y5))
	elif b <= 1.15e+146:
		tmp = c * (y0 * (z * -y3))
	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(y * Float64(a * Float64(x * b)))
	tmp = 0.0
	if (b <= -3.7e-66)
		tmp = t_1;
	elseif (b <= 9e-169)
		tmp = Float64(k * Float64(i * Float64(z * Float64(-y1))));
	elseif (b <= 2700000.0)
		tmp = Float64(k * Float64(y * Float64(i * y5)));
	elseif (b <= 1.15e+146)
		tmp = Float64(c * Float64(y0 * Float64(z * Float64(-y3))));
	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 = y * (a * (x * b));
	tmp = 0.0;
	if (b <= -3.7e-66)
		tmp = t_1;
	elseif (b <= 9e-169)
		tmp = k * (i * (z * -y1));
	elseif (b <= 2700000.0)
		tmp = k * (y * (i * y5));
	elseif (b <= 1.15e+146)
		tmp = c * (y0 * (z * -y3));
	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[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e-66], t$95$1, If[LessEqual[b, 9e-169], N[(k * N[(i * N[(z * (-y1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2700000.0], N[(k * N[(y * N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+146], N[(c * N[(y0 * N[(z * (-y3)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.7000000000000002e-66 or 1.15e146 < b

   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 32.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 45.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 45.7%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 45.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 46.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 35.5%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -3.7000000000000002e-66 < b < 8.9999999999999997e-169

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 35.8%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 35.8%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 35.8%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 35.8%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 35.6%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in i around inf 22.9%

      \[\leadsto -\color{blue}{k \cdot \left(i \cdot \left(y1 \cdot z\right)\right)} \]

   if 8.9999999999999997e-169 < b < 2.7e6

   1. Initial program 49.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 49.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 38.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.7%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 38.7%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 38.5%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 38.5%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 38.5%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 38.5%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 38.5%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in y2 around 0 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(i \cdot y5\right)\right)} \]
   11. Step-by-step derivation

       1. *-commutative 41.6%

          \[\leadsto k \cdot \left(y \cdot \color{blue}{\left(y5 \cdot i\right)}\right) \]

   12. Simplified 41.6%

       \[\leadsto \color{blue}{k \cdot \left(y \cdot \left(y5 \cdot i\right)\right)} \]

   if 2.7e6 < b < 1.15e146

   1. Initial program 36.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(b \cdot y0 - i \cdot y1\right)\right) + \left(\left(x \cdot y2 - z \cdot y3\right) \cdot \left(c \cdot y0 - a \cdot y1\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\right) - \left(\left(t \cdot y2 - y \cdot y3\right) \cdot \left(c \cdot y4 - a \cdot y5\right) - \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right)} \]

   4. Taylor expanded in z around -inf 44.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 44.1%

         \[\leadsto \color{blue}{-\left(\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + t \cdot \left(a \cdot b - c \cdot i\right)\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right) \cdot z} \]

      2. associate--l+ 44.1%

         \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right)} \cdot z \]

   6. Simplified 44.1%

      \[\leadsto \color{blue}{-\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 + \left(t \cdot \left(a \cdot b - c \cdot i\right) - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)\right) \cdot z} \]

   7. Taylor expanded in t around 0 44.2%

      \[\leadsto -\color{blue}{\left(\left(c \cdot y0 - a \cdot y1\right) \cdot y3 - \left(y0 \cdot b - y1 \cdot i\right) \cdot k\right)} \cdot z \]

   8. Taylor expanded in c around inf 24.9%

      \[\leadsto -\color{blue}{c \cdot \left(y0 \cdot \left(y3 \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-169}:\\ \;\;\;\;k \cdot \left(i \cdot \left(z \cdot \left(-y1\right)\right)\right)\\ \mathbf{elif}\;b \leq 2700000:\\ \;\;\;\;k \cdot \left(y \cdot \left(i \cdot y5\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(z \cdot \left(-y3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \end{array} \]

Alternative 32: 29.0% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-223} \lor \neg \left(y \leq 1.45 \cdot 10^{-44}\right):\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= y -6.6e-223) (not (<= y 1.45e-44)))
   (* a (* b (- (* x y) (* z t))))
   (* a (* t (- (* y2 y5) (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y <= -6.6e-223) || !(y <= 1.45e-44)) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((y <= (-6.6d-223)) .or. (.not. (y <= 1.45d-44))) then
        tmp = a * (b * ((x * y) - (z * t)))
    else
        tmp = a * (t * ((y2 * y5) - (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((y <= -6.6e-223) || !(y <= 1.45e-44)) {
		tmp = a * (b * ((x * y) - (z * t)));
	} else {
		tmp = a * (t * ((y2 * y5) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (y <= -6.6e-223) or not (y <= 1.45e-44):
		tmp = a * (b * ((x * y) - (z * t)))
	else:
		tmp = a * (t * ((y2 * y5) - (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((y <= -6.6e-223) || !(y <= 1.45e-44))
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(z * t))));
	else
		tmp = Float64(a * Float64(t * Float64(Float64(y2 * y5) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((y <= -6.6e-223) || ~((y <= 1.45e-44)))
		tmp = a * (b * ((x * y) - (z * t)));
	else
		tmp = a * (t * ((y2 * y5) - (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[y, -6.6e-223], N[Not[LessEqual[y, 1.45e-44]], $MachinePrecision]], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(N[(y2 * y5), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.59999999999999988e-223 or 1.4500000000000001e-44 < y

   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 35.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 40.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.6%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 40.6%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 40.6%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   if -6.59999999999999988e-223 < y < 1.4500000000000001e-44

   1. Initial program 41.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 42.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 42.7%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 42.7%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in t around inf 35.3%

      \[\leadsto a \cdot \color{blue}{\left(\left(y5 \cdot y2 + -1 \cdot \left(z \cdot b\right)\right) \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y5 \cdot y2 + -1 \cdot \left(z \cdot b\right)\right)\right)} \]

      2. mul-1-neg 35.3%

         \[\leadsto a \cdot \left(t \cdot \left(y5 \cdot y2 + \color{blue}{\left(-z \cdot b\right)}\right)\right) \]

      3. unsub-neg 35.3%

         \[\leadsto a \cdot \left(t \cdot \color{blue}{\left(y5 \cdot y2 - z \cdot b\right)}\right) \]

      4. *-commutative 35.3%

         \[\leadsto a \cdot \left(t \cdot \left(\color{blue}{y2 \cdot y5} - z \cdot b\right)\right) \]

      5. *-commutative 35.3%

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5 - \color{blue}{b \cdot z}\right)\right) \]

   9. Simplified 35.3%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-223} \lor \neg \left(y \leq 1.45 \cdot 10^{-44}\right):\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5 - z \cdot b\right)\right)\\ \end{array} \]

Alternative 33: 18.6% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -68000000000000:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -1.4 \cdot 10^{-87}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -68000000000000.0)
   (* y (* a (* x b)))
   (if (<= y3 -1.4e-87)
     (* k (* i (* y y5)))
     (if (<= y3 7.2e+51) (* a (* (* x y) b)) (* y5 (* j (* y0 y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -68000000000000.0) {
		tmp = y * (a * (x * b));
	} else if (y3 <= -1.4e-87) {
		tmp = k * (i * (y * y5));
	} else if (y3 <= 7.2e+51) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = y5 * (j * (y0 * y3));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-68000000000000.0d0)) then
        tmp = y * (a * (x * b))
    else if (y3 <= (-1.4d-87)) then
        tmp = k * (i * (y * y5))
    else if (y3 <= 7.2d+51) then
        tmp = a * ((x * y) * b)
    else
        tmp = y5 * (j * (y0 * y3))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -68000000000000.0) {
		tmp = y * (a * (x * b));
	} else if (y3 <= -1.4e-87) {
		tmp = k * (i * (y * y5));
	} else if (y3 <= 7.2e+51) {
		tmp = a * ((x * y) * b);
	} else {
		tmp = y5 * (j * (y0 * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -68000000000000.0:
		tmp = y * (a * (x * b))
	elif y3 <= -1.4e-87:
		tmp = k * (i * (y * y5))
	elif y3 <= 7.2e+51:
		tmp = a * ((x * y) * b)
	else:
		tmp = y5 * (j * (y0 * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -68000000000000.0)
		tmp = Float64(y * Float64(a * Float64(x * b)));
	elseif (y3 <= -1.4e-87)
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	elseif (y3 <= 7.2e+51)
		tmp = Float64(a * Float64(Float64(x * y) * b));
	else
		tmp = Float64(y5 * Float64(j * Float64(y0 * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -68000000000000.0)
		tmp = y * (a * (x * b));
	elseif (y3 <= -1.4e-87)
		tmp = k * (i * (y * y5));
	elseif (y3 <= 7.2e+51)
		tmp = a * ((x * y) * b);
	else
		tmp = y5 * (j * (y0 * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -68000000000000.0], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, -1.4e-87], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 7.2e+51], N[(a * N[(N[(x * y), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(y5 * N[(j * N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -6.8e13

   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 24.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 36.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 36.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 36.2%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 36.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 30.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 29.0%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -6.8e13 < y3 < -1.4e-87

   1. Initial program 25.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 25.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 29.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 29.8%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 29.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 29.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 29.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 29.8%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 29.8%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 33.0%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 33.0%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 33.0%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 33.0%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 33.0%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 33.0%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 33.0%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 33.0%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 33.0%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in i around inf 33.2%

       \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5\right)\right)} \]

   if -1.4e-87 < y3 < 7.20000000000000022e51

   1. Initial program 42.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 46.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 42.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 42.8%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 42.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 26.5%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 26.5%

         \[\leadsto a \cdot \left(y \cdot \color{blue}{\left(x \cdot b\right)}\right) \]

      2. associate-*r* 28.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(y \cdot x\right) \cdot b\right)} \]

      3. *-commutative 28.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(x \cdot y\right)} \cdot b\right) \]

   10. Simplified 28.2%

       \[\leadsto a \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot b\right)} \]

   if 7.20000000000000022e51 < y3

   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 45.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 38.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.6%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 38.6%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 38.6%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 38.6%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 38.6%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 38.6%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in j around -inf 33.1%

      \[\leadsto \color{blue}{\left(\left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right) \cdot j\right)} \cdot y5 \]
   8. Step-by-step derivation

      1. *-commutative 33.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(y0 \cdot y3 + -1 \cdot \left(i \cdot t\right)\right)\right)} \cdot y5 \]

      2. mul-1-neg 33.1%

         \[\leadsto \left(j \cdot \left(y0 \cdot y3 + \color{blue}{\left(-i \cdot t\right)}\right)\right) \cdot y5 \]

      3. unsub-neg 33.1%

         \[\leadsto \left(j \cdot \color{blue}{\left(y0 \cdot y3 - i \cdot t\right)}\right) \cdot y5 \]

      4. *-commutative 33.1%

         \[\leadsto \left(j \cdot \left(\color{blue}{y3 \cdot y0} - i \cdot t\right)\right) \cdot y5 \]

      5. *-commutative 33.1%

         \[\leadsto \left(j \cdot \left(y3 \cdot y0 - \color{blue}{t \cdot i}\right)\right) \cdot y5 \]

   9. Simplified 33.1%

      \[\leadsto \color{blue}{\left(j \cdot \left(y3 \cdot y0 - t \cdot i\right)\right)} \cdot y5 \]

   10. Taylor expanded in y3 around inf 29.2%

       \[\leadsto \left(j \cdot \color{blue}{\left(y0 \cdot y3\right)}\right) \cdot y5 \]
   11. Step-by-step derivation

       1. *-commutative 29.2%

          \[\leadsto \left(j \cdot \color{blue}{\left(y3 \cdot y0\right)}\right) \cdot y5 \]

   12. Simplified 29.2%

       \[\leadsto \left(j \cdot \color{blue}{\left(y3 \cdot y0\right)}\right) \cdot y5 \]
3. Recombined 4 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y3 \leq -68000000000000:\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{elif}\;y3 \leq -1.4 \cdot 10^{-87}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \mathbf{elif}\;y3 \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(\left(x \cdot y\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y5 \cdot \left(j \cdot \left(y0 \cdot y3\right)\right)\\ \end{array} \]

Alternative 34: 22.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+39} \lor \neg \left(b \leq 15.2\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -1.6e+39) (not (<= b 15.2)))
   (* a (* y (* x b)))
   (* k (* i (* y y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -1.6e+39) || !(b <= 15.2)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = k * (i * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((b <= (-1.6d+39)) .or. (.not. (b <= 15.2d0))) then
        tmp = a * (y * (x * b))
    else
        tmp = k * (i * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -1.6e+39) || !(b <= 15.2)) {
		tmp = a * (y * (x * b));
	} else {
		tmp = k * (i * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (b <= -1.6e+39) or not (b <= 15.2):
		tmp = a * (y * (x * b))
	else:
		tmp = k * (i * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((b <= -1.6e+39) || !(b <= 15.2))
		tmp = Float64(a * Float64(y * Float64(x * b)));
	else
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((b <= -1.6e+39) || ~((b <= 15.2)))
		tmp = a * (y * (x * b));
	else
		tmp = k * (i * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[b, -1.6e+39], N[Not[LessEqual[b, 15.2]], $MachinePrecision]], N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.59999999999999996e39 or 15.199999999999999 < b

   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 32.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 44.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in y around inf 33.2%

      \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]

   if -1.59999999999999996e39 < b < 15.199999999999999

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 40.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 27.7%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 27.7%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 27.7%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 27.7%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 27.7%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in i around inf 20.9%

       \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+39} \lor \neg \left(b \leq 15.2\right):\\ \;\;\;\;a \cdot \left(y \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 35: 22.4% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+39} \lor \neg \left(b \leq 57000\right):\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (or (<= b -3.5e+39) (not (<= b 57000.0)))
   (* y (* a (* x b)))
   (* k (* i (* y y5)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -3.5e+39) || !(b <= 57000.0)) {
		tmp = y * (a * (x * b));
	} else {
		tmp = k * (i * (y * y5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if ((b <= (-3.5d+39)) .or. (.not. (b <= 57000.0d0))) then
        tmp = y * (a * (x * b))
    else
        tmp = k * (i * (y * y5))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if ((b <= -3.5e+39) || !(b <= 57000.0)) {
		tmp = y * (a * (x * b));
	} else {
		tmp = k * (i * (y * y5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if (b <= -3.5e+39) or not (b <= 57000.0):
		tmp = y * (a * (x * b))
	else:
		tmp = k * (i * (y * y5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if ((b <= -3.5e+39) || !(b <= 57000.0))
		tmp = Float64(y * Float64(a * Float64(x * b)));
	else
		tmp = Float64(k * Float64(i * Float64(y * y5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if ((b <= -3.5e+39) || ~((b <= 57000.0)))
		tmp = y * (a * (x * b));
	else
		tmp = k * (i * (y * y5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[Or[LessEqual[b, -3.5e+39], N[Not[LessEqual[b, 57000.0]], $MachinePrecision]], N[(y * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(i * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5000000000000002e39 or 57000 < b

   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 32.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in a around inf 43.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

      2. mul-1-neg 43.1%

         \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

   6. Simplified 43.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

   7. Taylor expanded in b around inf 44.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

   8. Taylor expanded in x around -inf 34.0%

      \[\leadsto \color{blue}{y \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]

   if -3.5000000000000002e39 < b < 57000

   1. Initial program 40.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   3. Simplified 45.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

   4. Taylor expanded in y5 around inf 40.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5} \]
   5. Step-by-step derivation

      1. mul-1-neg 40.1%

         \[\leadsto \left(\color{blue}{\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right)} + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + -1 \cdot \left(y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)\right)\right) \cdot y5 \]

      2. mul-1-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \color{blue}{\left(-y0 \cdot \left(k \cdot y2 + -1 \cdot \left(y3 \cdot j\right)\right)\right)}\right)\right) \cdot y5 \]

      3. mul-1-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \left(k \cdot y2 + \color{blue}{\left(-y3 \cdot j\right)}\right)\right)\right)\right) \cdot y5 \]

      4. sub-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) + \left(-y0 \cdot \color{blue}{\left(k \cdot y2 - y3 \cdot j\right)}\right)\right)\right) \cdot y5 \]

      5. sub-neg 40.1%

         \[\leadsto \left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \color{blue}{\left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)}\right) \cdot y5 \]

   6. Simplified 40.1%

      \[\leadsto \color{blue}{\left(\left(-i \cdot \left(t \cdot j - k \cdot y\right)\right) + \left(a \cdot \left(t \cdot y2 - y \cdot y3\right) - y0 \cdot \left(k \cdot y2 - y3 \cdot j\right)\right)\right) \cdot y5} \]

   7. Taylor expanded in k around inf 27.7%

      \[\leadsto \color{blue}{-1 \cdot \left(k \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 27.7%

         \[\leadsto \color{blue}{\left(-1 \cdot k\right) \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right)} \]

      2. neg-mul-1 27.7%

         \[\leadsto \color{blue}{\left(-k\right)} \cdot \left(\left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right) \cdot y5\right) \]

      3. *-commutative 27.7%

         \[\leadsto \left(-k\right) \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y \cdot i\right) + y0 \cdot y2\right)\right)} \]

      4. +-commutative 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 + -1 \cdot \left(y \cdot i\right)\right)}\right) \]

      5. mul-1-neg 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(y0 \cdot y2 + \color{blue}{\left(-y \cdot i\right)}\right)\right) \]

      6. unsub-neg 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \color{blue}{\left(y0 \cdot y2 - y \cdot i\right)}\right) \]

      7. *-commutative 27.7%

         \[\leadsto \left(-k\right) \cdot \left(y5 \cdot \left(\color{blue}{y2 \cdot y0} - y \cdot i\right)\right) \]

   9. Simplified 27.7%

      \[\leadsto \color{blue}{\left(-k\right) \cdot \left(y5 \cdot \left(y2 \cdot y0 - y \cdot i\right)\right)} \]

   10. Taylor expanded in i around inf 20.9%

       \[\leadsto \color{blue}{k \cdot \left(i \cdot \left(y \cdot y5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+39} \lor \neg \left(b \leq 57000\right):\\ \;\;\;\;y \cdot \left(a \cdot \left(x \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(i \cdot \left(y \cdot y5\right)\right)\\ \end{array} \]

Alternative 36: 16.9% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(y \cdot \left(x \cdot b\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* y (* x b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (y * (x * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (y * (x * b));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (y * (x * b))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(y * Float64(x * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (y * (x * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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 38.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y3, -j, k \cdot y2\right), y1 \cdot y4 - y0 \cdot y5, \mathsf{fma}\left(t \cdot y2 - y \cdot y3, a \cdot y5 - c \cdot y4, \mathsf{fma}\left(x \cdot y2 - z \cdot y3, c \cdot y0 - a \cdot y1, \mathsf{fma}\left(t \cdot j - y \cdot k, \mathsf{fma}\left(b, y4, y5 \cdot \left(-i\right)\right), \mathsf{fma}\left(\mathsf{fma}\left(x, y, z \cdot \left(-t\right)\right), a \cdot b - c \cdot i, \left(x \cdot j - z \cdot k\right) \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\right)\right)\right)\right)} \]

4. Taylor expanded in a around inf 41.2%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 41.2%

      \[\leadsto a \cdot \left(\color{blue}{\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(-1 \cdot \left(t \cdot z\right) + y \cdot x\right)\right)\right) \]

   2. mul-1-neg 41.2%

      \[\leadsto a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\color{blue}{\left(-t \cdot z\right)} + y \cdot x\right)\right)\right) \]

6. Simplified 41.2%

   \[\leadsto \color{blue}{a \cdot \left(\left(-y1 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) + \left(\left(t \cdot y2 - y \cdot y3\right) \cdot y5 + b \cdot \left(\left(-t \cdot z\right) + y \cdot x\right)\right)\right)} \]

7. Taylor expanded in b around inf 31.6%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot \left(y \cdot x - t \cdot z\right)\right)} \]

8. Taylor expanded in y around inf 21.5%

   \[\leadsto a \cdot \color{blue}{\left(y \cdot \left(b \cdot x\right)\right)} \]

9. Final simplification 21.5%

   \[\leadsto a \cdot \left(y \cdot \left(x \cdot b\right)\right) \]

Developer target: 27.7% 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 2023195 
(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)))))